8.EE.A.4 8th Grade Expressions & Equations

Operations with Scientific Notation

Perform operations with numbers expressed in scientific notation, and choose units of appropriate size for measurements.

How to explain it

At this standard, students multiply, divide, add, and subtract numbers in scientific notation by operating on the coefficients and the powers of 10 separately, matching exponents before adding or subtracting, and renormalizing every result into 1 ≤ |c| < 10.

The anchor students hold onto: Multiply/Divide: operate on the coefficients, then add or subtract the exponents. Add/Subtract: match the exponents first, then combine coefficients. Renormalize the result.

Sets up Algebra 1 exponent rules and polynomial operations — the same coefficient-and-exponent decomposition reappears whenever like-base powers are multiplied or divided.

Worked examples

Example 1 Multiplication

(3 × 10⁴)(2 × 10³)

Step 1Multiply coefficients: 3 · 2 = 6

Step 2Add exponents: 4 + 3 = 7

Step 3(3 × 10⁴)(2 × 10³) = 6 × 10⁷

Answer6 × 10⁷

Example 2 Division

(8 × 10⁹) ÷ (4 × 10²)

Step 1Divide coefficients: 8 ÷ 4 = 2

Step 2Subtract exponents: 9 − 2 = 7

Step 3(8 × 10⁹) ÷ (4 × 10²) = 2 × 10⁷

Answer2 × 10⁷

Example 3 Add (Match First)

(4 × 10⁶) + (2 × 10⁵)

Step 1Match exponents: 2 × 10⁵ = 0.2 × 10⁶

Step 2Add coefficients: 4 + 0.2 = 4.2

Step 3(4 × 10⁶) + (2 × 10⁵) = 4.2 × 10⁶

Answer4.2 × 10⁶

Common mistakes

What students write Adding both the coefficients AND the exponents of (3 × 10⁵) + (4 × 10³), writing 7 × 10⁸ — treating add/subtract like multiply.

The fix Add/subtract requires equal powers of 10 first. Rewrite 4 × 10³ as 0.04 × 10⁵, then add coefficients: 3.04 × 10⁵.

What students write Leaving a result like 30 × 10⁷ or 0.3 × 10¹⁰ as the final answer when the coefficient is outside 1 ≤ |c| < 10.

The fix Renormalize: slide the decimal so 1 ≤ |c| < 10 and adjust the exponent. 30 × 10⁷ = 3.0 × 10⁸.

Teacher tip

Head off the two predictable errors before they happen. First: Add/subtract requires equal powers of 10 first. Rewrite 4 × 10³ as 0.04 × 10⁵, then add coefficients: 3.04 × 10⁵. Second: Renormalize: slide the decimal so 1 ≤ |c| < 10 and adjust the exponent. 30 × 10⁷ = 3.0 × 10⁸.