Represent hundredths
Theory
Representing hundredths is a Year 4 maths skill: showing hundredths as a fraction like \(\dfrac{1}{100}\) and as a decimal like \(0.01\), reading a hundred grid, using place value to two decimal places, and connecting tenths and hundredths. This page explains the hundredths place, the role of the hundred grid and number line, and how \(10\) hundredths make one tenth. Curriculum: VC2M4N01 / AC9M4N01.
A hundredth is one of \(100\) equal parts of a whole. If you split one whole into \(100\) equal parts, each part is a hundredth. You can write it as the fraction \(\dfrac{1}{100}\) or as the decimal \(0.01\).
Decimals use place value, just like whole numbers. The first place after the decimal point is tenths and the second place is hundredths. In \(0.24\) the 2 means \(2\) tenths and the 4 means \(4\) hundredths.
A hundred grid is a square split into \(100\) small squares. Each small square is one hundredth, so shading squares is an easy way to show a decimal. Ten small squares in a row make one tenth, which is why \(10\) hundredths \(= 1\) tenth.
Hundredths do not need formulas, but these place value facts help you build and rename decimals.
How to represent a number in hundredths
- Count the hundredths. On a hundred grid, count the shaded squares. On a number line, count the small steps of \(0.01\).
- Write the fraction. Put the number of hundredths over \(100\), like \(\dfrac{8}{100}\).
- Write the decimal. Put the tenths in the first place after the point and the hundredths in the second place, so \(\dfrac{8}{100} = 0.08\).
Between two tenths. The gap from \(0.6\) to \(0.7\) splits into \(10\) hundredths: \(0.61,\ 0.62,\ \ldots,\ 0.69\). The halfway mark is \(0.65\).
Which is larger? Compare the tenths digit first. \(0.4\) is \(40\) hundredths, so it is larger than \(0.38\), which is only \(38\) hundredths.
Wholes too. A digit before the point counts ones, so \(2.46\) is \(2\) ones, \(4\) tenths and \(6\) hundredths: \(2 + 0.4 + 0.06\).
| \(\text{shaded}\) | \(=\) | \(8\text{ hundredths}\) |
| \(\text{fraction}\) | \(=\) | \(\dfrac{8}{100}\) |
| \(\text{decimal}\) | \(=\) | \(0.08\) |
The \(8\) sits in the hundredths place, so the answer is \(0.08\).
| \(\text{tenths digit}\) | \(=\) | \(5\) |
| \(\text{hundredths digit}\) | \(=\) | \(7\) |
| \(0.57\) | \(=\) | \(5\text{ tenths} + 7\text{ hundredths}\) |
So \(0.57\) is \(5\) tenths and \(7\) hundredths.
| \(\text{each step}\) | \(=\) | \(0.01\) |
| \(7\text{ steps}\) | \(=\) | \(0.07\) |
The arrow points to \(0.07\).
| \(70\text{c}\) | \(=\) | \(\dfrac{70}{100}\text{ of }\$1\) |
| \(\dfrac{70}{100}\) | \(=\) | \(0.70 = \$0.70\) |
| \(0.70\) | \(=\) | \(0.7 = 7\text{ tenths}\) |
So \(70\)c is \(\$0.70\), the same as \(7\) tenths of a dollar. Since \(\$1\) is \(100\) cents, each cent is one hundredth of a dollar.
Common pitfalls
Frequently asked questions
What is a hundredth?
A hundredth is one of \(100\) equal parts of a whole. As a fraction it is \(\dfrac{1}{100}\) and as a decimal it is \(0.01\).
How do you write hundredths as a decimal?
Put the hundredths in the second place after the decimal point. Eight hundredths is \(0.08\) and thirty-six hundredths is \(0.36\).
Is 0.05 the same as 0.5?
No. \(0.05\) is \(5\) hundredths and \(0.5\) is \(5\) tenths. \(0.5\) is ten times bigger than \(0.05\).
How many hundredths are in one tenth?
There are \(10\) hundredths in \(1\) tenth, so \(0.10\) is the same as \(0.1\).
How do you write a decimal like 0.02 as a fraction?
Count the hundredths and write them over \(100\). \(0.02\) is \(2\) hundredths, which is \(\dfrac{2}{100}\).
Why does 0.8 equal 0.80?
Eight tenths is the same as \(80\) hundredths, so \(0.8\) and \(0.80\) have the same value. The extra zero adds no hundredths.