Convert Decimal to Fraction
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Example 1) Convert 0.815 to a fraction in simplest form.

Step 1) Put the decimal over a denominator of 1.

\[ 0.815 = {0.815 \over 1} \]

Step 2) Multiply the numerator and denominator by 10ⁿ where n is the number of decimal places the decimal has.

The decimal has 3 decimal places. So 10³ = 10 x 10 x 10 = 1000

\[ {0.815 \over 1} = {0.815 \over 1} \times {1000 \over 1000} = {0.815 \times 1000 \over 1 \times 1000} = {815 \over 1000} \]

Step 3) To find the simplest form, divide the numerator and denominator by 5.

\[ {815 \over 1000} = {815 ÷ 5 \over 1000 ÷ 5} = {163 \over 200} \]

Final answer: \[ 0.815 \; = \; {163 \over 200 } \]

Example 2) Convert 2.36 to a mixed fraction.

Step 1) Put the decimal over a denominator of 1.

\[ 2.36 = {2.36 \over 1} \]

Step 2) Multiply the numerator and denominator by 10ⁿ where n is the number of decimal places the decimal has.

The decimal has 2 decimal places. So 10² = 10 x 10 = 100

\[ {2.36 \over 1} = {2.36 \over 1} \times {100 \over 100} = {2.36 \times 100 \over 1 \times 100} = {236 \over 100} \]

Step 3) To simplify the fraction, divide the numerator and denominator by 4.

This gives us: \[ {236 \over 100} = {236 ÷ 4 \over 100 ÷ 4} = {59 \over 25} \]

Finally we need to convert this into a mixed fraction (or mixed number): \[ {59 \over 25} = 2 {9 \over 25} \]

Our final answer is: \[ 2.36 \; = \; {59 \over 25} = 2 {9 \over 25} \]

Example 3) Convert 1.45 to an improper fraction.

Step 1) Put the decimal over a denominator of 1.

\[ 1.45 = {1.45 \over 1} \]

Step 2) Multiply the numerator and denominator by 10ⁿ where n is the number of decimal places the decimal has.

The decimal has 2 decimal places. So 10² = 10 x 10 = 100

\[ {1.45 \over 1} = {1.45 \over 1} \times {100 \over 100} = {1.45 \times 100 \over 1 \times 100} = {145 \over 100} \]

Step 3) To simplify the fraction, divide the numerator and denominator by 5.

This gives us: \[ {145 \over 100} = {145 ÷ 5 \over 100 ÷ 5} = {29 \over 20} \]

Our final answer is: \[ 1.45 \; = \; {29 \over 20} \]