# 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.**

- It is known, that we can represent any number as number divided by 1: `a=a/1`. Do this.
- Simultaneously multiply numerator and denominator by 10, until you get whole number in numerator.
- Reduce fraction.

**Example 1**. Convert 0.8 into fraction.

First we write it as `0.8/1`.

Since numerator is not integer, we multiply both numerator and denominator by 10 (using equivalence of fractions): `(0.8*color(red)(10))/(1*color(red)(10))=8/10`.

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

Reduce fraction: `8/10=(4*color(blue)(2))/(5*color(blue)(2))=4/5`.

**Answer**: `0.8=4/5`.

Next example.

**Example 2**. Convert 0.25 into fraction.

First we write it as `0.25/1`.

Since numerator is not integer, we multiply both numerator and denominator by 10: `(0.25*color(red)(10))/(1*color(red)(10))=2.5/10`.

Numerator is still not integer, so we multiply it by 10 once more: `2.5/10=(2.5*color(red)(10))/(10*color(red)(10))=25/100`.

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

Reduce fraction: `25/100=(color(blue)(25))/(4*color(blue)(25))=1/4`.

**Answer**: `0.25=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 `0.00345/1`.

There are 5 digits after the dot, so we multiply numerator and denominator by `10^5=100000`: `2.5/10=(0.00345*color(red)(100000))/(1*color(red)(100000))=345/100000`.

Reduce fraction: `345/10000=(69*color(blue)(5))/(20000*color(blue)(5))=69/20000`.

**Answer**: `0.00345=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 `39/50`). Now, you can write it as mixed number: `5.78=5 39/50`.

**Exercise 1.** Convert 0.32 to fraction.

**Answer**: `8/25`.

Next exercise.

**Exercise 2.** Convert 0.037 to fraction.

**Answer**: `37/1000`. Note, that fraction is irreducible.

Next exercise.

**Exercise 3.** Convert -0.85 to fraction.

**Answer**: `-17/20`.

Next exercise.

**Exercise 5.** Convert 7.2 to fraction.

**Answer**: `7 1/5`.

Last exercise.

**Exercise 5.** Convert -9.12 to fraction.

**Answer**: `-9 3/25`. Hint: ignore minus sign, perform conversion, and then place minus in front of the result.