0.175 Repeating as an Equivalent Fraction
In mathematics, a repeating decimal is a decimal that has a sequence of digits that repeats indefinitely. One such example is 0.175 repeating, where the sequence "75" repeats indefinitely. But did you know that a repeating decimal can be equivalent to a fraction? In this article, we'll explore how to convert 0.175 repeating into an equivalent fraction.
What is a Repeating Decimal?
A repeating decimal is a decimal that has a sequence of digits that repeats indefinitely. For example, 0.12341234... is a repeating decimal where the sequence "1234" repeats indefinitely. Repeating decimals can be written in a more concise way using a vinculum, which is a horizontal line above the repeating sequence. For example, 0.1234̄ is a more concise way of writing 0.12341234...
Converting 0.175 Repeating into an Equivalent Fraction
To convert 0.175 repeating into an equivalent fraction, we can use the following steps:
Step 1: Let x = 0.175 Repeating
Let's let x = 0.175 repeating.
Step 2: Multiply Both Sides by 100
Multiply both sides of the equation by 100 to get rid of the decimal point.
100x = 17.575 repeating
Step 3: Subtract the Original Equation
Subtract the original equation from the new equation to eliminate the repeating sequence.
100x - x = 17.575 - 0.175 99x = 17.4
Step 4: Divide Both Sides by 99
Divide both sides of the equation by 99 to solve for x.
x = 17.4 / 99 x = 44 / 253
And there you have it! The equivalent fraction of 0.175 repeating is 44/253.
Conclusion
In conclusion, we've successfully converted 0.175 repeating into an equivalent fraction, which is 44/253. This process can be applied to any repeating decimal to find its equivalent fraction. Repeating decimals may seem complicated at first, but with a few simple steps, we can convert them into more familiar fractions.
