Turning repeating decimals to fractions are quite simple. All you need to do is take a look at what numbers are being repeated. For this question, as the 7 and the 2 are being repeated, we can see that there are only two numbers being repeated. So we put two 9's as the denominator for the fraction and 72 as the numerator. So a simple way to put this would be, however many numbers that are being repeated, that's how many 9's are needed for the denominator. Therefore, 0.72 repeating is 72/99 and simplified is 8/11.
Chat with our AI personalities
Well, isn't that just a happy little question! When we have a repeating decimal like 0.72, we can turn it into a fraction by setting it as x and subtracting x/100 to get 0.72 repeating. Solving this equation will give us the fraction 8/11, a lovely little fraction that represents our repeating decimal.
To express 0.72 repeating as a fraction, we can let x = 0.7272... and multiply it by 100 to shift the decimal point two places to the right, giving us 100x = 72.7272.... Now, subtract the original equation from the new one to eliminate the repeating decimal, resulting in 99x = 72. This simplifies to x = 72/99. Finally, we reduce the fraction by dividing both the numerator and denominator by the greatest common divisor, which is 9 in this case, yielding the simplified fraction 8/11. Therefore, 0.72 repeating is equivalent to the fraction 8/11.
Oh honey, 0.72 repeating is just 72/99. It's like trying to catch a greased pig - slippery but not impossible. So, there you have it, a fraction as sassy as me.
Suppose f = 0.7272..
Then 100f = 72.7272...
So, subtracting the first from the second, 99f = 72
ie f = 72/99 = 8/11
9.555... repeating as an improper fraction in its simplest form is 86/9
To convert a one digit repeating decimal, make a fraction of that digit over 9, so 55/99 = 5/9 You can convert any repeating digits by putting them over the same number of 9s.
2/3 2/3 = 0.66666....
I assume that the decimal part is repeating to infinity. Then 1.571429 written as a fraction is 1 and 4/7.
3.72 = 372/100 = 93/25