Resources For Teachers For Tutors For Students & Parents AI New Pricing
Create Free Account
Year 5 Maths Decimals

Represent decimals to thousandths

20 practice questions 0 video lessons Theory + worked examples
Practice 20 questions
Practice questions

Every question with a fully worked solution.

Start practising
Create a free accountTrack your progress and save your work as you go.
Create free account

Theory

Each place to the right of the decimal point is ten times smaller than the place before it: tenths, hundredths, then thousandths. This Year 5 maths page shows how to read and write decimals such as \(3.274\), find the place and value of any digit, partition a decimal by place value, and use thousandths in measurement (\(1\text{ mm} = 0.001\text{ m}\)).

The decimal point separates the whole number from the parts of a whole. The places after it are tenths (\(0.1\)), hundredths (\(0.01\)) and thousandths (\(0.001\)).

The place of a digit is the column it is in. Its value is how much it is worth there. In \(3.274\), the \(7\) is in the hundredths place and its value is \(0.07\).

To partition a decimal, write it as the sum of the values of its digits: \(3.274 = 3 + 0.2 + 0.07 + 0.004\). A zero digit adds nothing, so it gets no part.

To read a decimal, say the whole number, then “and”, then the digits after the point as a number of the last place: \(1.608\) is one and six hundred and eight thousandths.

In measurement, \(1\text{ m} = 1000\text{ mm}\), \(1\text{ L} = 1000\text{ mL}\) and \(1\text{ kg} = 1000\text{ g}\), so one thousandth of a metre, litre or kilogram is \(1\) mm, \(1\) mL or \(1\) g.

Place value chart for 3.274 A place value chart with columns Ones, Tenths, Hundredths and Thousandths holding the digits 3, 2, 7 and 4, with a red decimal point after the ones. Underneath, the values 3, 0.2, 0.07 and 0.004. OnesTenthsHundredthsThousandths 3274 30.20.070.004
\(3.274 = 3 + 0.2 + 0.07 + 0.004\).
Place value chart for 5.003 A place value chart with columns Ones, Tenths, Hundredths and Thousandths holding the digits 5, 0, 0 and 3. The zeros hold the tenths and hundredths places. The values are 5, 0, 0 and 0.003. OnesTenthsHundredthsThousandths 5003 5000.003
The zeros hold their places: \(5.003 = 5 + 0.003\).
A strip 37 millimetres long on a ruler A ruler marked in centimetres with millimetre marks. A strip starts at 0 and ends seven small marks past the 3, so it is 37 millimetres, or 0.037 metres, long. 012345 cm
\(37\text{ mm} = 0.037\text{ m}\): each millimetre is a thousandth of a metre.

Each place is ten times smaller than the place to its left:

\[ 1 = 10 \text{ tenths} \]
1=10 tenths
\[ 0.1 = 10 \text{ hundredths} \]
0.1=10 hundredths
\[ 0.01 = 10 \text{ thousandths} \]
0.01=10 thousandths
\[ 3.274 = 3 + 0.2 + 0.07 + 0.004 \]
3.274=3+0.2+0.07+0.004
\[ 1\text{ mm} = 0.001\text{ m} \]
1 mm =0.001 m
Zeros are placeholders. In \(0.056\) the zero in the tenths place keeps the \(5\) in the hundredths place. Without it, \(0.56\) is a different number.
Read the last place. The last digit tells you what to call the number: \(0.056\) ends in the thousandths place, so it is fifty-six thousandths.

How to find the value of a digit

  1. Count places after the decimal point: 1st tenths, 2nd hundredths, 3rd thousandths.
  2. Write the digit in that place with zeros before it: a \(9\) in the thousandths place is worth \(0.009\).

How to write a decimal from words

  1. Find the last place named (tenths, hundredths or thousandths).
  2. Write the number so that its last digit lands in that place, filling gaps with zeros.
Example 1 — Words to decimal
Write each as a decimal.
(i) four thousandths
(ii) fifty-six thousandths
(iii) three hundred and twelve thousandths
Solution
\(4 \text{ thousandths}\)\(=\)\(0.004\)
\(56 \text{ thousandths}\)\(=\)\(0.056\)
\(312 \text{ thousandths}\)\(=\)\(0.312\)
0.004,0.056,0.312

(i) \(0.004\)
(ii) \(0.056\)
(iii) \(0.312\)

Example 2 — Place and value
In \(7.519\), which place is the \(9\) in, and what is its value?
Solution

The \(9\) is the third digit after the decimal point.

9 in 7.519 is worth 0.009

The thousandths place; its value is \(0.009\).

Example 3 — Partition
Partition \(8.62\) by place value.
Solution
\(8.62\)\(=\)\(8 + 0.6 + 0.02\)
8.62=8+0.6+0.02

\(8 + 0.6 + 0.02\).

Example 4 — Build a decimal
A decimal has \(6\) ones, \(0\) tenths, \(4\) hundredths and \(9\) thousandths. Write it.
Solution
\(6 + 0.04 + 0.009\)\(=\)\(6.049\)
6+0.04+0.009=6.049

\(6.049\).

Example 5 — In words
Write \(1.608\) in words.
Solution

The digits after the point are \(608\), ending in the thousandths place.

One and six hundred and eight thousandths.

Example 6 — Measurement
(i) A strip is \(0.375\) m long. How many millimetres is that?
(ii) A jug holds \(2.35\) L. How many millilitres is that?
Solution
\(0.375 \times 1000\)\(=\)\(375\)
\(2.35 \times 1000\)\(=\)\(2350\)
0.375 m =375 mm ,2.35 L =2350 mL

(i) \(375\) mm
(ii) \(2350\) mL

Example 7 — Equal or not?
Which of these is not equal to \(0.8\) m: \(800\) mm, \(80\) hundredths of a metre, \(80\) mm?
Solution
\(0.8 \times 1000\)\(=\)\(800\)
0.8 m =800 mm

\(80\) mm is only \(0.08\) m, so it is not equal to \(0.8\) m.

Example 8 — Find the mistake
Ivy says \(0.3\) and \(0.03\) are the same because both have a \(3\). Explain why she is wrong.
Solution

In \(0.3\) the \(3\) is in the tenths place; in \(0.03\) it is in the hundredths place.

The values are \(0.3\) and \(0.03\). \(0.3\) is ten times as big.

Common pitfalls

Leaving out placeholder zeros. Fifty-six thousandths is \(0.056\), not \(0.56\).
Naming the place by the digit, not the column. In \(7.519\) the \(9\) is in the thousandths place even though it is the biggest digit.
Adding a part for a zero. \(5.003 = 5 + 0.003\); there is no tenths or hundredths part to write.
Mixing up 0.08 m and 0.8 m. \(0.8\text{ m} = 800\text{ mm}\) but \(0.08\text{ m} = 80\text{ mm}\).

Frequently asked questions

What is a thousandth?

One part when a whole is split into \(1000\) equal parts. It is written \(0.001\).

How do you find the value of a digit in a decimal?

Find its place, then write the digit in that place: in \(7.519\) the \(9\) is worth \(0.009\).

How do you partition a decimal?

Write it as the sum of the values of its digits: \(8.62 = 8 + 0.6 + 0.02\).

How do you say 1.608?

One and six hundred and eight thousandths.

How many millimetres are in 0.375 m?

\(375\) mm, because \(1\) m is \(1000\) mm.

More in Decimals
Compare & order decimals
20 questions