annabelbrooke
contestada

Convert the following into fractions in their simplest form
1) 0.1
6) 0.13
2) 0.8
7) 0.48
3) 0.3
8) 0.63
4) 0.6
9) 0.255
5) 0.222222...
10) 0.45454545...

Respuesta :

Answer:

1/10

13/100

4/5

12/25

3/10

63/100

3/5

51/200

2/9

5/11

To prove the last 2 recurring ones:

0.222222... = x

10x = 10 * 0.22222... =  2.222222....

Notice how the decimal part of 10x is the same as for x:

10x - x = 2.2222222... - 0.222222... = 2

10x - x = 9x = 2

x = 2/9

Same procedure for the other one but times by 100 instead:

x = 0.454545...

100x = 45.454545...

100x - x = 45.454545... - 0.454545... = 45

100x - x = 99x = 45

x = 45/99 = 5/11

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