Stage 8 · Fractions & decimals
Fractions and decimals
Scale the bottom to 10, 100 or 1000.
How to do it
Method
Scale the bottom to 10, 100 or 1000
35 = 610 = 0.6
Another way
Top ÷ bottom
3 ÷ 5 = 0.6
In full
Fraction to decimal: scale the denominator up to 10, 100 or 1000, then write it as a decimal: 35 = 610 = 0.6; 720 = 35100 = 0.35; 38 = 3751000 = 0.375. Decimal to fraction: write it over 10, 100 or 1000, then simplify: 0.75 = 75100 = 34. You can also divide the numerator by the denominator: 3 ÷ 5 = 0.6 — the same answer.
Worked examples
Have a go first, then open each one for the answer and the working.
Example 1
14 = ?
Answer as a decimal
Show the answer and working
Answer: 14 = 0.25
14: scale it to a denominator of 100, multiplying top and bottom by 25: 1 × 25 = 25, 4 × 25 = 100 → 25100 = 0.25
Example 2
78 = ?
Answer as a decimal
Show the answer and working
Answer: 78 = 0.875
78: scale it to a denominator of 1000, multiplying top and bottom by 125: 7 × 125 = 875, 8 × 125 = 1000 → 8751000 = 0.875
Example 3
0.02 = ?
Answer in simplest form
Show the answer and working
Answer: 0.02 = 150
0.02: write it over 100, 0.02 × 100 = 2 → 2100; simplify, dividing top and bottom by their highest common factor 2: 2 ÷ 2 = 1, 100 ÷ 2 = 50 → 150
Example 4
0.42 = ?
Answer in simplest form
Show the answer and working
Answer: 0.42 = 2150
0.42: write it over 100, 0.42 × 100 = 42 → 42100; simplify, dividing top and bottom by their highest common factor 2: 42 ÷ 2 = 21, 100 ÷ 2 = 50 → 2150
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