Concept 8 of 8
Fractions ↔ Decimals
Today's big idea
Fraction ↔ decimal: divide top by bottom, or put over 10/100/1000.
One value, two costumes: divide top by bottom, or read off the place name.
How it works
👀 What's going on?
One shirt is a fifth off and the next is 0.2 off. That is the same discount wearing two costumes. Swapping between the forms settles most comparing questions.
💡 Here's the trick
Look at the table above. Every pair on it names one value twice. Top shared by bottom gives you the decimal, and the place name gives you the bottom back.
🪄 How to do it
- 1.Pick a pair from the table above and note which way you are going.
- 2.Fraction to decimal: divide the top by the bottom.
- 3.Decimal to fraction: write it over 10, 100 or 1000, then simplify.
✍️ Try it
Write 7/20 as a decimal. Then write 0.24 as a fraction in its lowest terms.
7 shared by 20 is 0.35. For the second, 0.24 is 24/100, and dividing both parts by 4 gives 6/25.
⚠️ Watch out
You might be thinking 3/8 is 0.38, because the digits look the same. Divide instead. 3 shared by 8 is 0.375, which sits just below 0.38.
🌟 Why this matters
Sale signs, cricket averages and phone storage swap between the two forms freely. Comparing them means putting them all into one form.
Exam tip: Learn the halves, quarters, fifths and eighths by heart, and ordering becomes instant.
Watch me solve one
Quanta solves it
“Watch how I think through one of these — then you try.”
THE PROBLEM
“Convert 3/8 to a decimal.”
- 1
Divide top by bottom
3 ÷ 8 — long-divide. 🌉
- 2
Carry the remainder
3.000 ÷ 8 → 0.3 rem 6 → 0.37 rem 4 → 0.375 rem 0. ✓
- 3
Read off the decimal
0.375
- 4
Answer ✓
3/8 = 0.375
Now you try one — same steps, different story 👇
See it in action
⚡ Time to play!
Match each fraction to its decimal equivalent!
ROUND 1 OF 2 · MATCH ALL 5 PAIRS
FRACTION
DECIMAL
Quick check
✅ VERIFICATION
Which of these is the smallest?
⚡ Finish the activity above first to answer.
Keep going!