Decimals

The digits after the decimal point are tenths, hundredths and thousandths. To add or subtract, line up the decimal points so equal place values sit above each other — write 5.70 − 2.85, not 5.7 − 2.85, so both have two decimal places. To multiply, ignore the points, multiply as whole numbers, then put back as many decimal places as the two factors had together: 0.6 × 0.4 = 24 with two decimal places = 0.24.

Multiplying by 10, 100 or 1000 moves the decimal point one, two or three places to the right; dividing moves it the same number of places to the left. So 3.6 × 10 = 36 and 48 ÷ 100 = 0.48. This is also the trick for dividing by a decimal: scale both numbers up until the divisor is whole. 2.4 ÷ 0.8 becomes 24 ÷ 8 = 3.

To round to a number of decimal places, look at the next digit along. If it is 5 or more, round up; if it is below 5, round down. So 4.62 to 1 decimal place is 4.6 (the next digit, 2, is below 5), while 7.348 to 2 decimal places is 7.35 (the next digit, 8, is 5 or more).

Every fraction becomes a decimal when you divide the top by the bottom. If the denominator (in lowest terms) is built only from the primes 2 and 5, the decimal stops — it terminates — like 3/8 = 0.375. Otherwise it repeats forever: 1/3 = 0.333… is a recurring decimal. When a recurring decimal turns up in money, round to the nearest cent: sharing $10.00 three ways gives 3.333…, which rounds to $3.33 each.