Year 4AC9M4N01

Decimals: Tenths

Recognise and extend the application of place value to tenths and hundredths and use the conventions of decimal notation to name and represent decimals.

Read this first

A decimal point shows where the whole numbers stop and the parts begin. The first column after the point is tenths.

This is 3.4. There are 3 whole ones and 4 tenths.

Words you need

Decimal point: The dot that separates wholes from parts.
Tenths: One whole split into 10 equal pieces. The first column after the point.

Worked example

e.g. What is the 7 worth in 2.7?

Put the number in columns. The point sits after the ones.
Find the 7. It sits after the point, in the tenths column.
So the 7 is worth 7 tenths, which we write as $\tfrac{7}{10}$ .
2.7 means 2 wholes and 7 tenths.

Find the column first, same as with whole numbers. The column tells you what the digit is worth.

Practice

The pictures fade as you go. By the last few you are on your own.

1What fraction is shaded? Write it as a decimal too.with a picture

Answer

\tfrac{3}{10}

, which is 0.3.

2What is the 5 worth in 8.5?with a picture

Answer5 tenths, or

\tfrac{5}{10}

, which is the same as a half.

3Write

\tfrac{9}{10}

as a decimal.with a hint

Need a hint?

Tenths go in the first column after the point.

Answer0.9.

4Which is bigger: 4.2 or 4.8?with a hint

Need a hint?

The wholes match. Compare the tenths.

Answer4.8. Both have 4 wholes, and 8 tenths beats 2 tenths.

5Write 6.1 in words.on your own

AnswerSix and one tenth.

6Write

\tfrac{4}{10}

as a decimal.on your own

Answer0.4.

7Put these in order, smallest first: 2.5, 2.1, 2.9on your own

Answer2.1, 2.5, 2.9.

8A bottle holds 1.5 litres. How would you say that?on your own

AnswerOne and five tenths litres, or one and a half litres.

Think about it

Why is 0.5 the same as a half?

One good answer0.5 is 5 tenths. Five tenths fills half the bar, because 10 tenths make one whole.

Sam says 4.10 is bigger than 4.9 because 10 is bigger than 9. What went wrong?

One good answerHe compared the digits instead of the columns. 4.9 is 9 tenths, and 4.10 is 1 tenth and 0 hundredths. So 4.9 is bigger.

How many tenths make one whole?

One good answer10. That is why we call them tenths.

Common mistakes

Reading 3.4 as three point four as if 4 were a whole number.

The 4 is 4 tenths, not 4 ones. Check which side of the point it sits.

Thinking a longer decimal is always bigger.

Compare column by column, starting from the left. 0.9 beats 0.15.

Forgetting the 0 before the point in 0.7.

Write the 0 so nobody misreads the number. It shows there are no whole ones.