P5 Decimals: The Decimal Point Slide Trick

Multiplying and dividing decimals by 10, 100, and 1000 doesn’t require long multiplication. There’s a simple trick — just slide the decimal point. Let’s master it.

The Big Idea: Sliding the Decimal Point

Here’s the secret that makes decimals easy:

Multiplying by 10, 100, or 1000? Slide the decimal point to the RIGHT.
Dividing by 10, 100, or 1000? Slide the decimal point to the LEFT.

How many places? Count the zeros.

Operation	Zeros	Slide Direction	Places
$\times 10$	1 zero	Right →	1 place
$\times 100$	2 zeros	Right →	2 places
$\times 1000$	3 zeros	Right →	3 places
$\div 10$	1 zero	← Left	1 place
$\div 100$	2 zeros	← Left	2 places
$\div 1000$	3 zeros	← Left	3 places

💡 The Zero-Count Rule

Count the number of zeros in 10, 100, or 1000. That’s exactly how many places the decimal point moves. Multiply = right, Divide = left.

Part 1: Multiplying by 10, 100, 1000

Multiplying by 10

Slide the decimal point 1 place to the right.

Example: Multiply by 10

Calculate: $1.25 \times 10$

Step 1: 10 has 1 zero → slide decimal 1 place right

Step 2: $1.25 → 12.5$

Answer: $12.5$

Multiplying by 100

Slide the decimal point 2 places to the right.

Example: Multiply by 100

Calculate: $0.41 \times 100$

Step 1: 100 has 2 zeros → slide decimal 2 places right

Step 2: $0.41 → 4.1 → 41$

Answer: $41$

Multiplying by 1000

Slide the decimal point 3 places to the right. If you run out of decimal digits, add zeros.

Example: Multiply by 1000

Calculate: $0.41 \times 1000$

Step 1: 1000 has 3 zeros → slide decimal 3 places right

Step 2: $0.41 → 4.1 → 41 → 410$ (add a zero — we only had 2 decimal digits)

Answer: $410$

⚠️ Watch Out: Adding Zeros

When you run out of decimal digits, fill in with zeros. For example, $0.5 \times 1000$ : slide 3 places right → $0.5 → 5 → 50 → 500$ . Don’t forget those extra zeros!

Quick Practice: Multiply

Try these in your head before checking:

Question	Answer
$0.3 \times 10$	$3$
$5.6 \times 10$	$56$
$2.002 \times 100$	$200.2$
$0.058 \times 1000$	$58$
$0.485 \times 10$	$4.85$

Part 2: Dividing by 10, 100, 1000

Now we reverse direction — slide the decimal point to the LEFT.

Dividing by 10

Slide the decimal point 1 place to the left.

Example: Divide by 10

Calculate: $12.4 \div 10$

Step 1: 10 has 1 zero → slide decimal 1 place left

Step 2: $12.4 → 1.24$

Answer: $1.24$

Dividing by 100

Slide the decimal point 2 places to the left. Add leading zeros if needed.

Example: Divide by 100

Calculate: $7.5 \div 100$

Step 1: 100 has 2 zeros → slide decimal 2 places left

Step 2: $7.5 → 0.75 → 0.075$ (add a leading zero)

Answer: $0.075$

Dividing by 1000

Example: Divide by 1000

Calculate: $234 \div 1000$

Step 1: 234 is a whole number, so write it as $234.0$

Step 2: 1000 has 3 zeros → slide decimal 3 places left

Step 3: $234.0 → 23.4 → 2.34 → 0.234$

Answer: $0.234$

💡 Leading Zeros

When dividing makes the number smaller than 1, always write a zero before the decimal point: $0.234$ , not $.234$ .

Quick Practice: Divide

Question	Answer
$45.6 \div 10$	$4.56$
$1.3 \div 10$	$0.13$
$12.4 \div 100$	$0.124$
$234 \div 1000$	$0.234$
$7.5 \div 100$	$0.075$

Part 3: The Decomposition Trick (x20, x300, x5000…)

What about multiplying by numbers like 20, 300, or 5000? Here’s where it gets clever.

Break the number down:

$20 = 2 \times 10$
$300 = 3 \times 100$
$5000 = 5 \times 1000$

Then do it in two steps: multiply by the digit first, then slide the decimal.

Example: Multiply by 200

Calculate: $1.9 \times 200$

Step 1: Break down: $200 = 2 \times 100$

Step 2: Multiply by 2 first: $1.9 \times 2 = 3.8$

Step 3: Then multiply by 100 (slide 2 places right): $3.8 → 380$

Answer: $380$

Example: Multiply by 3000

Calculate: $5.7 \times 3000$

Step 1: Break down: $3000 = 3 \times 1000$

Step 2: Multiply by 3 first: $5.7 \times 3 = 17.1$

Step 3: Then multiply by 1000 (slide 3 places right): $17.1 → 17100$

Answer: $17{,}100$

The same idea works for division:

Example: Divide by 400

Calculate: $100.4 \div 400$

Step 1: Break down: $400 = 4 \times 100$

Step 2: Divide by 4 first: $100.4 \div 4 = 25.1$

Step 3: Then divide by 100 (slide 2 places left): $25.1 → 0.251$

Answer: $0.251$

Part 4: Unit Conversions with Decimals

This is where the decimal point slide becomes super useful in real life. All the common unit conversions use 10, 100, or 1000!

