0.151 Repeating as a Fraction
Converting 0.151 Repeating to a Fraction
The decimal 0.151 repeating can be converted to a fraction by following a few simple steps.
Step 1: Identify the Repeating Pattern Let's identify the repeating pattern in the decimal 0.151 repeating. In this case, the repeating pattern is 151.
Step 2: Set Up an Equation Let x = 0.151 repeating
Multiply both sides of the equation by 1000 to eliminate the decimal places:
1000x = 151.151 repeating
Step 3: Subtract the Original Equation Subtract the original equation from the new equation:
1000x - x = 151.151 - 0.151
Step 4: Simplify the Equation Simplify the equation by combining like terms:
999x = 151
Step 5: Divide by the Coefficient Divide both sides of the equation by 999:
x = 151/999
The Final Answer Therefore, 0.151 repeating as a fraction is:
151/999
This fraction is in its simplest form, and it represents the decimal 0.151 repeating.
