Fractions as decimals
Make the bottom number 10, 100 or 1000.
Sharing ribbon
Neenu has 29 m of red ribbon and shares it equally with Anu. They get 14 m each and 1 m is left. Shared between the two, that 1 m gives each girl 12 m more.
How do we write 12 as a decimal?
What this lesson covers
The idea
A division of counting numbers can be written as a fraction and converted to a decimal by finding an equivalent fraction whose denominator is 10, 100, 1000, and so on, when one exists.
Sharing ribbon
Neenu has 29 m of red ribbon and shares it equally with Anu. They get 14 m each and 1 m is left. Shared between the two, that 1 m gives each girl 1/2 m more.
How do we write 1/2 as a decimal?
- 0.2
- 0.5
- 1.2
Test the bottom number
A fraction is easy to write as a decimal when its bottom number is 10, 100, 1000 … Test which of these the bottom number can become. When one fits, say what to multiply by.
An equivalent fraction with 10, 100, 1000 …
Multiply the top and the bottom by the same number: the fraction stays equal. Choose the number that turns the bottom into 10, 100, 1000 … Then the decimal is easy to read.
4 is not a factor of 10, but it is a factor of 100: 4 × 25 = 100. For 10/3 nothing works: 3 does not divide 10, 100 or 1000. Each time 1 is left over.
A division of counting numbers can be written as a fraction. Find an equivalent fraction whose denominator is 10, 100, 1000, … (when one exists) and write it as a decimal.
- Fraction | Multiply top and bottom by …
- 1/2 | 5 → 5/10 = 0.5
- 29/4 | 25 → 725/100 = 7.25
- 3/8 | 125 → 375/1000 = 0.375
Notes
To write a fraction as a decimal, find an equivalent fraction with 10, 100, 1000, … at the bottom, if there is one. Not every fraction has one: 10/3 does not.
Check yourself
Write 3/5 as a decimal.
Answer: 0.6
3/5 = (3 × 2)/(5 × 2) = 6/10 = 0.6.
Which fraction can be written with a bottom number 10, 100, 1000 …?
Write 7/8 as a decimal. (Think of 1000.)
Answer: 0.875
7/8 = (7 × 125)/(8 × 125) = 875/1000 = 0.875.
Why can 10/3 not be written with a bottom number 10, 100, 1000 …?
- 7/20 — correct. 20 × 5 = 100, so 7/20 = 35/100 = 0.35.
- 4/7. 7 is not a factor of 10, 100, 1000 …, so no such fraction exists.
- 5/6. 6 is not a factor of 10, 100, 1000 … (each leaves a remainder), so no such fraction exists.
- Because 3 is an odd number. The bottom 5 is odd too, but 1/5 = 2/10 = 0.2 works. Oddness is not the problem.
- Because 10/3 is bigger than 1. 29/4 is bigger than 1 as well, and it works: 7.25.
- Because 3 does not divide 10, 100, 1000, …: each time 1 is left over — correct. Yes. 10 ÷ 3, 100 ÷ 3, 1000 ÷ 3 all leave a remainder of 1.