Scientific Notation
Large Numbers in Scientific Notation
Draw a line matching each number in standard form to its scientific notation.
Small Numbers in Scientific Notation
Draw a line matching each decimal to its scientific notation.
Is It Scientific Notation?
Circle YES if the number is correctly written in scientific notation, or NO if it is not.
4.5 x 10^3
45 x 10^2
0.9 x 10^5
1.0 x 10^-3
12.3 x 10^6
Converting to Scientific Notation
Write each number in scientific notation. Remember: a x 10^n where 1 <= a < 10.
Earth's mass: 5,970,000,000,000,000,000,000,000 kg
Width of a human hair: 0.00007 m
Speed of light: 300,000,000 m/s
Diameter of a hydrogen atom: 0.000000000106 m
Converting from Scientific Notation
Write each number in standard (decimal) form.
6.022 x 10^23 (Avogadro number)
1.6 x 10^-19 (charge of an electron in coulombs)
9.46 x 10^15 (one light-year in metres)
Calculating with Scientific Notation
Solve these calculations. Write your answer in scientific notation.
(3 x 10^4) x (2 x 10^3) =
(8 x 10^6) / (4 x 10^2) =
(5 x 10^-3) x (4 x 10^-2) =
Order from Smallest to Largest
Sort these numbers from smallest (1st) to largest (5th).
Real-World Application
Use scientific notation to answer this question.
The distance from Earth to the Sun is 1.5 x 10^11 metres. Light travels at 3 x 10^8 m/s. How many seconds does it take for light to travel from the Sun to Earth? Show your working.
Multiplying Numbers in Scientific Notation
Multiply the following numbers. Multiply the front numbers and add the exponents. Write answers in correct scientific notation.
(2 x 10^4) x (3 x 10^5) =
(1.5 x 10^3) x (4 x 10^2) =
(6 x 10^-2) x (5 x 10^-4) =
(2.5 x 10^6) x (4 x 10^3) =
Dividing Numbers in Scientific Notation
Divide the following numbers. Divide the front numbers and subtract the exponents. Write answers in correct scientific notation.
(9 x 10^8) / (3 x 10^5) =
(6 x 10^6) / (2 x 10^-2) =
(7.5 x 10^9) / (2.5 x 10^4) =
Adding Numbers in Scientific Notation
To add numbers in scientific notation, first convert them to the same power of 10, then add the front numbers. Example: 3 x 10^4 + 2 x 10^3 = 30 x 10^3 + 2 x 10^3 = 32 x 10^3 = 3.2 x 10^4.
5 x 10^5 + 3 x 10^4 =
2.4 x 10^6 + 6 x 10^5 =
8 x 10^-3 + 4 x 10^-4 =
Scientific Notation in Context
Draw a line matching each scientific fact to its value in scientific notation.
Correct Scientific Notation After Calculation
A student calculates and gets the answers below. Circle YES if they correctly expressed the answer in scientific notation, NO if they need to adjust.
Answer: 0.5 x 10^4
Answer: 12 x 10^5
Answer: 7.8 x 10^-2
Scientific Notation in the Real World
Explore large and small numbers in everyday science.
- 1Find three large scientific measurements (e.g. distances in space, national debt) and write them in scientific notation.
- 2Look up the size of a virus (in nanometres or metres) and write it in scientific notation. How does it compare to the diameter of a human hair?
- 3Use a calculator to compute (6.022 x 10^23) x (1.6 x 10^-19). Describe what these two numbers represent in science.
Converting Larger Numbers to Scientific Notation
Write each number in correct scientific notation. Show how many places you moved the decimal point.
23,000,000 = (moved ___ places left) =
4,500,000,000 = (moved ___ places left) =
750,000 =
99,100,000,000,000 =
Converting Small Numbers to Scientific Notation
Write each small number in correct scientific notation.
0.00023 =
0.0000000081 =
0.000000000001 (one trillionth) =
0.00000000529 (Bohr radius of hydrogen atom in metres) =
Positive or Negative Exponent?
Circle whether the exponent in the scientific notation form will be POSITIVE or NEGATIVE.
A number greater than 1 (e.g. 4,500,000)
A number between 0 and 1 (e.g. 0.0034)
A number between 1 and 10 (e.g. 7.2)
A number less than 0.001
Standard Form Back to Decimal
Convert each scientific notation number back to standard decimal form.
