Convert .45 repeated to a rational simplest form

Answer 1

To convert .45 repeating to a rational simplest form, let's call the repeating decimal x.

Since .45 is equivalent to 45/100, we can write:

x = 45/100 + x/100

Multiplying both sides by 100 to eliminate the decimal:

100x = 45 + x

Subtracting x from both sides:

99x = 45

Dividing both sides by 99:

x = 45/99

Thus, .45 repeating can be written in rational simplest form as 45/99.