PSLE Mathematics Learning Guide · Guide 55 · Companion to Guide 19
Return to the PSLE Learning Guide · Parent guide: Decimal Operations
“Move the decimal point” can produce quick answers, but it teaches the wrong thing if taken literally. The decimal point is a fixed notation marker. The digits change place value when a number is multiplied or divided by powers of ten.
Multiply by 10 and every digit becomes worth ten times as much. Divide by 10 and every digit becomes worth one tenth as much. The written decimal representation changes because the place-value positions of the digits change relative to the decimal point.
This page is a narrow companion to Guide 19: Keep Decimal Place Value Stable Through Multiplication and Division. It drills the Primary 5 syllabus skill of multiplying and dividing decimals up to 3 decimal places by 10, 100, 1000 and their multiples without calculator.
The MOE Primary Mathematics syllabus updated October 2025 provides current curriculum context. All examples and solutions below are original eduKate teaching material.
Read each decimal digit by place
3.472 means:
- 3 ones;
- 4 tenths;
- 7 hundredths;
- 2 thousandths.
Multiply by 10:
3.472 × 10 = 34.72.
The 3 now represents 3 tens, the 4 represents 4 ones, the 7 represents 7 tenths, and the 2 represents 2 hundredths.
Every digit’s value became ten times larger.
Multiply by 100 as two ×10 scalings
0.583 × 100.
First ×10: 5.83.
Second ×10: 58.3.
0.583 × 100 = 58.3.
The number did not gain two mysterious spaces. Its digits each moved into place values one hundred times as large.
Multiply by 1000 as three place-value scales
4.026 × 1000 = 4026.
4 ones become 4 thousands; 2 hundredths become 2 tens; 6 thousandths become 6 ones.
The internal zero matters. A careless “shift the digits” routine can easily turn 4.026 into 4260 or 402.6.
Division scales place values down
37.5 ÷ 10 = 3.75.
The 3 tens become 3 ones, the 7 ones become 7 tenths, and the 5 tenths become 5 hundredths.
Check by multiplication:
3.75 × 10 = 37.5.
Divide by 100 in two ×1/10 steps
482.6 ÷ 100.
÷10 → 48.26.
÷10 → 4.826.
Answer: 4.826.
Insert place-holder zeros when smaller places are needed
7.2 ÷ 1000.
7.2 = 7.200.
Scale down three powers of ten:
0.0072.
The zeros show empty ones, tenths and hundredths places before the 7 reaches thousandths.
Trailing zeros can make place value visible without changing value
5.4 = 5.40 = 5.400.
If dividing 5.4 by 100, writing 5.400 first can make the movement of place value easier to see:
5.400 ÷ 100 = 0.054.
A multiple such as 30 is a small-number factor times 10
2.4 × 30 = 2.4 × 3 × 10.
2.4 × 3 = 7.2.
7.2 × 10 = 72.
This factorisation separates the decimal arithmetic from the power-of-ten scaling.
Multiply by 400 as ×4 then ×100
0.625 × 400.
0.625 × 4 = 2.5.
2.5 × 100 = 250.
A direct place-value-and-factor route is much safer than attaching zeros to 0.625.
Multiply by 5000 through ×5 and ×1000
1.24 × 5000.
1.24 × 5 = 6.2.
6.2 × 1000 = 6200.
Estimate: 1.24 is a little above 1, so the answer should be a little above 5000. 6200 fits.
Division by 30 means division by both 3 and 10
96 ÷ 30.
30 = 3×10.
96 ÷ 3 = 32.
32 ÷ 10 = 3.2.
Equivalently: 96÷10=9.6, then 9.6÷3=3.2.
Do not calculate 96÷3×10. That would reverse the effect of the factor 10.
Divide by 400 using factors
84 ÷ 400.
84 ÷ 4 = 21.
21 ÷ 100 = 0.21.
Check: 0.21×400=84.
Predict how multiplication or division by a power of ten changes size
For a positive number:
- ×10, ×100, ×1000 → larger;
- ÷10, ÷100, ÷1000 → smaller.
So 0.48×100 cannot be 0.0048. The answer must be larger than 0.48.
Likewise 72.5÷1000 must be smaller than 72.5.
Appending a zero does not multiply a decimal by 10
3.7 written as 3.70 has exactly the same value.
Therefore “add one zero to multiply by 10” is false for decimals.
Correct:
3.7×10 = 37.
The lesson is why a whole-number zero trick should never be treated as the underlying mathematics.
A safer classroom phrase
Instead of saying “move the decimal point two places”, say:
“Scale every digit two place-value positions larger.”
Or, when writing quickly:
“The digits shift relative to the decimal point because the number is ×100.”
This preserves the correct mathematical cause.
Measurement conversions use the same decimal scaling
1 m = 100 cm.
2.35 m = 2.35×100 cm = 235 cm.
Conversely:
235 cm ÷100 = 2.35 m.
The unit conversion and place-value scaling are connected. Guide 2 owns general unit alignment, while Guides 43 and 44 apply it specifically to length and mass.