3.7 x 10^5 =
2.04 x 10^8 =
5.9 x 10^-4 =
1.23 x 10^-7 =
Multiplying in Scientific Notation — Extended Practice
Multiply these numbers. Write answers in correct scientific notation.
(4 x 10^3) x (5 x 10^4) =
(7 x 10^-3) x (3 x 10^-4) =
(2.5 x 10^6) x (4 x 10^2) =
(6 x 10^-5) x (5 x 10^8) =
Dividing in Scientific Notation — Extended Practice
Divide these numbers. Write answers in correct scientific notation.
(8 x 10^9) / (2 x 10^4) =
(4.5 x 10^7) / (9 x 10^3) =
(3 x 10^-2) / (6 x 10^-5) =
(1.2 x 10^8) / (4 x 10^-3) =
Adding and Subtracting — Same Exponents
When exponents are the same, add or subtract the front numbers. Adjust to correct scientific notation if needed.
(3 x 10^5) + (2 x 10^5) =
(7.2 x 10^8) - (3.1 x 10^8) =
(9 x 10^-4) + (5 x 10^-4) = (Note: adjust if front number >= 10)
(8.5 x 10^6) - (6.5 x 10^6) =
Adding and Subtracting — Different Exponents
Convert both numbers to the same power of 10 first, then add or subtract.
(4 x 10^6) + (3 x 10^5) = (Convert 3 x 10^5 to ___ x 10^6) =
(7 x 10^4) - (5 x 10^3) =
(2.3 x 10^7) + (8 x 10^5) =
Match to the Equivalent Standard Form
Draw a line from each scientific notation number to its standard decimal form.
Scientific Notation Word Problems
Use scientific notation to solve each problem. Show your working.
A computer processor executes 3 x 10^9 operations per second. How many operations does it execute in 1 hour? Give your answer in scientific notation.
The human body contains approximately 3.7 x 10^13 cells. If each cell contains 3 x 10^9 DNA base pairs, what is the total number of DNA base pairs in the body? Write in scientific notation.
Scientific Notation in Astronomy
Use the facts provided to answer each question in scientific notation.
The Sun is 1.5 x 10^11 m from Earth. Neptune is 4.5 x 10^12 m from the Sun. How much farther from the Sun is Neptune than Earth?
Light travels at 3 x 10^8 m/s. How far does light travel in one year (3.15 x 10^7 seconds)? This is called one light-year.
The nearest star to Earth (after the Sun) is 4.07 x 10^16 m away. How many light-years away is it?
Sort by Size: A Comparison Challenge
Sort these measurements from smallest to largest. First convert each to the same power of 10.
Scientific Notation in Biology
Use scientific notation to answer these biology questions.
A red blood cell is 8 x 10^-6 m in diameter. A bacterium is 2 x 10^-6 m wide. How many times wider is a red blood cell than the bacterium?
A single strand of human hair is about 7 x 10^-5 m wide. A coronavirus particle is about 1.2 x 10^-7 m wide. How many coronavirus particles would fit across the width of a hair?
Comparing Scientists' Data
A scientist records the following data. Answer the comparison questions.
Sample A has a mass of 3.2 x 10^-5 kg. Sample B has a mass of 4.8 x 10^-6 kg. Which sample is heavier? How many times heavier?
Two bacteria populations: Colony X has 2.4 x 10^8 bacteria. Colony Y has 6 x 10^7 bacteria. What is the combined population? Write in scientific notation.
Scientific Notation Operations — Mixed Practice
Solve each calculation. Write answers in correct scientific notation.
(5 x 10^3)^2 =
(2 x 10^4) x (3 x 10^5) + (4 x 10^9) =
(6 x 10^6) / (2 x 10^-2) - (5 x 10^7) =
Converting Between Units Using Scientific Notation
Use scientific notation to convert between units.
1 kilometre = 10^3 metres. The distance Sydney to Melbourne is 878 km. Write this in metres in scientific notation.
1 nanometre = 10^-9 metres. A computer chip feature is 5 nm wide. Write this in metres in scientific notation.
1 microsecond = 10^-6 seconds. A computer instruction takes 0.5 microseconds. Write in seconds in scientific notation.
Scientific Notation in Finance
Australia's national GDP is approximately $2.1 x 10^12 (2.1 trillion dollars). Use this to answer the questions.
