Concept 7 of 8
× & ÷ Decimals
Today's big idea
Multiplying by 10 slides the point one place right, dividing slides it left.
Each zero moves the decimal point one place: right to multiply, left to divide.
How it works
👀 What's going on?
Multiplying by ten does not really change the digits at all. It just moves the point one step to the right. Dividing walks that same point back the other way.
💡 Here's the trick
Look at the arrows above. Times ten slides the point one place right, and times a hundred slides it two places. Dividing slides it the same number of places left.
🪄 How to do it
- 1.Read the arrows above and count the zeros in 10, 100 or 1000.
- 2.Slide the point that many places, right to times and left to divide.
- 3.For decimal times decimal, multiply first, then count the places back.
✍️ Try it
Work out 3.7 times 100. Then work out 0.3 times 0.2.
A hundred has two zeros, so the point moves two places right to give 370. For the second, 3 times 2 is 6, and two places back give 0.06.
⚠️ Watch out
You might be thinking that 0.5 times 0.8 has to beat both of them. It gives 0.4, which is smaller than either. Two numbers under one always shrink.
🌟 Why this matters
Changing metres to centimetres, or paise to rupees, is a point slide. Price per gram and floor area both need the decimal times.
Exam tip: Count the decimal places in both numbers before you write a single digit down.
Watch me solve one
Quanta solves it
“Watch how I think through one of these — then you try.”
THE PROBLEM
“Find: 0.45 × 100.”
- 1
100 has TWO zeros
So slide the point 2 places. 🛝
- 2
× → slide RIGHT
Multiplying makes the value BIGGER.
- 3
Move the point
0.45 → 4.5 → 45.
- 4
Answer ✓
0.45 × 100 = 45
Now you try one — same steps, different story 👇
See it in action
⚡ Time to play!
Multiply by 10/100/1000 → slide RIGHT. Divide by 10/100/1000 → slide LEFT.
EXPRESSION · ROUND 1 OF 3
0.6 × 10
Quick check
✅ VERIFICATION
What is 58 ÷ 100?
⚡ Finish the activity above first to answer.
Keep going!
Up next: Fractions ↔ Decimals
Top ÷ bottom = decimal.