# Converting Decimals To Fractions

## Related calculator: Decimal to Fraction Calculator

So, how to convert decimals to fractions?

It appears, that we have enough knowledge to do that.

Steps for converting decimals to fractions.

1. It is known, that we can represent any number as number divided by 1: $a=\frac{a}{1}$. Do this.
2. Simultaneously multiply numerator and denominator by 10, until you get a whole number in the numerator.
3. Reduce the fraction.

Example 1. Convert 0.8 into fraction.

First we write it as $\frac{0.8}{1}$.

Since numerator is not integer, we multiply both numerator and denominator by 10 (using equivalence of fractions): $\frac{{{0.8}\cdot{\color{red}{{{10}}}}}}{{{1}\cdot{\color{red}{{{10}}}}}}=\frac{{8}}{{10}}$.

Now, numerator is integer, so we proceed to the next step.

Reduce fraction: $\frac{{8}}{{10}}=\frac{{{4}\cdot{\color{blue}{{{2}}}}}}{{{5}\cdot{\color{blue}{{{2}}}}}}=\frac{{4}}{{5}}$.

Answer: ${0.8}=\frac{{4}}{{5}}$.

Next example.

Example 2. Convert 0.25 into fraction.

First we write it as $\frac{{0.25}}{{1}}$.

Since numerator is not integer, we multiply both numerator and denominator by 10: $\frac{{{0.25}\cdot{\color{red}{{{10}}}}}}{{{1}\cdot{\color{red}{{{10}}}}}}=\frac{{2.5}}{{10}}$.

Numerator is still not integer, so we multiply it by 10 once more: $\frac{{2.5}}{{10}}=\frac{{{2.5}\cdot{\color{red}{{{10}}}}}}{{{10}\cdot{\color{red}{{{10}}}}}}=\frac{{25}}{{100}}$.

Now, numerator is integer, so we proceed to the next step.

Reduce fraction: $\frac{{25}}{{100}}=\frac{{{\color{blue}{{{25}}}}}}{{{4}\cdot{\color{blue}{{{25}}}}}}=\frac{{1}}{{4}}$.

Answer: ${0.25}=\frac{{1}}{{25}}$.

You probably already noticed, that instead of multiplying by 10 each time, we could use powers of 10. Since in 0.25 there are 2 digits to the right of the dot, than, to obtain integer we could multiply by ${{10}}^{{2}}={100}$.

Example 3. Convert 0.00345 into fraction.

First we write it as $\frac{{0.00345}}{{1}}$.

There are 5 digits after the dot, so we multiply numerator and denominator by ${{10}}^{{5}}={100000}$: $\frac{{2.5}}{{10}}=\frac{{{0.00345}\cdot{\color{red}{{{100000}}}}}}{{{1}\cdot{\color{red}{{{100000}}}}}}=\frac{{345}}{{100000}}$.

Reduce fraction: $\frac{{345}}{{10000}}=\frac{{{69}\cdot{\color{blue}{{{5}}}}}}{{{20000}\cdot{\color{blue}{{{5}}}}}}=\frac{{69}}{{20000}}$.

Answer: ${0.00345}=\frac{{69}}{{20000}}$.

If you have decimal, whose integer part is greater than 0, like 5.78, then separate it like ${5}+{0.78}$ and convert 0.78 into fraction (it is $\frac{{39}}{{50}}$). Now, you can write it as mixed number: ${5.78}={5}\frac{{39}}{{50}}$.

Exercise 1. Convert 0.32 to fraction.

Answer: $\frac{{8}}{{25}}$.

Next exercise.

Exercise 2. Convert 0.037 to fraction.

Answer: $\frac{{37}}{{1000}}$. Note, that fraction is irreducible.

Next exercise.

Exercise 3. Convert -0.85 to fraction.

Answer: $-\frac{{17}}{{20}}$.

Next exercise.

Exercise 5. Convert 7.2 to fraction.

Answer: ${7}\frac{{1}}{{5}}$.

Last exercise.

Exercise 5. Convert -9.12 to fraction.

Answer: $-{9}\frac{{3}}{{25}}$. Hint: ignore minus sign, perform conversion, and then place minus in front of the result.