Concept 9 of 9
The Grid Translator: Fractions to Decimals
Today's big idea
A decimal is a fraction of tenths or hundredths wearing a tidier outfit.
75 of the 100 squares are shaded, which is 75/100 and also 0.75.
How it works
👀 What's going on?
Remember the place-value rooms from chapter 2? The house carries straight on to the right of the ones, into tenths and then hundredths. That is the whole of what a decimal is.
💡 Here's the trick
Look at the grid above. It holds 100 little squares and 75 of them are shaded, which is 75/100. Written as a decimal that is 0.75. The first digit after the point counts tenths and the second counts hundredths, so 75 hundredths fills both places.
🪄 How to do it
- 1.Check the bottom number, as the picture above uses 100, which means two decimal places.
- 2.Write the top number into those places.
- 3.Put a zero in front if the top is too short to reach the tenths place.
✍️ Try it
Write 6/10 as a decimal, then write 9/100. Why does only one of them need a zero?
6/10 needs one decimal place, so it is 0.6. 9/100 needs two places and the 9 only fills one, so a zero holds the tenths spot and it is 0.09. Without that zero you would write 0.9, which is ten times too big.
Decimal times decimal works on the same idea, a part of a part. To place the point, count the decimal places in both numbers and give the answer that many. 0.45 has two and 0.6 has one, so 45 x 6 = 270 becomes 0.270, which is 0.27.
⚠️ Watch out
You might be thinking 0.9 and 0.09 are close enough to swap. They are not. 0.9 is nine tenths and 0.09 is nine hundredths, so one is ten times the other. Count the places every single time.
🌟 Why this matters
Money is written this way (Rs 4.50), and so are heights, race times and shopping weights. A decimal is a fraction in a tidier outfit.
Exam tip: Reading the bottom number first tells you how many decimal places the answer needs.
Watch me solve one
Quanta solves it
“Watch how I think through one of these — then you try.”
THE PROBLEM
“Write 8/100 as a decimal.”
- 1
Check the bottom
Bottom is 100 → 2 places after the decimal point.
- 2
Write the top
Top is 8. We need 2 digits — pad with a leading 0.
- 3
Slot under the decimal
Tenths place: 0. Hundredths place: 8 → 0.08
- 4
Decimal ✓
8/100 = 0.08
Now you try one — same steps, different story 👇
See it in action
⚡ Time to play!
Paint squares on the 100-grid. Then pull the lever to translate the fraction into a decimal!
FRACTION
0/100
Quick check
✅ VERIFICATION
Write 0.7 as a fraction.
⚡ Finish the activity above first to answer.
Keep going!