Working with Decimals

In short: To add or subtract decimals, line up the decimal points. To multiply, ignore the points, multiply, then give the answer as many decimal places as the question has in total, so $0.3\times 0.2=0.06$.

Before you start

• Place value after the point: in $3.465$ the 4 is 4 tenths, the 6 is 6 hundredths and the 5 is 5 thousandths.
• $0.1=\frac{1}{10}$, $0.01=\frac{1}{100}$, $0.001=\frac{1}{1000}$.
• Multiplying and dividing by 10, 100 and 1000 (see the previous chapter).

Adding and subtracting: line up the points

Missing numbers

Use the opposite operation.

Multiplying decimals

Dividing decimals

Dividing by 10, 100 or 1000 moves the digits right, so the number gets smaller.

$5÷10=0.5$ and $2.25÷20=2.25÷2÷10=1.125÷10=0.1125$.

Thousandths in real life

$0.001$ is one thousandth. Lots of metric units use it:

Quick summary

• To add or subtract, line up the decimal points and fill gaps with zeros.
• To multiply, ignore the points, multiply, then give the answer as many decimal places as the question has in total.
• $\times 0.1$, $\times 0.01$ and $\times 0.001$ are the same as $÷10$, $÷100$ and $÷1000$.
• Find a missing number with the opposite operation.
• Halfway between two numbers: add them and halve.

Quiz