0580

Number Toolkit

Number

Adding and subtracting decimals

  • Line the decimal points up underneath one another before adding or subtracting
  • Fill any short columns with zeros so every number has the same number of decimal places
  • The decimal point in the answer sits directly below the points in the question

Multiplying decimals

  • Multiplying by a power of ten turns a decimal into an integer, and the change is undone at the end
    • For 1.4 × 2.05, work out 14 × 205 = 2 870, then divide by 10 and by 100 to give 2.87
  • Counting decimal places gives the same result: the answer has as many decimal places as the two numbers together
    • 1.4 has one and 2.05 has two, so the answer has three before trailing zeros are removed
  • An estimate settles where the point belongs: 1.4 × 2.05 is roughly 1.5 × 2 = 3, so 2.87 is sensible and 28.7 is not

Dividing decimals

  • Multiply both numbers by the same power of ten until the divisor is a whole number
    • 3.15 ÷ 0.05 becomes 315 ÷ 5 = 63
  • The answer is unchanged because both numbers were scaled equally
Exam tip

Estimate before writing a decimal answer down. Every slip in these methods moves the point by a factor of ten, and a one-line estimate is what tells you 2.87 is right and 28.7 is not.

Worked example

Subtracting decimals in a money context

A length of ribbon measures 7.5 m. A piece measuring 0.86 m is cut off. Work out the length remaining.

Solution:

  • Estimate first: 7.5 − 0.9 = 6.6 m
  • Write 7.5 as 7.50 so both numbers have two decimal places
  • Hundredths: 0 is smaller than 6, so exchange from the tenths column, giving 10 − 6 = 4
  • Tenths: 4 is smaller than 8, so exchange from the ones column, giving 14 − 8 = 6
  • Ones: 6 − 0 = 6
  • The remaining length is 6.64 m, which is close to the estimate