Calculations in chemistry may involve multiplying or dividing numbers expressed in scientific notation. When numbers expressed in scientific notation are combined by multiplication or division, the two parts of the number are combined separately. The rules below are for various operations involving the powers of 10 part of a number expressed in scientific notation.
When
powers to the same base (10 for example)
are
divided,
the exponent in the result is the exponent on the numerator minus the exponent on the denominator.
| 10b | = 10b–a | | 105 | = 105 – ( –3) = 108 |
| 10a | 10–3 |
Note from the example that subtracting a negative number is equivalent to adding a positive one
Example: 6 –. (–3) = 6 + 3 = 9
When
powers to the same base multiplied, the
exponents are
added.
| 10a × 10b = 10a+b | | 10–5 × 103 = 10–2 |