Represent tenths
Theory
Representing tenths is a Year 4 maths skill: splitting a whole into 10 equal parts and writing each part as a fraction like \(\dfrac{1}{10}\) or a decimal like \(0.1\). This page shows tenths on a bar and a number line, explains the tenths place, links fractions and decimals, and counts on past one whole to numbers like \(1.5\). Curriculum: VC2M4N01 / AC9M4N01.
A tenth is one of 10 equal parts of a whole. If you cut a strip into 10 equal pieces, each piece is one tenth. One tenth is written as the fraction \(\dfrac{1}{10}\) or as the decimal \(0.1\).
The first digit after the decimal point is the tenths place. In \(0.3\) the 3 means 3 tenths, so \(\dfrac{3}{10} = 0.3\). In the same way \(\dfrac{7}{10} = 0.7\) and \(\dfrac{9}{10} = 0.9\). The fraction and the decimal are two ways to write the same amount.
10 tenths fill the whole, so \(\dfrac{10}{10} = 1.0\). Counting in tenths goes \(0.1,\ 0.2,\ 0.3,\ \ldots,\ 0.9,\ 1.0\), just like counting the shaded parts of a bar one at a time. After one whole the count keeps going: \(1.0,\ 1.1,\ 1.2,\ \ldots\) The digit before the point counts wholes (the ones place) and the digit after it counts tenths.
Tenths do not need formulas, but these facts help you swap between fractions and decimals.
How to represent a tenth
- Check the parts. Make sure the whole is split into 10 equal parts. Only then does each part show one tenth.
- Count the tenths. Count how many parts are shaded, or how many steps the arrow is along the number line.
- Write it two ways. Put that count over 10 for the fraction, and write the same digit just after the decimal point for the decimal.
Past one whole. On a number line from \(0\) to \(2\), the marks after \(1\) read \(1.1,\ 1.2,\ 1.3\) and so on. Every \(10\) tenths makes another whole, so \(15\) tenths is \(1\) whole and \(5\) tenths, written \(1.5\).
| \(\text{first bar}\) | \(=\) | \(10\text{ tenths} = 1\text{ whole}\) |
| \(\text{second bar}\) | \(=\) | \(2\text{ tenths}\) |
| \(1\text{ whole and }2\text{ tenths}\) | \(=\) | \(1.2\) |
The whole bar goes before the point and the \(2\) tenths after it, so the shaded amount is \(1.2\).
| \(15\text{ tenths}\) | \(=\) | \(10\text{ tenths} + 5\text{ tenths}\) |
| \(10\text{ tenths}\) | \(=\) | \(1\text{ whole}\) |
| \(15\text{ tenths}\) | \(=\) | \(1.5\) |
The 1 whole goes before the point and the 5 tenths after it, so \(15\) tenths is \(1.5\). That is more than \(1\).
| \(0\text{ to }1\) | \(=\) | \(10\text{ tenths}\) |
| \(\text{arrow}\) | \(=\) | \(2\text{ tenths along}\) |
The arrow points to \(0.2\).
| \(2\text{ tenths}\) | \(=\) | \(0.2\text{ L}\) |
| \(10 - 2\) | \(=\) | \(8\text{ more tenths}\) |
| \(0.2 + 0.8\) | \(=\) | \(1.0\text{ L}\) |
8 more tenths fill the litre, since 10 tenths make one whole.
Common pitfalls
Frequently asked questions
How do you write tenths as a decimal?
Count how many of the ten equal parts you have and write that digit just after the decimal point. One tenth is \(0.1\). If you have more than ten tenths, the extra wholes go before the point: fifteen tenths is \(1.5\).
What is 1/10 as a decimal?
One tenth is written as \(0.1\). The 1 sits in the tenths place, the first spot after the decimal point.
How many tenths are in 2 wholes?
Every whole is made of \(10\) tenths, so \(2\) wholes is \(20\) tenths. As a decimal that is \(2.0\), the same as \(2\).
What is the tenths place in a decimal?
The tenths place is the first digit after the decimal point. In \(5.2\) the 2 is in the tenths place, so it is worth 2 tenths, or \(0.2\). The 5 is in the ones place and is worth 5 wholes.
How do you tell which tenth is bigger?
More tenths means a bigger amount. \(0.8\) is 8 tenths and \(0.2\) is 2 tenths, so \(0.8\) is bigger. Any amount past \(1\), like \(1.1\), is bigger than every tenth below \(1\).
How do you show tenths on a number line?
Split the space from \(0\) to \(1\) into 10 equal steps. Each step is one tenth, so the marks read \(0.1,\ 0.2,\ 0.3\) and so on up to \(1.0\). On a line from \(0\) to \(2\), keep going after \(1\): \(1.1,\ 1.2,\ 1.3\) and so on up to \(2.0\).