Key Conversion Facts

Conversion	Factor	Operation
m → cm	1 m = 100 cm	$\times 100$
cm → m	100 cm = 1 m	$\div 100$
km → m	1 km = 1000 m	$\times 1000$
m → km	1000 m = 1 km	$\div 1000$
kg → g	1 kg = 1000 g	$\times 1000$
g → kg	1000 g = 1 kg	$\div 1000$
ℓ → ml	1 ℓ = 1000 ml	$\times 1000$
ml → ℓ	1000 ml = 1 ℓ	$\div 1000$

💡 Big to Small = Multiply, Small to Big = Divide

Going from a bigger unit to a smaller unit? Multiply (the number gets bigger). Going from smaller to bigger? Divide (the number gets smaller).

Example: Length Conversion

Convert 0.45 m to centimetres.

m → cm: multiply by 100 (slide 2 places right)

$0.45 \times 100 = 45$

Answer: 45 cm

Example: Mass Conversion

Convert 2.5 kg to grams.

kg → g: multiply by 1000 (slide 3 places right)

$2.5 \times 1000 = 2500$

Answer: 2500 g

Example: Volume Conversion

Convert 3500 ml to litres.

ml → ℓ: divide by 1000 (slide 3 places left)

$3500 \div 1000 = 3.5$

Answer: 3.5 ℓ

Mixed Units

Sometimes you need to handle mixed units like “3 m 28 cm”:

Example: Mixed Units

Convert 3 m 28 cm to centimetres.

Step 1: Convert the metres: $3 \text{ m} = 3 \times 100 = 300 \text{ cm}$

Step 2: Add the centimetres: $300 + 28 = 328 \text{ cm}$

Answer: 328 cm

Part 5: Word Problems

Now let’s put it all together with word problems — the kind you’ll see on tests.

Single-Step Word Problems

Word Problem 1

Mrs Tan buys 3 packets of rice. Each packet weighs 2.5 kg. What is the total mass of the rice?

Identify: 3 groups of 2.5 → Multiplication

$3 \times 2.5 = 7.5$

Answer: 7.5 kg

Word Problem 2

A ribbon is 4.8 m long. It is cut into 6 equal pieces. How long is each piece?

Identify: Sharing equally → Division

$4.8 \div 6 = 0.8$

Answer: 0.8 m

Multi-Step Word Problems

Word Problem 3: Multi-Step

Mr Lim bought 6 notebooks at $2.45 each. He paid with a $20 note. How much change did he receive?

Step 1: Total cost = $6 \times \$ 2.45 = $14.70$

Step 2: Change = $\$ 20 - $14.70 = $5.30$

Answer: $5.30

Word Problem 4: With Unit Conversion

A water tank contains 8.5 ℓ of water. 2350 ml is used. How much water is left in litres?

Step 1: Convert 2350 ml to litres: $2350 \div 1000 = 2.35$ ℓ

Step 2: Subtract: $8.5 - 2.35 = 6.15$ ℓ

Answer: 6.15 ℓ

Challenge Problem

Challenge: Perimeter with Decimals

The perimeter of a rectangle is 56.8 cm. Its length is 3 times its breadth. Find the length.

Step 1: Let breadth = 1 unit, then length = 3 units

Step 2: Perimeter = $2 \times (3 + 1) = 8$ units

Step 3: $8 \text{ units} = 56.8 \text{ cm}$

Step 4: $1 \text{ unit} = 56.8 \div 8 = 7.1 \text{ cm}$

Step 5: Length = $3 \times 7.1 = 21.3 \text{ cm}$

Answer: 21.3 cm

Common Mistakes to Avoid

❌ Mistake 1: Sliding the Wrong Way

Multiplying should make the number bigger (slide right). Dividing should make it smaller (slide left). If your answer goes the wrong direction, you slid the wrong way!

❌ Mistake 2: Forgetting to Add Zeros

$0.5 \times 1000 = 500$ , not $5$ . When you run out of decimal digits while sliding right, fill in with zeros.

❌ Mistake 3: Missing Leading Zeros

$7.5 \div 100 = 0.075$ , not $75$ . Always place a zero before the decimal point when the answer is less than 1.

⚠️ Mistake 4: Unit Conversion Direction

Converting kg to g? The number should get bigger (multiply by 1000). Converting ml to ℓ? The number should get smaller (divide by 1000). Always check: does my answer make sense?

Cheat Sheet: The Complete Decimal Slide

Operation	Direction	Places	Example
$\times 10$	Right →	1	$3.45 → 34.5$
$\times 100$	Right →	2	$3.45 → 345$
$\times 1000$	Right →	3	$3.45 → 3450$
$\div 10$	← Left	1	$3.45 → 0.345$
$\div 100$	← Left	2	$3.45 → 0.0345$
$\div 1000$	← Left	3	$3.45 → 0.00345$
$\times 20$	$\times 2$ , then $\times 10$	—	$3.45 \times 2 = 6.9 → 69$
$\div 300$	$\div 3$ , then $\div 100$	—	$93 \div 3 = 31 → 0.31$

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P5 Decimals: The Decimal Point Slide Trick (x10, x100, x1000)