Question

what fraction is equivalent to this decimal 0.733333333333

Answer 1

The decimal \(0.733333333333 \ldots\) can be expressed as a fraction. This decimal is a repeating decimal, where "3" repeats indefinitely. We can denote it as:

\[
x = 0.733333333333\ldots
\]

To convert this into a fraction, we can separate the non-repeating and repeating parts:

1. Let \(y = 0.733333333333\ldots\)
2. To isolate the repeating part, we can multiply both sides by 10 (to shift one decimal place):

\[
10y = 7.3333333333\ldots
\]

3. Now, to eliminate the repeating part, subtract \(y\) from \(10y\):

\[
10y - y = 7.3333333333\ldots - 0.7333333333\ldots
\]

This simplifies to:

\[
9y = 6.6
\]

4. To deal with the \(6.6\), multiply both sides by 10 to shift the decimal again:

\[
9y = 66
\]

5. Now, divide both sides by 9:

\[
y = \frac{66}{90}
\]

Now simplify the fraction:

\[
\frac{66}{90} = \frac{11}{15}
\]

Thus, the fraction equivalent to the decimal \(0.733333333333\ldots\) is:

\[
\frac{11}{15}
\]