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Multiplying and dividing in scientific notation, step by step

Work the coefficients, work the powers — then check the answer is still IN scientific notation.

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The question

(6 × 10⁸) ÷ (1.5 × 10⁻²)

(6 × 10⁸) ÷ (1.5 × 10⁻²)
6÷1.5=4
8−−2=10
4 × 10¹⁰
1 ≤ 4 < 10
(6 × 10⁸) ÷ (1.5 × 10⁻²)=4 × 10¹⁰
  1. A number in scientific notation is two things multiplied: a coefficient and a power of ten. They travel separately — the coefficients divide with each other and the powers subtract with each other — so take them one at a time.
  2. Divide the coefficients: 6 ÷ 1.5 = 4.
  3. Now the powers. Dividing powers of the same base SUBTRACTS the exponents: 8 − −2 = 10. So the powers give 10¹⁰.
  4. Put them together: 4 × 10¹⁰. Now CHECK it — a coefficient has to be at least 1 and less than 10, and 4 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 4 × 10¹⁰ — 6 ÷ 1.5 = 4 and the powers give 10¹⁰.

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 divide with each other and the powers subtract with each other — so take them one at a time.

  2. 02

    Divide the coefficients: 6 ÷ 1.5 = 4.

  3. 03

    Now the powers. Dividing powers of the same base SUBTRACTS the exponents: 8 − −2 = 10. So the powers give 10¹⁰.

  4. 04

    Put them together: 4 × 10¹⁰. Now CHECK it — a coefficient has to be at least 1 and less than 10, and 4 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 4 × 10¹⁰ — 6 ÷ 1.5 = 4 and the powers give 10¹⁰.

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