.063 Repeating as a Fraction
Introduction
In mathematics, repeating decimals are decimals that have a sequence of digits that repeats indefinitely. One common example of a repeating decimal is 0.063, which has a repeating pattern of 063. But have you ever wondered what this repeating decimal represents as a fraction? In this article, we'll explore how to convert 0.063 repeating as a fraction.
What is a Repeating Decimal?
A repeating decimal is a decimal number that has a sequence of digits that repeats indefinitely. For example, 0.12341234... is a repeating decimal because the sequence "1234" repeats indefinitely. Repeating decimals can be converted into fractions, which can be useful for mathematical calculations and problem-solving.
Converting 0.063 Repeating as a Fraction
To convert 0.063 repeating as a fraction, we can use the following steps:
Step 1: Let x = 0.063
Let's start by assigning the value 0.063 to a variable x.
Step 2: Multiply x by 1000
Multiply both sides of the equation by 1000 to get rid of the decimal point.
1000x = 63.063
Step 3: Subtract x from both sides
Subtract x from both sides of the equation to get:
999x = 63
Step 4: Divide both sides by 999
Divide both sides of the equation by 999 to solve for x.
x = 63/999
Step 5: Simplify the fraction
Simplify the fraction by dividing both the numerator and denominator by their greatest common divisor, which is 9.
x = 7/111
Therefore, 0.063 repeating as a fraction is equal to 7/111.
Conclusion
In conclusion, we have successfully converted 0.063 repeating as a fraction, which is equal to 7/111. This conversion can be useful for mathematical calculations and problem-solving, and it's a great example of how repeating decimals can be converted into fractions.
