.63 Repeating as a Fraction
Introduction
.63 repeating is a decimal number that has a repeating pattern of 63. Have you ever wondered what this number looks like as a fraction? In this article, we will explore how to convert .63 repeating to a fraction and understand its properties.
Converting .63 Repeating to a Fraction
To convert a repeating decimal to a fraction, we can use the following steps:
- Let x be the repeating decimal number, which is .63 in our case.
- Multiply x by 100 to move the decimal point two places to the right.
- Subtract x from the resulting number to eliminate the decimal part.
- Simplify the fraction.
Let's apply these steps to .63 repeating:
x = .63
Multiply x by 100:
100x = 63.63
Subtract x from the resulting number:
100x - x = 63.63 - .63 99x = 63
Divide both sides by 99:
x = 63/99
Simplify the fraction:
x = 7/11
Therefore, .63 repeating as a fraction is 7/11.
Properties of the Fraction
The fraction 7/11 has several interesting properties:
- It is a proper fraction, meaning the numerator (7) is less than the denominator (11).
- It is an irreducible fraction, meaning it cannot be simplified further.
- The decimal representation of 7/11 is .63 repeating, which is a non-terminating decimal.
Conclusion
In this article, we have successfully converted .63 repeating to a fraction, which is 7/11. We have also explored some of the properties of this fraction, including its proper and irreducible nature, and its non-terminating decimal representation. I hope this helps you better understand decimal numbers and their equivalent fractions!