Australia's population is approximately 2.6 x 10^7. What is the GDP per person? Write in scientific notation and as a standard number.
If the government spends 25% of GDP on education, health and welfare, how much money is this? Write in scientific notation.
The world GDP is approximately 10 times Australia's GDP. Write the world GDP in scientific notation.
Scientific Notation — Extending to Powers
Evaluate each expression. Use the rule (a x 10^n)^m = a^m x 10^(nm).
(2 x 10^3)^2 =
(3 x 10^2)^3 =
(5 x 10^-2)^2 =
(2 x 10^4)^3 =
Identify the Largest and Smallest
For each set, circle the largest number.
3.7 x 10^5 , 9.9 x 10^4 , 1.1 x 10^6
6 x 10^-4 , 2 x 10^-3 , 8 x 10^-5
4.8 x 10^7 , 4.9 x 10^6 , 5.0 x 10^7
Real Measurement Estimation with Scientific Notation
Estimate each answer in scientific notation. You may need to round your estimates.
Estimate the number of grains of sand on all Earth's beaches. A rough estimate is 7.5 x 10^18. Write this in standard form (as many zeros as you can count).
The International Space Station orbits at about 400 km altitude. Write this height in metres in scientific notation.
A human heart beats about 70 times per minute. In a 80-year lifetime (approx 4.2 x 10^7 minutes), how many times does the heart beat? Write in scientific notation.
Compound Problems: Scientific Notation Across Topics
Each problem combines scientific notation with another Year 9 topic.
A cylinder has radius 3 x 10^2 m and height 4 x 10^3 m. Use V = pi r^2 h (pi approx 3.14) to find the volume in scientific notation.
A square paddock has area 9 x 10^8 m^2. Find the exact side length in scientific notation.
The Scientific Notation Number Hunt
Find scientific notation in newspapers, online articles, and textbooks.
- 1Find one number from a science article, one from economics/news, and one from a biology source. Write each in scientific notation and explain what the number represents.
- 2Compare the mass of a proton (1.67 x 10^-27 kg) and an electron (9.11 x 10^-31 kg). How many times heavier is a proton than an electron?
- 3Research the national debt of Australia. Write it in scientific notation. How does it compare to Australia's GDP (approximately 2.1 x 10^12 AUD)?
Scientific Notation: Errors and Corrections
Each student has made an error. Identify the error and write the correct answer.
Student writes: 65,000 = 6.5 x 10^3. Identify the error and correct it.
Student writes: (3 x 10^4) x (2 x 10^5) = 6 x 10^20. Identify the error and correct it.
Student writes: 0.00045 = 4.5 x 10^4. Identify the error and correct it.
Student writes: 8 x 10^6 + 3 x 10^5 = 11 x 10^11. Identify the errors and correct.
Scientific Notation Challenge: Multi-Step Problems
Solve these multi-step problems. Show all working in scientific notation.
A spaceship travels at 3.5 x 10^4 km/h. The Moon is 3.84 x 10^5 km from Earth. How long would the spaceship take to reach the Moon? Give your answer in hours in scientific notation.
A factory produces 2.4 x 10^6 units per day. Each unit has mass 3.5 x 10^-3 kg. What is the total mass of units produced per day in standard form? Write in scientific notation.
Scientific Measurements — Match the Context
Draw a line from each measurement to the most appropriate context.
Comprehensive Scientific Notation Review
Show complete working for all parts. This review covers every skill in the worksheet.
Convert to scientific notation: (a) 304,000,000 (b) 0.0000000504
Convert to standard form: (a) 2.7 x 10^5 (b) 8.1 x 10^-6
Calculate in scientific notation: (3.6 x 10^8) / (9 x 10^3)
Calculate in scientific notation: (2.5 x 10^4) x (4 x 10^-7) + (6 x 10^-4)
A spacecraft travels 1.2 x 10^9 km in 6 x 10^2 days. What is its speed in km/day? In km/h?
Scientific Notation: Physics Applications
Use scientific notation to solve these physics problems.
The wavelength of visible light is approximately 5 x 10^-7 m. A beam of light passes through 2 x 10^4 complete wavelengths. What distance does it travel?
A proton has mass 1.67 x 10^-27 kg. How much mass do 5 x 10^24 protons have in total?
The speed of light is 3 x 10^8 m/s. How long does it take light to travel 9.46 x 10^15 m (one light-year)?
