Multiplying in scientific notation

Multiplying in scientific notation

Multiplying in scientific notation

Scientific notation makes multiplying very large or very small numbers easy, because you can deal with the coefficients and the powers of ten separately.

Multiply coefficients, add exponents

To work out (3 × 10²) · (4 × 10³):

  • multiply the coefficients: 3 · 4 = 12
  • add the exponents: 2 + 3 = 5

This gives 12 × 10⁵.

Renormalise the answer

A proper answer needs a coefficient between 1 and 10. Here 12 is too big, so rewrite 12 as 1.2 × 10¹ and add 1 to the exponent:

12 × 10⁵ = 1.2 × 10⁶.

Three rules that always help

  • Multiply the coefficients and add the exponents.
  • If the new coefficient is 10 or more, divide it by 10 and add 1 to the exponent.
  • The final coefficient must be between 1 and 10.

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