What fraction is equal to 0.77777777?

Answer 1

To express the decimal 0.77777777 as a fraction, we can observe a pattern in its digits. The number 7 repeats infinitely, indicating a recurring decimal. To convert this into a fraction, consider the repeating part

7

‾

7

.

Let

�

=

7

‾

x=0.

7

. To find a fraction equivalent, let's call it

�

y, we recognize that if we multiply

�

x by an appropriate power of 10, the repeating part will shift to the left of the decimal point.

Let

10

�

=

7

‾

10x=7.

7

. Subtracting

�

x from

10

�

10x, we get

9

�

=

7

9x=7, indicating that

�

=

7

9

x=

9

7

​

.

So, the fraction equivalent to 0.77777777 is (\frac{7}{9}).

In simpler terms, the fraction

7

9

9

7

​

represents the repeating decimal 0.77777777. This is because, in the fraction, the numerator (7) corresponds to the repeating digit (7), and the denominator (9) represents the number of digits in the repeating block (a single 7 in this case). Understanding patterns in repeating decimals helps reveal their fractional equivalents without explicitly resorting to equations.