Order of Magnitude Estimation
An order of magnitude estimate rounds to the nearest power of 10. For example, 4,700 ≈ 10^3.7 ≈ 10^4 (to nearest order of magnitude).
Estimate the order of magnitude of the number of seconds in a year. (365 days x 24 h x 3600 s)
Estimate the order of magnitude of the number of heartbeats in a human lifetime (80 years). Use 70 beats per minute.
Is 5.5 x 10^8 closer in order of magnitude to 10^8 or 10^9? Explain.
Science Facts: Smallest to Largest
Sort these scientific quantities from smallest to largest. Use their scientific notation values.
Scientific Notation and Area
Use scientific notation to calculate areas of very large or very small regions.
The surface area of Earth is approximately 5.1 x 10^14 m^2. About 71% is ocean. What area of Earth's surface is ocean? Write in scientific notation.
A computer chip has a surface area of 4 x 10^-4 m^2. It contains 5 x 10^9 transistors. What is the area per transistor in scientific notation?
Adjust to Correct Scientific Notation
A student's calculation gives the result shown. Circle the correctly adjusted scientific notation form.
Calculation gives: 14 x 10^6
Calculation gives: 0.25 x 10^8
Calculation gives: 60 x 10^-4
Calculation gives: 0.08 x 10^-3
Scientific Notation in Chemistry
Use given values to answer these chemistry questions.
One mole of any element contains 6.022 x 10^23 atoms. How many atoms are in 3 moles of copper?
If each water molecule has mass 2.99 x 10^-26 kg, what is the mass of 6.022 x 10^23 water molecules?
A solution contains 4.5 x 10^20 ions per millilitre. How many ions are in 2.5 x 10^2 mL?
Scientific Notation with Decimal Front Numbers
Some problems give front numbers that are not whole numbers. Handle these carefully.
Convert to scientific notation: 0.00000308 =
Convert to scientific notation: 27,400,000,000 =
Calculate: (1.5 x 10^4) x (2.4 x 10^3) =
Calculate: (7.2 x 10^9) / (1.8 x 10^4) =
Scientific Notation: News Story Calculations
Each scenario is inspired by real news. Use scientific notation to compute the answer.
The Australian government's 2023 federal budget was approximately $640 billion. Write this in scientific notation (1 billion = 10^9).
Australia's population is 2.6 x 10^7. The federal budget above gives each Australian approximately how much? Write in scientific notation and standard form.
A major fire burns an area of 2 x 10^10 m^2. If the affected region has a tree density of 500 trees per 10^4 m^2, how many trees are affected?
Scientific Notation: Explain Your Thinking
Answer these conceptual questions in full sentences.
Explain why scientists use scientific notation rather than writing out all the zeros in a large or small number.
Why must the front number in scientific notation be at least 1 and less than 10? What would go wrong if it were 0.5 or 15?
Two students are comparing 3 x 10^8 and 5 x 10^7. Student A says 5 x 10^7 is larger because 5 > 3. Explain the error.
Connecting Scientific Notation to Index Laws
Use index laws to simplify each expression, then write in scientific notation.
(10^3)^2 = 10^___ =
10^8 / 10^5 = 10^___ =
(2 x 10^3)^3 = 2^___ x 10^___ = ___ x 10^___
(10^-2)^4 = 10^___ =
Comparison Word Problems
Use scientific notation to compare quantities and answer in context.
The energy released by the Sun each second is 3.8 x 10^26 joules. The energy in one kilogram of TNT is 4.6 x 10^6 joules. How many kilograms of TNT would produce the same energy as the Sun releases in 1 second?
The human brain has approximately 8.6 x 10^10 neurons. If each neuron connects to an average of 7 x 10^3 other neurons, how many connections exist in total? Write in scientific notation.
Final Extension: Scientific Notation and Ratios
Use ratios involving scientific notation to answer each question.
The diameter of the Sun is 1.39 x 10^9 m. The diameter of Earth is 1.28 x 10^7 m. How many times larger (in diameter) is the Sun than Earth?
A blue whale can weigh up to 1.5 x 10^5 kg. A hummingbird weighs about 3 x 10^-3 kg. How many hummingbirds would equal the mass of one blue whale?
Bacteria divide every 20 minutes under ideal conditions. Starting with 1 bacterium, after 10 hours (30 doublings), how many bacteria are there? Write as a power of 2 and then in scientific notation.
