0.16 overline 3 can be Expressed as a Fraction
In mathematics, a repeating decimal or recurring decimal is a decimal representation of a number that eventually becomes periodic, repeating in a predictable cycle. One such example is 0.16 overline 3, which can be expressed as a fraction.
What is 0.16 overline 3?
0.16 overline 3 is a repeating decimal where the digit 3 repeats indefinitely. It can also be written as 0.163636..., where the 3's go on forever.
Converting 0.16 overline 3 to a Fraction
To convert 0.16 overline 3 to a fraction, we can use the following steps:
Step 1: Let x = 0.163636...
Let x = 0.163636..., where x is a variable representing the repeating decimal.
Step 2: Multiply x by 100
Multiply x by 100 to get:
100x = 16.363636...
Step 3: Subtract x from 100x
Subtract x from 100x to get:
99x = 16.2
Step 4: Divide by 99
Divide both sides by 99 to get:
x = 16.2/99
Step 5: Simplify the Fraction
Simplify the fraction by dividing both numerator and denominator by their greatest common divisor (GCD), which is 9.
x = 18/99 x = 2/11
Therefore, 0.16 overline 3 can be expressed as a fraction, which is:
2/11
In conclusion, the repeating decimal 0.16 overline 3 can be converted to a fraction, which is 2/11. This process can be applied to convert any repeating decimal to a fraction.
