Conversions

Fractions, decimals, percentages, and ratios all represent parts of a whole in different forms.

Fraction, decimal, percentage conversion chart

A fraction expresses a division of one quantity by another, while decimals provide a base-10 representation of that division.

Percentages convert fractions into parts per hundred, making it easier to compare proportions.

Ratios compare two quantities directly, often expressed as fractions or with a colon.

Understanding these connections helps in interpreting and converting between these formats, enhancing numerical literacy and problem-solving skills.

Fractions Percentages Decimals Ratio

Fraction to Percentage

Just divide the top number (numerator) by the bottom number (denominator), then multiply by 100 and add a % sign.

Examples

\[ \frac{3}{4} \] \[ = 0.75 \] \[ = 75\% \]

\[ \frac{2}{5} \] \[ = 0.4 \] \[ = 40\% \]

\[ \frac{7}{8} \] \[ = 0.875 \] \[ = 87.5\% \]

Alternatively, convert the fraction so that the denominator is 100, then write the new numerator with a % sign.

\[ \frac{1}{4} \] \[ = \frac{25}{100} \] \[ = 25\% \]

\[ \frac{3}{20} \] \[ = \frac{15}{100} \] \[ = 15\% \]

\[ \frac{7}{25} \] \[ = \frac{28}{100} \] \[ = 28\% \]

Fraction to Decimal

Just divide the top number (numerator) by the bottom number (denominator).

Examples

\[ \frac{1}{4} \] \[ = 0.25 \]

\[ \frac{3}{8} \] \[ = 0.375 \]

\[ \frac{7}{20} \] \[ = 0.35 \]

Percentage Conversions

Percentage to Decimal

Just divide the number by 100 and remove the % sign.

Examples

\[60\% = 0.6\]\[45\% = 0.45\]\[125\% = 1.25\]\[6\% = 0.06\]\[6\tfrac{3}{4}\% = 0.0675\]

Percentage to Fraction

Write the number over 100,then simplify as much as possible.

Examples

\[25\% = \frac{25}{100}\]\[= \frac{1}{4}\]

\[40\% = \frac{40}{100}\]\[= \frac{2}{5}\]

\[12\% = \frac{12}{100}\]\[= \frac{3}{25}\]

Decimal Conversions

Decimal to Percentage

Just multiply the number by 100 and add a % sign.

Examples

\[ 0.21 = 21\% \] \[ 0.128 = 12.8\% \] \[ 0.5 = 50\% \] \[ 4.125 = 412.5\% \] \[ 1.75 = 175\% \] \[ 1.78 = 178\% \] \[ 5.128 = 512.8\% \] \[ 2.5 = 250\% \]

Decimal to Fraction

Write the number without the decimal point.

If one digit after the decimal → put over 10
If two digits → put over 100
If three digits → put over 1000
If four digits → put over 10000

Then simplify!

Examples

\[ 0.7 = \frac{7}{10} \]

\[ 0.48 = \frac{48}{100} \] \[ = \frac{12}{25} \]

\[ 0.375 = \frac{375}{1000} \] \[ = \frac{3}{8} \]

\[ 0.0625 = \frac{625}{10000} \] \[ = \frac{1}{16} \]

$Man thinking about decimal to fraction conversions$