Comparing Measurements Using Scientific Notation
Convert all measurements to the same units (metres) in scientific notation, then compare.
Compare: 5 km, 4.8 x 10^3 m, and 500,000 cm. Which is largest?
Compare: 3 mm, 0.003 m, and 3 x 10^-3 m. Are they equal? Explain.
A microscope can resolve features as small as 2 x 10^-7 m. An electron microscope can resolve features 1000 times smaller. What is the resolution of the electron microscope?
Writing About Scale
Answer these questions to develop number sense for very large and small quantities.
A human lifetime is about 2.5 x 10^9 seconds. Is this more or less than 10^10 seconds? Explain how you decided.
The diameter of a hydrogen atom is about 10^-10 m. How many hydrogen atoms lined up in a row would span 1 metre?
If 1 million seconds have passed, approximately how many days is that? (Use 1 day = 8.64 x 10^4 seconds.)
Powers of 10 and Their Names
Draw a line from each power of 10 to its common name.
Applying SI Prefixes with Scientific Notation
Use the prefix table from the previous activity to convert each measurement.
3 gigabytes = 3 x 10^9 bytes. Write this in standard form.
5 nanoseconds = 5 x 10^-9 seconds. How many nanoseconds in one second?
A computer has 16 GB of RAM. Write 16 GB in bytes in scientific notation.
A radio wave has a wavelength of 300 megametres (300 Mm). Write this in metres in scientific notation.
Scientific Notation: Self-Assessment
Attempt each problem. After completing this worksheet, rate your confidence (1 = not confident, 5 = very confident) for each skill.
Convert 6,400,000,000 to scientific notation. Confidence rating: ___/5
Multiply (4.5 x 10^6) x (2 x 10^-3). Confidence rating: ___/5
Add (3.4 x 10^5) + (6.6 x 10^4). Confidence rating: ___/5
Explain to a Year 7 student what scientific notation is and why we use it. Confidence rating: ___/5
Scientific Notation Treasure Hunt — Context Clues
Read each clue and identify the quantity being described. Write it in scientific notation.
I am the approximate number of cells in a human body: 37 trillion. Write me in scientific notation.
I am the mass of a grain of sand: about 0.0000004 kg. Write me in scientific notation.
I am the diameter of a human red blood cell: 8 millionths of a metre. Write me in scientific notation.
I am the distance light travels in one year (a light-year): 9.461 x 10^15 metres. Convert me to km in scientific notation.
Scientific Notation and Speed Calculations
Use the formula distance = speed x time (or rearrangements) to solve each problem.
A radio signal travels at 3 x 10^8 m/s. How long does it take to reach a satellite 3.6 x 10^7 m away? Write in scientific notation and in milliseconds.
A comet travels at 5 x 10^4 km/h. How far does it travel in 3.65 x 10^2 days? Write in km in scientific notation.
Scientific Notation: Spot the Largest
Circle the largest number in each set without converting to standard form.
1.1 x 10^6 , 9.9 x 10^5 , 1.09 x 10^6
7.5 x 10^-8 , 3.2 x 10^-7 , 8.9 x 10^-8
4.0 x 10^12 , 4.0 x 10^11 , 4.0 x 10^13
Scientific Notation Mastery: Final Assessment
Complete all parts without notes. This is the final mastery assessment for scientific notation.
Convert: (a) 4,070,000,000 to scientific notation (b) 7.3 x 10^-5 to standard form
Calculate: (5.4 x 10^6) / (9 x 10^-2). Show all steps and write the answer in correct scientific notation.
A virus is 1.2 x 10^-7 m long. A bacterium is 3 x 10^-6 m long. How many viruses would fit end to end along one bacterium? Write in scientific notation.
Australia's population (2.6 x 10^7) increases by 1.4% per year. After 10 years, the population is approximately 2.6 x 10^7 x 1.014^10. Calculate 1.014^10 using a calculator (approx 1.149) and find the predicted population in scientific notation.
Estimating with Scientific Notation
Estimate the answer to each question by rounding to one significant figure first, then calculate.
Estimate: (4.8 x 10^5) x (2.1 x 10^3). Round 4.8 to 5 and 2.1 to 2, then calculate. Precise answer:
Estimate: (9.2 x 10^8) / (3.1 x 10^3). Round then calculate. Precise answer:
Estimate: (1.97 x 10^6) x (5.04 x 10^2). Estimate first, then get the precise answer.
