Comparing decimals

​​In a nutshell

Being able to compare the sizes of different decimals allows them to be placed in order. A number line can be useful to help visualise this process.

Which is bigger?

In order to decide which number is larger, its placement and position on a number line can be looked at. The further up the number line it is, the bigger its size.

Example 1

Which is bigger: $$4.2$$ or $$4.7$$?

$$\begin{array}{cccccccccccccc}&&&& \\& &&&\downarrow &&&&&&&&&&\downarrow &&&&\\\bold4&&4.1&&\underline{4.2}&&4.3&&4.4&&4.5&&4.6&&\underline{4.7}&&4.8 &&4.9&&\bold5\\|&&|&&|&&|&&|&&|&&|&&|&&|&&|&&| \\ \hline\end{array}$$​​

Notice how $$4.7$$ is positioned further up the number line than $$4.2$$.​

What's more, $$4.2$$ and $$4.7$$ both share the same digit in their ones column whilst the digits in the tenths column differ. 

$$7$$​ is greater than $$2$$​ and so:

$$4.7$$ is greater than $$4.2$$.

Ordering decimals

To order a set of decimals, compare them with each other and decide which are bigger.

Procedure

Example 2

Place the numbers $$1.72, 2.52, 1.68$$ and $$1.73$$ in order from smallest to largest.

Look at the digits in the ones column: $$1,2,1$$ and $$1$$.

$$2$$​ is the only differing digit. It is bigger than $$1$$​, so $$2.52$$ is the largest number.

Look at the remaining digits in the tenths column: $$7,6$$ and $$7.$$​

$$6$$​ is the only differing digit. It is smaller than $$7$$​, so $$1.68$$ is less than $$1.72$$ and $$1.73$$.

Look at the remaining digits in the hundredths column: $$2$$​ and $$3$$.

$$3$$​ is bigger than $$2$$​ so $$1.73$$ is greater than $$1.72$$.

Using the information gathered, place all four numbers in order.

$$\underline{1.68,1.72,1.73,2.52}$$