0.693 Repeating as a Fraction
The decimal 0.693 is a repeating decimal, and in this article, we will explore how to convert it to a 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 because the sequence "1234" repeats over and over.
Converting 0.693 to a Fraction
To convert 0.693 to a fraction, we can use the following steps:
- Let x = 0.693: We can start by letting x equal 0.693.
- Multiply both sides by 1000: Multiplying both sides of the equation by 1000 gives us 1000x = 693.693.
- Subtract x from both sides: Subtracting x from both sides of the equation gives us 999x = 693.
- Divide both sides by 999: Dividing both sides of the equation by 999 gives us x = 693/999.
Simplifying the Fraction
The fraction 693/999 can be simplified by dividing both the numerator and the denominator by their greatest common divisor (GCD).
The GCD of 693 and 999 is 69. Dividing both numbers by 69 gives us:
- 693 ÷ 69 = 10
- 999 ÷ 69 = 14.5
So, the simplified fraction is:
10/14.5
Conclusion
In this article, we have converted the repeating decimal 0.693 to a fraction, which is 10/14.5. This process involves multiplying both sides of the equation by a power of 10, subtracting x from both sides, and dividing both sides by the difference.
