Question

Please help me and fast :(

Find the rational form of the decimal number.

1. 0.55
2. 0.36
3. 0.128
4. 0.0545454
5. 0.04666666
Type answer below and explain answer.

Answer 1

9514 1404 393

Answer:

1. 11/20
2. 9/25
3. 16/125
4. 3/55
5. 7/150

Explanation:

It is helpful to know the decimal equivalents of 1/9 and 1/11:

1/9 = 0.1111...

1/11 = 0.09090909...

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1. 0.55 = 55/100 = 11/20

2. 0.36 = 36/100 = 9/25

3. 0.128 = 128/1000 = 16/125

4. 0.0545454... = (1/10)(6×1//11) = 6/110 = 3/55

5. 0.046666... = 4/100 + (1/100)6×1/9 = 1/25 + 1/150 = (6+1)/150 = 7/150

_____

In 4 and 5, we recognize that ...

0.545454... = 6/11 has been divided by 10 to get 0.0545454...

0.6666... = 6/9 = 2/3 has been divided by 100 to get 0.006666...