Connect fractions & decimals
Theory
Connecting fractions and decimals is a Year 4 maths skill: seeing that tenths and hundredths can be written as a fraction or as a decimal for the same amount, such as \(\dfrac{9}{10}=0.9\) and \(\dfrac{47}{100}=0.47\). This page uses hundred grids and number lines, and links the benchmark fractions \(\dfrac{1}{2}\), \(\dfrac{1}{4}\) and \(\dfrac{3}{4}\) to \(0.5\), \(0.25\) and \(0.75\). Curriculum: VC2M4N03 / AC9M4N03.
A fraction and a decimal can name the same amount. When one whole is split into 10 equal parts, each part is one tenth. When it is split into 100 equal parts, each part is one hundredth.
The first place after the decimal point counts tenths, so \(\dfrac{9}{10}=0.9\). The second place counts hundredths, so \(\dfrac{47}{100}=0.47\). The bottom number of the fraction tells you the place: a 10 means tenths, and a 100 means hundredths.
Some fractions are benchmarks worth remembering: \(\dfrac{1}{2}=0.5\), \(\dfrac{1}{4}=0.25\) and \(\dfrac{3}{4}=0.75\). On a number line the same point can wear both a fraction name and a decimal name.
These conversions are worth remembering. Read the fraction as tenths or hundredths and write the matching decimal.
How to connect a fraction and a decimal
- Name the parts. Decide whether you are working in tenths (out of 10) or hundredths (out of 100).
- Write the fraction. Put the number of shaded or counted parts on top, and 10 or 100 on the bottom.
- Write the decimal. Tenths fill the first decimal place; hundredths fill the first two places. So \(\dfrac{8}{10}=0.8\) and \(\dfrac{9}{100}=0.09\).
Halves, quarters and fifths. Rename them as tenths or hundredths first. A fifth is \(2\) tenths, so \(\dfrac{3}{5}=\dfrac{6}{10}=0.6\). Quarters work in hundredths: each quarter of \(100\) is \(25\), so the quarter marks on a \(0\) to \(1\) line are \(25\) hundredths apart.
Lengths over one metre. Since \(100\) cm is \(1\) m, \(160\) cm is \(1\) m and \(60\) cm, written \(1.60\) m or \(1.6\) m.
| \(\dfrac{9}{10}\) | \(=\) | \(9\text{ tenths}\) |
| \(9\text{ tenths}\) | \(=\) | \(0.9\) |
The 9 goes in the first decimal place, so the answer is \(0.9\).
| \(0.63\) | \(=\) | \(63\text{ hundredths}\) |
| \(0.63\) | \(=\) | \(\dfrac{63}{100}\) |
Two decimal places means hundredths, so the answer is \(\dfrac{63}{100}\).
| \(8\text{ of }10\) | \(=\) | \(\dfrac{8}{10}\) |
| \(\dfrac{8}{10}\) | \(=\) | \(0.8\) |
Eight parts of ten are shaded, so \(\dfrac{8}{10}=0.8\).
| \(60\text{ cm}\) | \(=\) | \(\dfrac{60}{100}\text{ m}\) |
| \(\dfrac{60}{100}\) | \(=\) | \(\dfrac{6}{10}=0.6\text{ m}\) |
So \(60\) cm is \(\dfrac{60}{100}\) of a metre, which is \(0.6\) m.
Common pitfalls
Frequently asked questions
How do you write a fraction as a decimal?
Read the fraction as tenths or hundredths. Tenths over 10 fill the first decimal place, so \(\dfrac{9}{10}=0.9\). Hundredths over 100 fill the first two places, so \(\dfrac{47}{100}=0.47\).
How can you work out a benchmark decimal?
Rename the fraction as hundredths, because \(100\) splits evenly into halves and quarters. One half of \(100\) is \(50\) and one quarter of \(100\) is \(25\), so the halves and quarters of one whole land on whole numbers of hundredths.
What is two fifths as a decimal?
Each fifth of a whole is \(2\) tenths, so two fifths is \(4\) tenths. That means \(\dfrac{2}{5}=0.4\).
Is 0.9 the same as 9 tenths?
Yes. The first place after the decimal point counts tenths, so \(0.9\) means 9 tenths, which is the fraction \(\dfrac{9}{10}\).
What is the difference between tenths and hundredths?
A tenth is one whole split into 10 equal parts and sits in the first decimal place. A hundredth is one whole split into 100 equal parts and sits in the second place. So \(0.8\) is 8 tenths but \(0.08\) is 8 hundredths, which is much smaller.
How do you write 0.35 as a fraction?
\(0.35\) has two decimal places, so it is 35 hundredths, the fraction \(\dfrac{35}{100}\).