Perform operations with numbers expressed in scientific notation, including problems where both decimal and scientific notation are used. Use scientific notation and choose units of appropriate size for measurements of very large or very small quantities (e.g., use millimeters per year for seafloor spreading). Interpret scientific notation that has been generated by technology
Official wording from the Common Core State Standards for Mathematics (© 2010 National Governors Association Center for Best Practices and Council of Chief State School Officers). View on thecorestandards.org
Scientific notation writes a number as a factor from 1 up to (but not including) 10 multiplied by a power of ten, as in 4.6 × 10⁸ or 2.5 × 10⁻⁷. Eighth graders move beyond writing numbers this way and start calculating with them. Multiplying and dividing are the friendlier operations: multiply or divide the decimal parts, add or subtract the exponents, and then adjust so the leading factor is between 1 and 10.
Adding and subtracting need more care, because the powers of ten must match first, just as place values must line up in ordinary addition. Students also handle problems that mix decimal and scientific forms, choose units that keep numbers reasonable (micrometers for bacteria, light-years or kilometers for space), and read calculator or spreadsheet output such as 3.2E-5, which means 3.2 × 10⁻⁵. Reading that output correctly, and rewriting it in the form a teacher or a textbook expects, is part of the skill.
Students write (4 × 10³)(5 × 10²) = 20 × 10⁵. That is correct in value but not scientific notation; it should be adjusted to 2 × 10⁶.
3 × 10⁴ + 2 × 10⁴ is 5 × 10⁴, not 5 × 10⁸. The exponent only changes when you multiply or divide.
6 × 10⁵ + 3 × 10⁴ is not 9 × 10⁵. Rewrite 3 × 10⁴ as 0.3 × 10⁵ first, giving 6.3 × 10⁵.
A display of 2.4E-6 does not mean 2.4 - 6 or 2.4 to the power 6. It is the calculator's shorthand for 2.4 × 10⁻⁶.
Light travels about 3 × 10⁸ meters per second. Earth is about 1.5 × 10¹¹ meters from the Sun. About how many seconds does sunlight take to reach Earth?
Answer: About 5 × 10² seconds, which is 500 seconds (a little over 8 minutes).
Pair each scientific notation calculation with a quick estimate in words ('about half a thousand') so students can spot when an adjustment has gone wrong. Science classes are natural partners: data on planets, cells or atoms gives authentic numbers, and comparing the same quantity in different units shows why scientists switch from meters to kilometers or micrometers.
Assessments frequently show a calculator screen with E notation, or ask for an answer 'in scientific notation', which means the leading factor must be at least 1 and less than 10. Build the habit of a final check: is the factor in range and does the size make sense?
Original questions written for this standard. Choose an option or type your answer, then press Check. Every question has a worked explanation.
Answer: B) 8 × 10⁸
Multiply 2 × 4 = 8 and add the exponents 5 + 3 = 8, giving 8 × 10⁸.
Answer: C) 3 × 10⁷
6 × 5 = 30 and 10⁴ × 10² = 10⁶, so the product is 30 × 10⁶. Rewrite 30 as 3 × 10¹ to get 3 × 10⁷.
Answer: 1100000 (also accepted: 1,100,000)
The powers match, so add the factors: 11 × 10⁵ = 1,100,000, which is 1.1 × 10⁶ in scientific notation.
Answer: 0.0042
4.2E-3 means 4.2 × 10⁻³. Move the decimal point three places left: 0.0042.
Answer: B) micrometers
0.00007 m is 70 micrometers. Using micrometers avoids writing many zeros or negative powers of 10.
Answer: 3000000 (also accepted: 3,000,000)
9 ÷ 3 = 3 and 10⁸ ÷ 10² = 10⁶. So the answer is 3 × 10⁶ = 3,000,000.
Choose a level of accuracy appropriate to limitations on measurement when reporting quantities.
A full lesson with slides, activities and an exit ticket on operations in scientific notation, pitched to grade 8 and editable in PowerPoint or Google Slides.
Make a lesson →A printable, differentiated worksheet on 8.EE.A.4 with an answer key, ready in about a minute.
Make a worksheet →Turn operations in scientific notation into a quiz students answer online that marks itself, with a class summary for you.
Build a test →A number written as a × 10ⁿ where a is at least 1 and less than 10, and n is an integer. Answers such as 25 × 10³ need adjusting to 2.5 × 10⁴.
Yes. 8.EE.A.4 includes all four operations, so students learn to rewrite one number to match the other's power of 10 before adding or subtracting.