How do make 0.7 repeating a fraction
To represent the repeating decimal 0.7̅ as a fraction, we need to understand its pattern.
When we see a decimal that repeats indefinitely, we can convert it into a fraction by considering its place value. Let's denote the number 0.7̅ as "x" for simplicity.
To eliminate the repeating part, we can multiply x by a power of 10 that shifts the decimal point to the right and aligns the repeating part:
10x = 7.7̅
Now, to eliminate the decimal part, we can subtract x from 10x:
10x - x = 7.7̅ - 0.7̅
This simplifies to:
9x = 7
Now, we can solve for x by dividing both sides by 9:
x = 7/9
Therefore, the fraction equivalent of 0.7̅ is 7/9.
0.77777 = 7/100,000
.77..... = 7/9
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