8.EE.4: Operations in Scientific Notation
Also written as 8.EE.A.4 and CCSS.MATH.CONTENT.8.EE.A.4 · Cluster: Work with radicals and integer exponents.
The Official Wording
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
Common Core State Standards, Grade 8, Expressions & Equations · Read it at the source · Checked October 14, 2026
What 8.EE.4 Means in Plain English
Eighth graders calculate in scientific notation. Multiplying, they handle front numbers and powers of 10 separately: (6 × 10⁴)(4 × 10³) = 24 × 10⁷ = 2.4 × 10⁸. Adding, they match powers first: 3.2 × 10⁵ + 4 × 10⁴ = 3.6 × 10⁵.
They read a calculator’s 4.1E-6 as 4.1 × 10⁻⁶ and pick units that keep numbers readable, like micrometers for a bacterium instead of kilometers. In high school, choosing and converting units on purpose becomes a standard of its own (HSN-Q.1).
8.EE.4 I Can Statements
- I can multiply and divide numbers in scientific notation.
- I can add and subtract after matching the powers of 10.
- I can read calculator output like 4.1E-6 and choose sensible units.
8.EE.4 Worked Example
Sunlight’s trip to Earth, with one number in scientific notation, one in ordinary form, and a unit to choose at the end.
Sunlight travels about 1.5 × 10⁸ km to reach Earth, moving at about 300,000 km per second. How long does the trip take? Give the answer in a sensible unit.
- Rewrite the speed in scientific notation so both numbers are in the same form.300,000 km/s = 3 × 10⁵ km/s
- Time is distance divided by speed. Divide the front numbers, then the powers of 10.(1.5 ÷ 3) × (10⁸ ÷ 10⁵) = 0.5 × 10³
- 0.5 is less than 1, so it is not yet scientific notation. Move one factor of 10 into it.0.5 × 10³ = 5 × 10² seconds
- 500 seconds is hard to picture. Minutes fit better: 500 = 8 × 60 + 20.500 seconds = 8 minutes 20 seconds
Check it: Multiply back: 500 s × 300,000 km/s = 150,000,000 km, which is 1.5 × 10⁸ km, the distance we started with.
Common Mistakes with 8.EE.4
Adding the exponents when adding numbers
2 × 10⁵ + 3 × 10⁴ = 5 × 10⁹
Try this: Rewrite one number so the powers match: 3 × 10⁴ = 0.3 × 10⁵, then add the fronts: 2.3 × 10⁵.
Stopping with a front number of 10 or more
(5 × 10³)(4 × 10²) = 20 × 10⁵
Try this: Check that the front number is at least 1 and less than 10; move a factor of 10 over: 2 × 10⁶.
Copying calculator notation as the answer
“The answer is 6.2E-5.”
Try this: Translate the E: 6.2E-5 means 6.2 × 10⁻⁵, or 0.000062, and write it that way with its unit.
Where 8.EE.4 Fits
Practice 8.EE.4
Quick Check
- Compute (3 × 10⁴)(5 × 10⁻⁷).
- Add 7.5 × 10⁶ + 450,000.
- Divide 8.4 × 10⁹ by 2.1 × 10³.