Litres and millilitres use ×1000
1 L = 1000 mL.
1.275 L = 1.275×1000 = 1275 mL.
450 mL = 450÷1000 = 0.45 L.
Guide 31 develops capacity/volume units more broadly.
Kilograms and grams also use ×1000
2.064 kg = 2064 g.
3750 g = 3.75 kg.
The numerical scaling is the same as L↔mL, though the measured quantity is different.
Main worked workshop: twenty original decimal-scaling tasks
1.
4.37×10.
Answer: 43.7.
2.
4.37×100.
Answer: 437.
3.
4.37×1000.
Answer: 4370.
4.
62.5÷10.
Answer: 6.25.
5.
62.5÷100.
Answer: 0.625.
6.
62.5÷1000.
Answer: 0.0625.
7.
0.048×1000.
Answer: 48.
8.
7.2÷1000.
Answer: 0.0072.
9.
3.6×40.
Reasoning: 3.6×4×10=14.4×10=144.
10.
1.25×600.
Answer: 1.25×6×100=7.5×100=750.
11.
0.84×3000.
Answer: 0.84×3×1000=2.52×1000=2520.
12.
72÷30.
Answer: 2.4.
13.
45÷500.
Answer: 0.09.
14.
9.6÷800.
Answer: 0.012.
15.
A learner writes 3.4×10=3.40.
Repair: 3.40 equals 3.4; multiplying by 10 gives 34.
16.
A learner writes 0.62÷100=0.062.
Repair: ÷10 gives 0.062; ÷100 gives 0.0062.
17.
2.305×100.
Answer: 230.5.
18.
230.5÷100.
Answer: 2.305.
19.
0.375×80.
Reasoning: 0.375×8=3; ×10=30.
20.
24÷600.
Answer: 24÷6÷100=4÷100=0.04.
Use inverse pairs as a routine check
If 2.305×100=230.5, then 230.5÷100=2.305.
If 0.375×80=30, then 30÷80=0.375.
An inverse check is especially valuable when several zeros make the written answer visually confusing.
Use magnitude estimates
4.98×200.
Estimate 5×200=1000.
Exact: 4.98×2×100=9.96×100=996.
996 is close to 1000.
An answer of 99.6 is ten times too small and should be rejected.
Internal and leading zeros reveal whether place value is secure
Try:
- 0.0406×1000=40.6;
- 4.006×100=400.6;
- 400.6÷100=4.006;
- 0.7÷1000=0.0007.
These examples are stronger diagnostics than numbers such as 2.5 where careless rules can accidentally succeed.
Separate the small-number operation from the power-of-ten operation
For 1.8×700:
First 1.8×7=12.6.
Then ×100=1260.
For 126÷700:
126÷7=18.
Then ÷100=0.18.
The same factor pair 7 and 100 appears in opposite operations.
Diagnose the first broken step
Factor error: 2.4×30 becomes 6.2×10 because 2.4×3 was wrong.
Place-value error: 2.4×3=7.2 is correct, but ×10 becomes 7.20 instead of 72.
Direction error: learner makes a number smaller after ×100.
Unit error: learner converts 1.2 m to 120 without writing cm.
Practise the broken step, not the entire topic indiscriminately.
Independent transfer check
- 0.706×10
- 0.706×1000
- 56.8÷100
- 6.3÷1000
- 1.25×40
- 0.84×700
- 36÷40
- 9.6÷800
- Convert 3.475 L to mL.
- Convert 2850 g to kg.
- Explain why writing 4.2 as 4.20 does not multiply it by 10.
- Explain why 0.58×100 must be larger than 0.58.
Independent-check answers
1. 7.06.
2. 706.
3. 0.568.
4. 0.0063.
5. 50.
6. 588.
7. 0.9.
8. 0.012.
9. 3475 mL.
10. 2.85 kg.
11. A trailing zero in the hundredths place adds zero value; 4.20 and 4.2 are equal.
12. Multiplication by 100 scales every positive place value one hundred times larger.
Parent and tutor guide
Ask the learner to name the place of one digit before and after ×10. For 2.47, ask what the 4 represents before and after multiplication. This makes the scaling visible.
Use zeros deliberately: 4.006×100, 0.7÷1000, 0.0405×100. These reveal whether the child understands place value or is reciting a movement rule.
Introduce multiples such as 30 and 400 by factorisation. Keep the power-of-ten part separate from the small-number multiplication or division.
Finish with measurement conversions so the learner sees that decimal scaling is not an isolated trick; it supports real metric relationships.
The learner’s final card
What is each digit worth now? How should ×10 or ÷10 change that value? Can I factor 300 as 3×100? If dividing by a product, did I divide by every factor? Should the answer be larger or smaller? Does the inverse operation return the original number?
Continue through Batch 14
Use Guide 53 and Guide 54. Continue with Guide 56: Core Angle Rules.
Return to the PSLE Learning Guide Mathematics route.
Sources and boundaries
MOE Primary Mathematics syllabus, updated October 2025; SEAB 2026 PSLE formats.
This is a subordinate companion to Guide 19. All examples and worked solutions are original eduKate teaching material.