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...

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

answer: 48

just remember to use pemdas:

parentheses

expressions

multiplication

division

addition

subtraction

  or  

step-by-step explanation:

if the four friends split the cost, p, of the pizza evenly, then each friend pays one-fourth of the cost of the pizza.

the expression is   or