Comparing and Rounding Decimals

What you will learn

• Compare and order decimals.
• Avoid the mistake that a longer decimal is a bigger one.
• Round to the nearest whole number or to a number of decimal places.

Before you start: you should know decimal place value and how to round whole numbers. See Decimals Explained and Rounding and Estimating.

The idea

Which is bigger, $0.7$ or $0.65$? Many people say $0.65$ because $65$ is bigger than $7$. But the digits sit in different columns. Line up the decimal points and pad with zeros so both have the same length: $0.70$ and $0.65$. Now it is clear that $70$ hundredths is more than $65$ hundredths.

Comparing step by step

1. Line up the decimal points.
2. Pad with zeros if you like.
3. Compare the digits from the left, the biggest place first. The first place where they differ decides.

Rounding

To round to a number of decimal places, find the last digit you keep and look at the next digit. If it is $5$ or more, round up. If it is $4$ or less, leave it.

Worked examples

Example 1: Compare

Which is bigger, $2.305$ or $2.35$?

1. Pad: $2.305$ and $2.350$.
2. Ones: $2$ and $2$. Tenths: $3$ and $3$. Hundredths: $0$ and $5$.
3. Five is more than nought.

Answer: $2.35$ is bigger.

Example 2: Round to 2 decimal places

Round $5.678$ to $2$ decimal places.

1. Keep $5.67$. The next digit is $8$.
2. Eight is $5$ or more, so round the $7$ up.

Answer: $5.68$

Example 3: Round to 1 decimal place

Round $0.0749$ to $1$ decimal place.

1. The tenths digit is $0$. The next digit is $7$.
2. Seven is $5$ or more, so round the $0$ up to $1$.

Answer: $0.1$

Watch out: when you round $4.96$ to one decimal place, the $9$ rounds up to $10$ and carries, giving $5.0$.

Why it matters

Race times, prices, measurements and test results are decimals. Putting them in order and rounding them sensibly lets you compare them fairly. Rounding is also how you check a calculation or report a result with the right amount of detail.