Question

. The rational number for 0.0555 ... is

Answer 1

Step 1: To convert 0.05 repeating into a fraction, begin writing this simple equation:

n = 0.05 (equation 1)

Step 2: Notice that there is 1 digits in the repeating block (5), so multiply both sides by 1 followed by 1 zeros, i.e., by 10.

10 × n = 0.55 (equation 2)

Step 3: Now subtract equation 1 from equation 2 to cancel the repeating block out.

10 × n = 0.55

1 × n = 0.05

9 × n = 0.5

The numerator of the fraction above is a decimal. We have to make it an integer by multiplying it by 10. By multiplying the numerator we should also multiply the denominator by the same amount. So,

0.5

9

= 0.5 × 10

9 × 10

= 5

90

.

5

90

could be the answer, but it still can be put in the simplest form, i.e., reduced.

To simplify this fraction, divide the numerator and denominator by 5 (the GCF - greatest common factor).

n = 5

90

= 5 ÷ 5

90 ÷ 5

= 1

18

. So,

0.05 = 1

18