Converting Fractions to Decimals

Steps for converting fraction into a decimal:

Find such integer number, that when multiplied by the denominator will give a power of 10 (10 or 100 or 1000 etc.)
Multiply both numerator and denominator by that number (this can be done because of equivalence of fractions)
As a result, we obtain a decimal fraction, that can be easily converted into a decimal.

As can be seen we use ease of converting decimal fraction and equivalence of fractions to convert arbitrary fraction.

Example 1. Convert $\frac{{4}}{{5}}$ into decimal.

By what integer number should we multiply 5 to get 10? By 2.

Now, multiply both numerator and denominator by 2: $\frac{{4}}{{5}}=\frac{{{4}\cdot{\color{red}{{{2}}}}}}{{{5}\cdot{\color{red}{{{2}}}}}}=\frac{{8}}{{10}}$ .

We obtained decimal fraction and it can be easy converted to decimal. Since ${10}={{10}}^{{{\color{blue}{{1}}}}}$ , we move decimal point one position to the left: $\frac{{8}}{{10}}={0.8}$ .

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

Let's do slightly harder example.

Example 2. Convert $\frac{{3}}{{8}}$ into decimal.

By what integer number should we multiply 8 to get ${{10}}^{{1}}={10}$ ? There is no such number.

By what integer number should we multiply 8 to get ${{10}}^{{2}}={100}$ ? There is no such number.

By what integer number should we multiply 8 to get ${{10}}^{{3}}={1000}$ ? By 125.

Now, multiply both numerator and denominator by 125: $\frac{{3}}{{8}}=\frac{{{3}\cdot{\color{red}{{{125}}}}}}{{{8}\cdot{\color{red}{{{125}}}}}}=\frac{{375}}{{1000}}$ .

Since ${1000}={{10}}^{{{\color{blue}{{3}}}}}$ , we move decimal point three places to the left: $\frac{{375}}{{1000}}={0.375}$ .

Answer: $\frac{{3}}{{8}}={0.375}$ .

We can convert improper fractions this way as well.

Example 3. Convert $\frac{{26}}{{25}}$ into decimal.

By what integer number should we multiply 25 to get ${{10}}^{{1}}={10}$ ? There is no such number.

By what integer number should we multiply 25 to get ${{10}}^{{2}}={100}$ ? By 4.

Now, multiply both numerator and denominator by 4: $\frac{{26}}{{25}}=\frac{{{26}\cdot{\color{red}{{{4}}}}}}{{{25}\cdot{\color{red}{{{4}}}}}}=\frac{{104}}{{100}}$ .

Since ${100}={{10}}^{{{\color{blue}{{2}}}}}$ , we move decimal point two places to the left: $\frac{{104}}{{100}}={1.04}$ .

Answer: $\frac{{26}}{{25}}={1.04}$ .

Note, that not all fractions can be converted into decimal. This occurs when we can't find such number, that when multiplied by denominator will give power of 10. This is true for prime numbers and their multiples. For example, $\frac{{1}}{{3}}$ , $\frac{{5}}{{70}}$ can' t be converted.

Exercise 1. Convert $\frac{{7}}{{20}}$ into decimal.

Answer: $\frac{{7}}{{20}}={0.35}$ .

Next exercise.

Exercise 2. Convert $\frac{{1}}{{80}}$ into decimal.

Answer: $\frac{{1}}{{80}}={0.0125}$ .

Next exercise.

Exercise 3. Convert $-\frac{{19}}{{4}}$ into decimal.

Answer: $-{4.75}$ .

Next exercise.

Exercise 4. Convert $\frac{{5}}{{11}}$ into decimal.

Answer: can't be converted.

We can convert mixed numbers as well!

Exercise 5. Convert mixed number ${3}\frac{{5}}{{16}}$ into decimal.

Either convert $\frac{{5}}{{16}}$ into decimal and add to 3: ${3}\frac{{5}}{{16}}={3}+{0.3125}={3.3125}$ .

Or convert mixed number into improper fraction, and then convert result into decimal.

Answer: ${3.3125}$ .

last one with mixed number.

Exercise 6. Convert mixed number $-{2}\frac{{11}}{{20}}$ into decimal.

Answer: $-{2.55}$ . Hint: ignore minus sign, perform conversion, and then place minus sign back.