0.77778 as a Fraction
Have you ever wondered what the repeating decimal 0.77778 looks like as a fraction? In this article, we'll explore how to convert this decimal to a fraction and simplify it to its most reduced form.
Converting 0.77778 to a Fraction
To convert a repeating decimal to a fraction, we can use the following formula:
a = fraction's numerator b = fraction's denominator r = repeating decimal
Let's use this formula to convert 0.77778 to a fraction:
r = 0.77778
First, we'll multiply both sides of the equation by 100,000 (since there are five repeating digits):
100,000r = 77,778
Next, we'll subtract the original decimal from both sides:
100,000r - r = 77,778 - 0.77778
This simplifies to:
99,999r = 77,778 - 0.77778 99,999r = 76,999
Now, we can divide both sides by 99,999:
r = 76,999 / 99,999
Simplifying the Fraction
To simplify the fraction, we can divide both the numerator and the denominator by their greatest common divisor (GCD). The GCD of 76,999 and 99,999 is 9,999.
r = (76,999 ÷ 9,999) / (99,999 ÷ 9,999) r = 7,7 / 9,9 r = 7/9
So, the simplified fraction of 0.77778 is 7/9.
Conclusion
In conclusion, we've successfully converted the repeating decimal 0.77778 to a fraction and simplified it to its most reduced form, which is 7/9. This technique can be applied to any repeating decimal to convert it to a fraction.
Remember
When converting a repeating decimal to a fraction, make sure to multiply both sides of the equation by a power of 10 that is greater than the number of repeating digits. This will ensure that you get the correct fraction.
