0.123 Repeating as a Fraction in Its Simplest Form
What is 0.123 Repeating?
0.123 repeating is a decimal number where the sequence "123" repeats indefinitely. This type of decimal is called a repeating decimal or a recurring decimal. It can be written as:
0.123123123... (where the sequence "123" goes on forever)
Converting 0.123 Repeating to a Fraction
To convert 0.123 repeating to a fraction, we can use the following steps:
Step 1: Let x = 0.123123...
Let x = 0.123123... (where x represents the repeating decimal)
Step 2: Multiply x by 1000
Multiply both sides of the equation by 1000 to get rid of the decimal places:
1000x = 123.123123...
Step 3: Subtract the Original Equation
Subtract the original equation from the new equation:
1000x - x = 123.123123... - 0.123123...
This simplifies to:
999x = 123
Step 4: Divide by 999
Divide both sides of the equation by 999:
x = 123/999
Step 5: Simplify the Fraction
Simplify the fraction by dividing both the numerator and denominator by their greatest common divisor (GCD):
x = 41/333
Therefore, 0.123 repeating as a fraction in its simplest form is:
41/333
This is the equivalent fraction of the repeating decimal 0.123.
