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What are decimals?

Part of MathsPlace 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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Times tables games, quizzes and songs

If you're getting ready for the multiplication tables check or you want to work on your skills, check out our times tables collection.

Times tables games, quizzes and songs
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More on Place value

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