Revision notes
Turn fractions into decimals (and back again) using tenths, hundredths and simple division.
Machines, calculators and price tags use decimals, but we often talk in fractions — "half a litre", "a quarter of the money". Being able to switch between the two makes you faster in the market and in exams.
The places after the decimal point are tenths, hundredths and thousandths.
So 0.7 = 710, 0.07 = 7100 and 0.375 = 3751000.
That means any fraction with a denominator of 10, 100 or 1000 can be written straight away as a decimal: 43100 = 0.43.
🔑 Key idea: 1 decimal place = tenths, 2 = hundredths, 3 = thousandths.
For 35, multiply top and bottom by 2 to get 610 = 0.6. This works because 35 and 610 are equivalent.
For 34, multiply by 25: 75100 = 0.75. For 38, multiply by 125: 3751000 = 0.375.
Going back is easy too: 0.35 = 35100, which simplifies to 720.
🔑 Key idea: A fraction is NOT "top point bottom": 34 is 0.75, not 3.4.
A fraction means the top divided by the bottom: 34 = 3 ÷ 4 = 0.75.
Some fractions never stop: 13 = 1 ÷ 3 = 0.333… The 3 repeats forever, so we call it a recurring decimal.
For recurring decimals we usually round, for example 23 = 0.666… ≈ 0.67 (to 2 decimal places).
🔑 Key idea: A fraction means top ÷ bottom: 34 = 3 ÷ 4.
Write 14 as a decimal.
Step 1: Make the denominator 100
14 = 25100 (× 25 top and bottom)
Step 2: Write as a decimal
25100 = 0.25
Why? 100 means 2 digits after the point.
Answer: 0.25
Ready to check you've got it? Scroll up and work through the lesson: the interactive visuals, practice questions and mastery check are all there.