# Year 9

## Number and Algebra

### Scientific notation

Scientific notation, or standard form, is a convenient way to represent very large or very small numbers. It allows the numbers to be easily recorded and read.

The star Sirius is approximately 75 684 000 000 000 km from the Sun. We can represent this number more compactly by moving the decimal point to just after the first non-zero digit and multiplying by an appropriate power of 10 to recover the original number. Thus

75 684 000 000 000 = 7.5684 × 10\(^{13}\)

If we move the decimal point 13 places to the right, inserting the necessary zeroes, we arrive back at the number we started with.

We can similarly deal with very small numbers using negative indices. For example, an Angstrom (Å) is a unit of length equal to 0.000 000 000 1 m, which is the approximate diameter of a small atom. We place the decimal point just after the first non-zero digit and multiply by the appropriate power of ten. Thus

0.000 000 000 1 = 1 × 10\(^{–10}\)

Hence, for example, the diameter of a uranium atom is 0.000 000 000 38 m which we may write as

3.8 × 10\(^{–10}\) m or 3.8 Å (because one Å = 10\(^{–10}\)m).