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Multiplying in scientific notation, step by step

Multiply the coefficients, add the powers — then check the answer is still in scientific notation.

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The question

(1.2 × 10⁻³) × (8 × 10²)

(1.2 × 10⁻³) × (8 × 10²)
1.2×8=9.6
−3+2=−1
9.6 × 10⁻¹
1 ≤ 9.6 < 10
(1.2 × 10⁻³) × (8 × 10²)=9.6 × 10⁻¹
  1. A number in scientific notation is two things multiplied: a coefficient and a power of ten. They travel separately — the coefficients multiply with each other and the powers add with each other — so take them one at a time.
  2. Multiply the coefficients: 1.2 × 8 = 9.6.
  3. Now the powers. Multiplying powers of the same base ADDS the exponents: −3 + 2 = −1. So the powers give 10⁻¹.
  4. Put them together: 9.6 × 10⁻¹. Now CHECK it — a coefficient has to be at least 1 and less than 10, and 9.6 is. Nothing left to do, and it was still worth looking: this is the step that catches the ones that are not.
  5. So the answer is 9.6 × 10⁻¹ — 1.2 × 8 = 9.6 and the powers give 10⁻¹.

How it works.

  1. 01

    A number in scientific notation is two things multiplied: a coefficient and a power of ten. They travel separately — the coefficients multiply with each other and the powers add with each other — so take them one at a time.

  2. 02

    Multiply the coefficients: 1.2 × 8 = 9.6.

  3. 03

    Now the powers. Multiplying powers of the same base ADDS the exponents: −3 + 2 = −1. So the powers give 10⁻¹.

  4. 04

    Put them together: 9.6 × 10⁻¹. Now CHECK it — a coefficient has to be at least 1 and less than 10, and 9.6 is. Nothing left to do, and it was still worth looking: this is the step that catches the ones that are not.

  5. 05

    So the answer is 9.6 × 10⁻¹ — 1.2 × 8 = 9.6 and the powers give 10⁻¹.

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