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Scale decimals and convert units

Track place values and unit size when multiplying or dividing by powers of ten.

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  • MOE teaching syllabus · Primary 5 Mathematics (taught from 2025)
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Follow each digit’s value

Watch the digits move into bigger places. The decimal point stays still.

Work without a calculator. Type numbers in the answer boxes. Each measurement box shows its unit.

Multiplying by 100 makes each digit worth 100 times as much. Follow the same digits of 3.047 in the table. The decimal point still separates ones from tenths.

Scale every place by 100

The before and after columns keep the same digits in order, including the zero. Each row follows one digit through multiplication by 100.

Follow each digit across its row. Add the values in the last column to find the new number.
Figure data

This table is included in print while it is open.

Each digit’s value before and after scaling
BeforeAfter × 100
3 × 13 × 100
0 × 0.10 × 10
4 × 0.014 × 1
7 × 0.0017 × 0.1
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3.047 = 3 + 0.04 + 0.007. Multiplying each contribution by 100 gives 300 + 4 + 0.7 = 304.7.

Try two different scale factors

Now scale 2.06 by two different factors.

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For 2.06 × 10, two ones become two tens and six hundredths become six tenths: 20.6. For 2.06 × 1000, they become two thousands and six tens: 2060. A final zero holds the empty ones place.

Which smaller place will each digit move into?

Divide and follow each digit

Dividing by 1000 makes each digit’s contribution one thousandth as large. In 0.406, follow the 4, the internal zero and the 6. The original zero between 4 and 6 still has a job after division.

Make every place one thousandth as large

The before and after columns keep the same digits in order, including the zero. Each row follows one digit through division by 1000.

Follow each digit across its row. Add the values in the last column to find the new number.
Figure data

This table is included in print while it is open.

Each digit’s value before and after scaling
BeforeAfter ÷ 1000
4 × 0.14 × 0.0001
0 × 0.010 × 0.00001
6 × 0.0016 × 0.000001
Show this calculationHide answer

0.406÷1000 = 0.0004 + 0.000006 = 0.000406. Writing 0.00046 would remove the empty place between 4 and 6 and change the value.

Divide with different factors

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6.08÷10 = 0.6 + 0.008 = 0.608. Also, 3.047÷100 = 0.03 + 0.0004 + 0.00007 = 0.03047.

Zeros at the start hold places before the first digit that is not zero. Zeros inside hold places between digits. Dividing zero by 10, 100 or 1000 still gives zero.

Will the answer be bigger or smaller than the starting number?

Check your understanding 1

Predict the size, then calculate

Find 0.607 × 10 and 0.607÷1000. Before calculating, decide which result will be larger than 0.607.

Result larger than the positive starting number 0.607
What must the zero between 6 and 7 do when scaling 0.607?
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0.607 × 10 = 6.07, which is larger than 0.607. 0.607÷1000 = 0.000607, which is smaller.

In the quotient, the original 6 tenths become 6 ten-thousandths. The tenths, hundredths and thousandths places before that 6 are empty. The zero between 6 and 7 still holds an empty place too.

Can you split the factor into two useful factors?

Split a multiple into useful factors

Find 1.24 × 300. Since 300 = 3 × 100, take three lots first, then scale that result by 100.

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1.24 × 300 = 1.24 × 3 × 100 = 3.72 × 100 = 372.

The order of those multiplication factors can change: 1.24 × 100 × 3 = 124 × 3 = 372. Both routes use both factors of 300.

Have you divided by both factors?

Divide by both factors

Find 37.2÷200. Since 200 = 100 × 2, divide by 100, then divide by 2. Each of the two operations makes the positive amount smaller.

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37.2÷200 = 37.2÷100÷2 = 0.372÷2 = 0.186.

Check in reverse: 0.186 × 2 × 100 = 0.372 × 100 = 37.2. The original division was by the product 100 × 2, so both factors divide.

Which second step will keep the division correct?

Check your understanding 2

Repair the second operation

Mina writes 6.4÷400 = (6.4÷100) × 4 = 0.256. Identify the wrong step, find the correct quotient and check it by multiplication.

Operation needed after dividing 6.4 by 100
After dividing by 100, how must you finish dividing by 400?
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6.4÷400 = 6.4÷100÷4 = 0.064÷4 = 0.016.

Check 0.016 × 400 = 6.4. Mina multiplied by 4 where she needed to divide by 4. Her result 0.256 is sixteen times the correct 0.016: multiplying by 4 instead of dividing by 4 introduces a factor of 4 × 4.

How many smaller units make one larger unit?

Count the smaller units

A distance of 2.375 km is unchanged when expressed in metres. Metres are smaller units, so more units are counted. Choose the right unit change to choose the factor; it is not always 1000.

Larger unitEqual number of smaller units
1 km1000 m
1 m100 cm
1 kg1000 g
1 ℓ1000 ml

ℓ and ml mean litre and millilitre. You may also see L and mL. Find the new numerical measure for each unchanged quantity.

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2.375 × 1000 = 2375, so 2.375 km = 2375 m. 3.08 × 100 = 308, so 3.08 m = 308 cm.

0.425 × 1000 = 425, so 0.425 kg = 425 g. 2.6 × 1000 = 2600, so 2.6 ℓ = 2600 ml. The measured quantities stay unchanged in all four conversions.

How many groups of the smaller unit make the larger unit?

Larger units need fewer units

To express 65 cm in metres, count groups of 100 cm. There is less than one complete group, so the answer must be less than one metre. For each conversion below, choose the factor from its own unit pair.

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65÷100 = 0.65 m, while 65÷1000 = 0.065 ℓ for the millilitre conversion. The same starting number can need a different divisor because the unit pair decides the factor.

1080÷1000 = 1.08 km and 425÷1000 = 0.425 kg. Use the reverse conversion to check each answer.

Can you write both measurements in the same unit?

Check your understanding 3

Which distance is longer?

Compare 1.08 km and 1080 m. Then find how much longer 1.8 km is than 1080 m. Keep the two kilometre measurements distinct.

1.08 km compared with 1080 m
Why convert the kilometre amounts to metres before comparing?
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1.08 km = 1080 m, so the first pair are equal. 1.8 km = 1800 m, which is 1800-1080 = 720 m longer than 1080 m. The zero in 1.08 changes the value.

Do you need one bottle's volume or the total volume?

Check your understanding 4

Find one total in two ways

Four bottles each contain 0.375 ℓ. Find the total in millilitres. Check by converting each bottle first and comparing with a calculation in litres.

Why can you convert one bottle first or the total first?
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4 × 0.375 = 1.5 ℓ, then 1.5 × 1000 = 1500 ml.

Alternatively, each bottle contains 0.375 × 1000 = 375 ml. Four bottles contain 4 × 375 = 1500 ml. Both routes preserve the same total volume.

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