Decimals

• Each place to the right of the decimal point is ten times smaller: tenths, hundredths, thousandths.
• Order decimals by comparing digits place by place, from the left.
• A terminating decimal is a fraction: 0.65 = 65/100 = 13/20.
• Convert a decimal to a percentage by multiplying by 100.
• Higher: convert recurring decimals to fractions by multiplying by powers of 10 and subtracting.

Tenths, hundredths, thousandths

The digits after the decimal point are tenths, hundredths, thousandths and so on. In 2.0461 the 4 is worth 4 hundredths and the 6 is worth 6 thousandths.

To order decimals, line up the decimal points (fill gaps with zeros if it helps) and compare from the left. 0.37 is bigger than 0.307, because 7 hundredths beats 0 hundredths. More digits does not mean bigger.

Terminating decimals only

A terminating decimal stops, so it is a fraction with a denominator of 10, 100, 1000 … Write it over the right power of 10, then simplify. Multiply by 100 for a percentage.

Multiply, subtract, the repeating tail cancels

A dot over a digit means it repeats: 0.32̇ = 0.3222… A dot over the first and last digits of a block means the whole block repeats: 0.4̇5̇ = 0.454545…

Let x be the decimal. Multiply by powers of 10 to get two numbers with the same recurring tail, then subtract so the tail cancels.