Scientific Notation: Geography Applications
Use scientific notation to explore geographic data.
Australia's area is approximately 7.7 x 10^6 km^2. Convert this to m^2 in scientific notation. (1 km = 10^3 m, so 1 km^2 = 10^6 m^2.)
The Great Barrier Reef covers approximately 3.4 x 10^5 km^2. What fraction of Australia's area does this represent? Give your answer in scientific notation.
The Pacific Ocean has an area of 1.65 x 10^8 km^2. How many times bigger is the Pacific Ocean than Australia?
Which Calculation Is Correct?
For each calculation, circle which student got the right answer.
2 x 10^4 + 3 x 10^3. Student A: 5 x 10^7. Student B: 2.3 x 10^4.
(6 x 10^5) / (2 x 10^2). Student A: 3 x 10^3. Student B: 3 x 10^7.
(4 x 10^-3)^2. Student A: 16 x 10^-6 = 1.6 x 10^-5. Student B: 8 x 10^-6.
Scientific Notation: Investigate a Real Science Story
A research team announces that a new virus has been discovered. It is 8 x 10^-8 m in diameter and replicates every 6 hours.
How many of these viruses placed end to end would span 1 cm (10^-2 m)?
Starting with one virus, after 48 hours (8 replications), how many viruses are there? (Each replication doubles the count.) Write in scientific notation.
If each virus has mass 3 x 10^-15 kg, what is the total mass after 48 hours?
Scientific Notation: Interdisciplinary Problems
Solve these problems that combine scientific notation with other mathematical ideas.
A square solar panel array has side length 3.2 x 10^2 m. What is its total area in m^2 in scientific notation? If it produces 5 x 10^2 watts per m^2, what is the total power output?
An investment of $5,000 grows by 7% per year. After 20 years it is approximately $5,000 x 1.07^20 = $5,000 x 3.87. Write both the original amount and the final amount in scientific notation. By how much (in scientific notation) has the investment grown?
Scientific Notation: Peer Teaching
Write an explanation of scientific notation that you could use to teach someone who has never seen it before.
Write a definition of scientific notation in your own words.
Give one example of a very large number in scientific notation from science, and explain why the notation is useful.
Give one example of a very small number in scientific notation, and explain why the notation is useful.
Write one worked example showing how to multiply two numbers in scientific notation, with full steps.
Scientific Notation: Three-Step Problems
Each problem requires three separate calculations. Plan each step before calculating.
Step 1: Write 8,500,000 in scientific notation. Step 2: Divide by 2.5 x 10^3. Step 3: Convert your answer back to standard form.
Step 1: Write 0.000042 in scientific notation. Step 2: Multiply by 6 x 10^8. Step 3: Is your answer greater than or less than one million? Justify.
Scientific Notation: Data Table Analysis
Use the data table to answer the questions.
Objects: Proton (1.67 x 10^-27 kg), Red blood cell (9 x 10^-12 kg), Bee (1.2 x 10^-4 kg), Human (7 x 10^1 kg), Blue whale (1.5 x 10^5 kg). How much heavier is a blue whale than a bee? Write in scientific notation.
Using the same data table, how many protons would have the same mass as a human? Write in scientific notation.
What is the range of masses (largest minus smallest) in the table? Write in scientific notation.
Astronomical Distances in Scientific Notation
Use the given distances to answer each question in scientific notation.
Mercury is 5.8 x 10^7 km from the Sun. Venus is 1.08 x 10^8 km from the Sun. How much farther from the Sun is Venus than Mercury?
Mars is 2.28 x 10^8 km from the Sun. Jupiter is 7.78 x 10^8 km from the Sun. What is the distance from Mars to Jupiter when both are on the same side of the Sun?
A spacecraft travels from Earth to Jupiter at 5 x 10^4 km/h. Earth is 1.5 x 10^8 km from the Sun and Jupiter is 7.78 x 10^8 km. Estimate the travel time.
Scientific Notation: Which Operation?
Identify the correct operation and result for each calculation.
(4 x 10^3) x (5 x 10^4)
(9 x 10^6) / (3 x 10^2)
(6 x 10^3) + (4 x 10^3)
Scientific Notation: Building Understanding Through Examples
Complete each analogy or explanation that shows how scientific notation works.
