Standard form

Last time

Before we start: last time, in Surds, you learned these points. Here they are again on one card. Keep them in mind, because today builds on them.

Very big, very small

The distance from the Sun is a hundred and fifty billion metres. The mass of an electron has thirty zeros after a decimal point. Writing these in full is a nightmare. Standard form is the scientist's shorthand. Today you write, compare and calculate with numbers like three point six times ten to the minus four.

What is standard form?

A number is in standard form when it is written as a times ten to the power n. The number a must be at least one, and less than ten: exactly one digit before the decimal point. The power n is an integer. Positive for big numbers, negative for small ones. So forty-five times ten cubed is not in standard form, because forty-five is bigger than ten.

Large numbers

To write a large number in standard form, place the decimal point after the first digit. Now count how many places the point moved. It moved seven places to the left, so the power is positive seven. So fifty-two million is five point two times ten to the seven.

Small numbers

For a small number, the point moves to the right to sit after the first non-zero digit. Take zero point zero zero zero three six. The point moved four places to the right, so the power is minus four. So it is three point six times ten to the minus four. Small number means negative power.