What are decimals?

Part ofMathsPlace valueYear 4

Tenths and hundredths

Two children, one is in a wheel chair. They are thinking about decimals, the numbers 0.1 and 0.01.

Decimals are a way of representing numbers that are not whole.

When 1 is divided into 10 equal parts, they are called tenths.

Tenths can be represented as decimals:

One tenth = \( \frac{1}{10} \) = 0.1

When 1 is divided into 100 equal parts, they are called hundredths.

Hundredths can be represented as decimals:

One hundredth = \( \frac{1}{100} \) = 0.01

Two children, one is in a wheel chair. They are thinking about decimals, the numbers 0.1 and 0.01.
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Activity: Understanding decimals

Complete this interactive activity to understand more about decimals, then put your knowledge to the test.

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Representing tenths

These pictures all show a whole divided into ten equal parts with one part shaded or one part full.

They all represent one-tenth of the whole.

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  1. A measuring jug with a capacity of 1 litre. One tenth of the jug contains water.
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Understanding decimal place value

You can change the value of a digit in a number depending on the position you write it.

Look at this place value chart.

A table with the following 5 headings, 'hundreds', 'tens', 'ones', 'tenths' and 'hundredths' with a decimal point separating the 'ones' and the 'tenths' column. The first row has a 1 in the 'hundreds' column and 0 in the rest. The second row has a 1 in the 'tens' column with 0 in the rest. The third row has a 1 in the 'ones' column with 0 in the rest. The fourth row has a 1 in the 'tenths' column with 0 in the rest. The fifth row has a 1 in the 'hundredths' column with 0 in the rest.

The digit 1 has the following values:

  • 100 when it is placed in the hundreds column.

  • 10 when it is placed in the tens column.

  • 1 when it is placed in the ones column.

From left to right, each place value column is ten times smaller than the previous column.

One tenth (\( \frac{1}{10} \)) is ten times smaller than 1 and you write it as a decimal by putting a 1 in the tenths column (0.1).

One hundredth (\( \frac{1}{100} \)) is ten times smaller than one tenth and you write it by putting a 1 in the hundredths column (0.01).

The decimal point needs to go after the ones, so that it separates the ones from the tenths and the hundredths.

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Example 1

4 smalls weights each weighing 1 tenth of a kilogram.

How would you represent 4 one-tenths of a kilogram using decimals?

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Example 2

A 100 square grid with 65 squares shaded.

Each square on this one hundred grid is one-hundredth of the whole.

There are 65 shaded squares. That is 65 one-hundredths.

How is this represented in decimals?

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Use your times tables and more maths skills to defeat monsters and reclaim the Kingdom of Mathematica

Play our fun maths game Guardians: Defenders of Mathematica
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