GCSE · Maths · AQA · Spec 8300 · Foundation
Terminating decimals and corresponding fractions
Quick: which is bigger, 3/8 or 0.4? Go with your gut for a second. Then let's find out properly, and see why you never need to guess again.
How to switch between the two names
Problem
Write 0.375 and 3.5 as fractions in their simplest form, then turn 3/8 and 7/2 back into decimals.
Maths · Number
Drag the shaded part along the bar. Each extra eighth adds exactly 0.125, so the whole family comes from one fact: 1/8 = 0.125.
WHAT YOU'VE LEARNED
A quick recap of today's lesson.
One number, two names: switch between them, then use it to put any mixed list in order.
What you need to know
- A terminating decimal stops: it has a last digit, like 0.375 or 3.5.
- A terminating decimal and its corresponding fraction are the same number, so they sit at the same point on a number line.
- Decimal to fraction: the place of the last digit gives the denominator (10 for tenths, 100 for hundredths, 1000 for thousandths, and so on); then simplify.
- Fraction to decimal: divide the numerator by the denominator, or make an equivalent fraction over 10, 100, 1000 and so on.
- To order a mixed list, put everything in the same form and compare place by place.
The big picture
A terminating decimal is one that stops, like 0.375 or 3.5. Every terminating decimal has a matching fraction with exactly the same value: 0.375 and 3/8 are one number written two ways, and so are 3.5 and 7/2. To go from decimal to fraction, the place of the last digit tells you the denominator (tenths, hundredths, thousandths and so on), then you simplify. To go from fraction to decimal, divide the numerator by the denominator, or build an equivalent fraction over 10, 100, 1000 and so on. Once everything is in one form, you can put a mixed list of fractions and decimals in order by comparing place values, not by counting digits.
Key points
Worked example
Problem
Which is larger, 11/4 or 2.7? Show how you know.
⚠ Watch out
Copying digits across instead of working out the value. 1/8 is not 0.18, and 3/8 is not 0.38: a fraction means numerator ÷ denominator, so 1/8 = 0.125 and 3/8 = 0.375. One slip like this quietly wrecks an ordering answer.
Memory hook
One number, two names. The last digit's place names the denominator: tenths, hundredths, thousandths.
Check yourself
Write 0.85 as a fraction in its simplest form. Then check it: divide your numerator by your denominator, and you should land back on exactly 0.85.
Flashcards
(6)What is a terminating decimal?
How do you turn a terminating decimal into a fraction?
Name two ways to turn a fraction into a decimal.
What decimal matches the improper fraction 7/2?
Does a decimal with more digits have to be bigger?
What is the first step when ordering a mix of fractions and decimals?
Tap any card to flip it, or use Study as deck to go through them one at a time. In the full lesson these run as a spaced-repetition deck — you rate each card Hard, Good or Easy and the tricky ones keep coming back until they stick.
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