Decimals and fractions (age 11+)
Work interchangeably with terminating decimals and their corresponding fractions (such as 3.5 and 7/2 or 0.375 and 3/8); convert fluently between the two forms
What a learner can do afterwards
- Convert any terminating decimal to a fraction in simplest form
- Convert any fraction with a denominator whose prime factors are only 2 and 5 to a terminating decimal
- Explain why some fractions produce terminating decimals and others do not
The lesson
You already know decimals and fractions can name the same number. Now you'll convert between them for any terminating decimal, simplify the fraction all the way, and understand why some fractions stop while others repeat forever.
To convert 0.375 to a fraction, write it over the matching power of ten: 0.375 = 375/1000. Both numbers share a factor of 125, so divide top and bottom by 125 to get 3/8.
To go the other way, look at the denominator. 8 = 2 x 2 x 2, so it only has 2s as prime factors. That means you can multiply top and bottom to reach a power of ten: 3/8 = 375/1000 = 0.375.
A fraction only becomes a terminating decimal when its simplest-form denominator is built from 2s and 5s alone. A denominator like 6 or 7 always leaves something over, so the decimal repeats no matter how far you divide.
If a fraction's simplest denominator has only 2s and 5s as prime factors, it terminates; convert by matching a power of ten, then simplify all the way.
Watch it
Where it sits
This opens up
Where this leads
Jobs that lean on this skill. Follow one to see everything it is built on.
8 questions wait behind this lesson, each with its answer explained. Every answer feeds the sky: stars light as they are learned, and dim when it is time to come back.