Beyond hundredths | Year 5

01 / LEARN

Understand the idea.

Every place is ten times smaller

After the decimal point, place values are tenths, hundredths and thousandths. Each place to the right is one tenth the size of the previous place: ten thousandths make one hundredth. The point separates whole-number places from fractional places.

In $2.305$ , the $3$ means three tenths, the $0$ keeps the hundredths place empty, and the $5$ means five thousandths. Read every decimal digit in order, or name the whole fraction part using its last place: $305$ thousandths.

The places in 2.305
Ones	Tenths	Hundredths	Thousandths
2	3	0	5

Build and rename decimal amounts

Expanded notation shows each contribution: $2.305 = 2 + 0.3 + 0.005$ . The missing hundredths contribute zero. Lining up decimal places makes the meaning of each digit clear when building a number from words.

Trailing zeros give an equivalent name: $0.6 = 0.60 = 0.600$ . Six tenths is also sixty hundredths and six hundred thousandths. Zeros between non-zero digits cannot simply be removed: $0.506$ differs from $0.56$ because the $6$ changes place.

2.305 = 2 + \frac{3}{10} + \frac{5}{1000}

02 / WORKED EXAMPLES

See the method in action.

EXAMPLE 01

Read a measuring value

In $4.072$ metres, what value does the digit 7 have?

Worked solution

1
Read the places after the decimal point.
$4.072 = 4 + \frac{0}{10} + \frac{7}{100} + \frac{2}{1000}$
The second decimal place is hundredths, so the 7 counts hundredths.
2
Write the value of seven hundredths.
$\frac{7}{100} = 0.07$
A zero is needed in the tenths place to keep 7 in the hundredths place.
3
Retain the measurement unit.
$0.07 m$
The digit contributes seven hundredths of a metre, rather than seven whole metres.

Answer

0.07 metre, or seven hundredths of a metre.

EXAMPLE 02

Build a number from parts

Write the decimal with six ones, two hundredths and nine thousandths.

Worked solution

1
Write the value of each named part.
$6 + \frac{2}{100} + \frac{9}{1000}$
The question names six ones, two hundredths and nine thousandths.
2
Include the empty tenths place.
$6 + 0.02 + 0.009$
There are no tenths, so the first decimal digit must be 0.
3
Combine the place-value parts.
$6 + 0.02 + 0.009 = 6.029$
The 2 stays in hundredths and the 9 stays in thousandths.

Answer

$6.029$ .

03 / YOUR TURN

Try it yourself.

Check your understanding

Write forty-three thousandths as a decimal.

Show answer & reasoning

$0.043$

Forty-three thousandths is $\frac{43}{1000} = 0.043$ . The zero tenths keeps $4$ in hundredths and $3$ in thousandths.

Keep practising

6 worksheet questions · 10 marks

Open worksheet Worked solutions

Read the questions online

What is the value of 8 in $5.081$ ?
1 mark
Write seven hundred and six thousandths as a decimal.
1 mark
Write $3.406$ in expanded decimal notation.
2 marks
Write a decimal with two ones, five hundredths and one thousandth.
2 marks
Are $0.7$ and $0.700$ equal? Explain with place value.
2 marks
Mila deletes the zero in $2.047$ and gets $2.47$ . Explain how the digit 4 changed value.
2 marks

Read the worked solutions

Equivalent correct methods earn the corresponding marks. Include units where asked.

What is the value of 8 in $5.081$ ?
1 mark
Eight is in the hundredths place.
$0.08$
Write seven hundred and six thousandths as a decimal.
1 mark
Seven hundred and six thousandths is $\frac{706}{1000}$ .
$0.706$
Write $3.406$ in expanded decimal notation.
2 marks
Three ones, four tenths, zero hundredths and six thousandths.
$3 + 0.4 + 0.006$
Write a decimal with two ones, five hundredths and one thousandth.
2 marks
No tenths are given, so use zero in the tenths place.
$2.051$
Are $0.7$ and $0.700$ equal? Explain with place value.
2 marks
Seven tenths is seventy hundredths or seven hundred thousandths. Trailing zeros rename the same value.
Yes.
Mila deletes the zero in $2.047$ and gets $2.47$ . Explain how the digit 4 changed value.
2 marks
In 2.047 the four is in the second decimal place.
In 2.47 it is in the first decimal place.
It changed from four hundredths to four tenths, becoming ten times as large.

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Curriculum reference & lesson scope

Australian Curriculum v9.0; SA Curriculum Mathematics 2026

Beyond hundredths; ordering/number lines; familiar fraction–decimal–percentage equivalents.

Official curriculum source ↗

In this lesson

Understand the idea.

Every place is ten times smaller

Build and rename decimal amounts

See the method in action.

Read a measuring value

Read the places after the decimal point.

Write the value of seven hundredths.

Retain the measurement unit.

Build a number from parts

Write the value of each named part.

Include the empty tenths place.

Combine the place-value parts.

Try it yourself.

Check your understanding

Keep practising