The idea, step by step
Each place is ten times the place to its right
Multiplying a whole number by 10 makes each digit's value ten times as large. For 34 × 10, three tens become three hundreds and four ones become four tens: 340. A zero holds the empty ones place.
Multiplying by 100 is multiplying by 10 twice. The digits take values two places higher. In 34 × 100 = 3,400, the 3 now represents 3,000 and the 4 represents 400. Explain this through value, not just a rule about writing zeroes.
Reverse the scaling and use known facts
Exact division by 10 reverses the place-value change: 340 ÷ 10 = 34. Division by 100 reverses two changes: 3,400 ÷ 100 = 34. A multiplication check confirms the result.
For a calculation such as 3 × 200, use 3 × 2 = 6, then remember each group contains two hundreds. The answer is six hundreds, or 600. Read zeroes carefully so you do not lose a factor of ten.
| Calculation | Value |
|---|---|
| 3 × 2 | 6 |
| 3 × 20 | 60 |
| 3 × 200 | 600 |
A common trap
Finding 32 × 10 by adding 10 and answering 42.
Instead: Multiplication makes ten equal groups, not one extra ten. Ten groups of 32 make 320.
See the thinking
Multiply by one hundred
Find 47 × 100.
- Multiplying by 100 scales every digit by one hundred.
- Four tens become four thousands; seven ones become seven hundreds.
- 4,000 + 700 = 4,700.
Use a basic fact
Find 6 × 40 and check it by division.
- 6 × 4 = 24.
- Forty is four tens, so the total is 24 tens: 240.
- Check: 240 ÷ 6 = 40.
Check your understanding
Find 4,300 ÷ 100.
Show answer
43.
43 × 100 = 4,300, so 43 is the quotient.
Your turn
6 questions · 7 marks · Work at your own pace.
Read the questions online
- Find 28 × 10.1 mark
- Find 63 × 100.1 mark
- Find 5,600 ÷ 100.1 mark
- Find 7 × 80.1 mark
- A carton holds 100 cards. How many cards are in 24 cartons?1 mark
- A learner says 9 × 300 = 270. Explain and correct the place-value error.2 marks
Read the worked solutions
Equivalent correct methods earn the corresponding marks. Include units where asked.
- Find 28 × 10.1 mark
Two tens become two hundreds; eight ones become eight tens.
280. - Find 63 × 100.1 mark
63 × 10 = 630, then 630 × 10 = 6,300.
6,300. - Find 5,600 ÷ 100.1 mark
56 × 100 = 5,600.
56. - Find 7 × 80.1 mark
7 × 8 = 56; 56 tens = 560.
560. - A carton holds 100 cards. How many cards are in 24 cartons?1 mark
24 × 100 = 2,400.
2,400 cards. - A learner says 9 × 300 = 270. Explain and correct the place-value error.2 marks
9 × 3 = 27, but these are hundreds, not tens.
27 hundreds = 2,700.
9 × 300 = 2,700.
Curriculum reference & lesson scope
Australian Curriculum v9 and SA Curriculum Mathematics
Facts to 10×10; related division; larger calculations; multiples/powers of ten; efficient strategies.
Official curriculum source ↗