Multiplying by 10 moves the decimal point one place to the right. Multiplying by 10^5 moves it ___ places to the ___.
Multiplying by 10^-3 moves the decimal point ___ places to the ___. Give an example: 7.5 x 10^-3 =
Just as we write 3.5 km instead of 3,500 m for convenience, we write 3.5 x 10^3 m instead of 3,500 m for precision and clarity. Give two more examples of quantities where scientific notation provides this convenience.
Create Your Own Scientific Notation Problem
Design two scientific notation word problems of your own. Solve them and write the full working.
Write your own multiplication problem using scientific notation. Include a real-world context, the calculation, and the answer.
Write your own division problem using scientific notation. Include a real-world context, the calculation, and the answer.
Scientific Notation: Media Hunt
Find scientific notation and very large/small numbers in the media and real world.
- 1Find a newspaper or online news article that mentions a very large or very small number (e.g. government budget, scientific discovery). Write the number in scientific notation and explain what it represents.
- 2Look at your phone's storage capacity. Is it in gigabytes (GB) or terabytes (TB)? Write the capacity in bytes in scientific notation.
- 3Research the speed of your home internet connection. If it is 100 Mbps (megabits per second), how many bits are transferred in an hour? Write in scientific notation.
Negative and Zero Exponents in Scientific Notation
Apply your knowledge of negative and zero exponents to these scientific notation problems.
Simplify: 10^-3 x 10^5 = 10^___ = Write in decimal form:
Write 1 (the number one) in scientific notation: 1 = ___ x 10^___
Write 10 in scientific notation: 10 = ___ x 10^___
Write 0.1 in scientific notation: 0.1 = ___ x 10^___
Practical Measurement Conversions
Use scientific notation to convert between measurement units efficiently.
Convert 4.5 x 10^6 millimetres to metres. (Divide by 10^3.)
Convert 2.3 x 10^8 centimetres to kilometres. (1 km = 10^5 cm.)
Convert 9.2 x 10^-4 kilograms to milligrams. (1 kg = 10^6 mg.)
Scientific Notation in Engineering
Engineers regularly work with quantities in scientific notation. Solve these engineering-inspired problems.
A power plant generates 3.5 x 10^9 watts. How many watts does it generate per minute? Per second?
A cable has resistance 1.7 x 10^-8 ohms per metre. For a cable 2.5 x 10^3 metres long, what is its total resistance?
Scientific Notation Comprehensive Final Assessment
Show complete working. This is the final scientific notation assessment.
(a) Convert 0.000000045 to scientific notation. (b) Convert 7.2 x 10^6 to standard form.
Calculate: (4 x 10^5) x (3 x 10^-2) and write the answer in scientific notation.
Calculate: (8.4 x 10^9) / (1.4 x 10^3) and write the answer in scientific notation.
A data centre processes 5 x 10^12 bytes per day. How many bytes does it process in 3.65 x 10^2 days (one year)?
Two planets are 4.5 x 10^8 km and 7.8 x 10^7 km from the Sun. What is the total distance if both planets are on opposite sides of the Sun?
Scientific Notation: Reflection and Extension
Answer these reflection questions to consolidate your learning.
What was the most challenging part of this worksheet? What strategy helped you most?
Write three numbers from different contexts (one very large, one close to 1, one very small) and convert each to scientific notation.
Scientific Notation: Quick Recall Match
Draw a line from each description to the correct scientific notation.
Extending Scientific Notation: Fractional Exponents Preview
Scientific notation uses integer exponents (whole numbers). But what would 10^0.5 mean? Investigate.
10^0 = 1 and 10^1 = 10. If the pattern is consistent, 10^0.5 should be the number that, when multiplied by itself, gives 10. What is this number?
Use a calculator to verify: 10^0.5 x 10^0.5 = ___. What does this confirm?
Predict the value of 10^0.25 (the fourth root of 10). Verify with a calculator.
Scientific Notation: Space Exploration Project
Research space distances and represent them using scientific notation.
- 1Look up the distances from the Sun to each planet in km. Write each in scientific notation. Create a scale diagram showing the relative distances.
- 2Research how long it takes light from each planet to reach Earth. Divide the distance (in km) by the speed of light (3 x 10^5 km/s) to find the travel time.
- 3Find out the diameter of each planet in km and write in scientific notation. Sort from smallest to largest. How does Earth compare?