What Is 0.16666 Repeating As A Fraction, 0.16666 repeating is a decimal number that goes on forever without ending. It is a recurring, General, what-is-0-16666-repeating-as-a-fraction, JPOSE
0.16666 repeating is a decimal number that goes on forever without ending. It is a recurring decimal, which means that the same digits keep repeating over and over again. So what is 0.16666 repeating as a fraction?
To convert a repeating decimal to a fraction, we need to follow a simple formula. Let x be the repeating decimal, and let n be the number of repeating digits. Then, we can write x as:
x = 0.16666... = 0.16 + 0.0066 + 0.000066 + ...
To see why this works, let's focus on the first three terms of the right-hand side:
0.16 = 16/100
0.0066 = 66/10000
0.000066 = 66/1000000
Notice that each term has a denominator that is a power of 10, depending on the position of the repeating digit. For example, the repeating digit in 0.16666... is the 6, which is in the hundredths place. So we divide by 100 to get 0.16, by 10000 to get 0.0066, and so on.
Now, we can add up all the terms on the right-hand side to get x as a fraction:
x = 0.16 + 0.0066 + 0.000066 + ...
= 16/100 + 66/10000 + 66/1000000 + ...
= 16/100 + 6/10000 + 6/1000000 + ...
= 16/100 + 6/100 * (1/10000 + 1/1000000 + ...)
= 16/100 + 6/100 * (1/10000) * (1 + 1/100 + 1/10000 + ...)
= 16/100 + 6/100 * (1/10000) * (1/(1-1/100))
= 16/100 + 6/10000 * (100/99)
= (16*99 + 6*100)/10000
= 1594/10000
Therefore, 0.16666 repeating as a fraction is 1594/10000. We can simplify this fraction by dividing both the numerator and denominator by their greatest common factor, which is 2:
1594/10000 = 797/5000
So, 0.16666 repeating as a fraction is equal to 797/5000.