0.123 Recurring as a Fraction in Simplest Form
What is a Recurring Decimal?
A recurring decimal, also known as a repeating decimal, is a decimal that has a sequence of digits that repeats indefinitely. For example, 0.123123123... is a recurring decimal.
Converting 0.123 Recurring to a Fraction
To convert 0.123 recurring to a fraction, we can use a simple trick. Let's define the recurring decimal as x:
x = 0.123123...
Step 1: Multiply x by 1000
Multiply x by 1000 to get:
1000x = 123.123123...
Step 2: Subtract x from 1000x
Subtract x from 1000x to get:
999x = 123
Step 3: Divide by 999
Divide both sides by 999 to get:
x = 123/999
Simplifying the Fraction
We can simplify the fraction by dividing both numerator and denominator by their greatest common divisor (GCD). The GCD of 123 and 999 is 41.
x = (123 ÷ 41) / (999 ÷ 41) x = 3/27
Simplest Form
The simplest form of 0.123 recurring as a fraction is:
3/27
or
1/9
Therefore, 0.123 recurring is equal to 1/9 in its simplest form as a fraction.
