Whole Numbers

Numbers in P5 suddenly get big — really big. You will see seven-digit numbers like the population of a country or the price of a HDB block of flats. The good news is that a big number follows the exact same rules as a small one. Once you can read it, group it, and keep your operations in the right order, a number with seven digits is no scarier than one with two. Let's build it up.

Parents: let your child predict before they reveal each step. The blue dotted words are tappable definitions, and the "Method tip" boxes name exactly what a PSLE marker rewards in the working — not just the final number.

By the end you'll be able to read numbers up to 10 million, do all four operations, follow the correct order of operations with brackets, and estimate to check your answer. Here we go.

Reading numbers to 10 million

A big number is easier to read when you split it into groups of three digits from the right. Each group has a place value. So 4 250 000 reads as "four million, two hundred and fifty thousand". The trick is to find the leading digit first, name its place, then read across.

Think of the population of a town: 1 080 600 is "one million, eighty thousand, six hundred". Notice the zeros in the hundred-thousands and thousands places — keep both columns as gaps, but do not read either zero aloud.

The upper boundary is 10 000 000, which reads as "ten million". It has a 1 in the ten-millions place and zero in every smaller place.

🔬

Place-value counters (P5)

🤔 Predict first: Starting at 9,900 and counting forward by 100, what boundary value comes next?

9,91010,00010,100

Scale whole numbers by 10, 100, 1000 and their multiples

Multiplying or dividing by a power of ten changes every digit's place. This is place-value scaling. A digit that moves one place left is worth ten times as much; a digit that moves one place right is worth ten times less. For a multiple such as 30 or 300, split it into a small factor and a power of ten. This shows the place-value change instead of relying on a rule about adding or removing zeroes.

For example, factor 30 as 3 × 10. First multiply by 3, then scale the result by 10.

Show the worked solution

Multiply by a multiple

$$240\times30=240\times3\times10$$

$$240\times3=720$$

$$720\times10=7{,}200$$

$$7{,}200\div30=240\text{ (check)}$$

Now factor 300 as 3 × 100. Dividing by 3 and then by 100 keeps the place-value steps visible.

Divide by a multiple

$$84{,}000\div300=84{,}000\div3\div100$$

$$84{,}000\div3=28{,}000$$

$$28{,}000\div100=280$$

$$280\times300=84{,}000\text{ (check)}$$

Practice the scale

Practice 1. Calculate 6 300 × 40. Show the factorisation of 40 and check your answer.

Show the solution

Practice 1

$$6{,}300\times40=6{,}300\times4\times10$$

$$6{,}300\times4=25{,}200$$

$$25{,}200\times10=252{,}000$$

$$252{,}000\div40=6{,}300\text{ (check)}$$

Practice 2. Calculate 720 000 ÷ 90. Show the factorisation of 90 and check your answer.

Show the solution

Practice 2

$$720{,}000\div90=720{,}000\div9\div10$$

$$720{,}000\div9=80{,}000$$

$$80{,}000\div10=8{,}000$$

$$8{,}000\times90=720{,}000\text{ (check)}$$

Practice 3. Calculate 4 008 × 2 000. Show the factorisation of 2 000 and check your answer.

Show the solution

Practice 3

$$4{,}008\times2{,}000=4{,}008\times2\times1{,}000$$

$$4{,}008\times2=8{,}016$$

$$8{,}016\times1{,}000=8{,}016{,}000$$

$$8{,}016{,}000\div2{,}000=4{,}008\text{ (check)}$$

The four operations

You already know how to add, subtract, multiply and divide. With big numbers, the only change is to line up your digits carefully by place value. When you long divide, keep each digit in its column so nothing drifts.

quotient1156

89248

8

bring down12

8

bring down44

40

bring down48

48

remainder0

9248 ÷ 8 = 1156

Check: 8 × 1156 = 9248

Imagine sharing 9 248 sweets equally among 8 classes. That is 9248 ÷ 8 = 1156 sweets per class. Check it: 1156 × 8 = 9248. The check is the part most students skip, but it catches mistakes fast.

quotient

66384

Completed 0 of 4 quotient-digit stages.

Order of operations and brackets

When a sum mixes operations, you cannot just work left to right. There is an order. Do anything inside brackets first, then multiply and divide, then add and subtract. This is the order of operations.

Try 20 + 3 × 4. The times comes first: 3 × 4 = 12, then 20 + 12 = 32. If you went left to right you would wrongly get 92. Now try a bracket: (20 + 3) × 4 = 23 × 4 = 92. The bracket changes everything.

Estimating to check

A smart student never trusts a big answer blindly. Before or after working, you estimate by rounding to get a rough size. If your real answer is far from your estimate, something went wrong.

Say you work out 4 980 × 19 and get 94 620. Round to 5000 × 20 = 100 000. Your answer 94 620 is close to 100 000, so it looks sensible. If you had got 9 462, the estimate would warn you that you slipped a place.

Watch out — these are easily mixed up

Quick recap

🎯 Mastery check

Answer all 8 — your progress is saved on this device.

1. How do you read the number 2 005 400?

   Two hundred thousand and fifty-fourTwo million, five thousand, four hundredTwenty-five million, four hundred

2. What is 7 + 4 × 6?

   663142

3. What is the value of (8 + 7) × 3?

   452924

4. A box holds 5 280 nails shared equally into 6 packs. How many nails per pack?

   quotient

   65280

   Completed 0 of 3 quotient-digit stages.

   880808888

5. Which is the best quick estimate for 397 × 21?

   400 × 20 = 8 000300 × 20 = 6 000400 × 30 = 12 000

6. In the sum 30 − 4 × 5, what should you do first, and what is the final answer?

   Subtract first, giving 130Multiply 4 × 5 first, giving a final answer of 10Multiply 4 × 5 first, giving a final answer of 50

7. What is 240 × 30?

   7 20072 000720

8. What is 84 000 ÷ 300?

   282802 800

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