Convert Percentages, Fractions, and Decimals

This tutorial explains how to convert between percentages, fractions, and decimals. Each question is solved step by step, followed by practice exercises with answers.


Question 1

Convert \(20\%\) to an equivalent fraction in reduced form.

Solution

A percentage is already a fraction with denominator \(100\).

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

Reduce the fraction by dividing both the numerator and denominator by \(20\):

\[ \frac{20}{100} = \frac{1}{5} \]

Therefore,

\[ 20\% = \frac{1}{5} \]

So, to convert a percentage into a fraction, write it over \(100\) and reduce.


Question 2

Convert the fraction \( \frac{3}{4} \) to a percentage.

Solution

First, convert the fraction to a decimal by dividing the numerator by the denominator:

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

Multiply the decimal by \(100\) to convert it to a percentage:

\[ 0.75 = \frac{75}{100} = 75\% \]

Question 3

Convert \(0.06\) to an equivalent fraction in reduced form.

Solution

Write the decimal as a fraction with denominator \(100\):

\[ 0.06 = \frac{6}{100} \]

Reduce the fraction by dividing both numerator and denominator by \(2\):

\[ \frac{6}{100} = \frac{3}{50} \]

Question 4

Convert \(0.1\) to a percentage.

Solution

Multiply the decimal by \(100\):

\[ 0.1 = \frac{10}{100} = 10\% \]

Question 5

Convert \( \frac{3}{5} \) into a decimal and a percentage.

Solution

Divide the numerator by the denominator to obtain the decimal:

\[ \frac{3}{5} = 0.6 \]

Multiply the decimal by \(100\) to obtain the percentage:

\[ 0.6 = \frac{60}{100} = 60\% \]

Question 6

Convert \(0.08\) into a percentage and a reduced fraction.

Solution

First, convert the decimal to a percentage:

\[ 0.08 = \frac{8}{100} = 8\% \]

Now reduce the fraction:

\[ \frac{8}{100} = \frac{2}{25} \]

Exercises

  1. Convert \(2.3\) into a percentage.
  2. Convert \( \frac{4}{5} \) into a percentage and a decimal.
  3. Convert \(50\%\) into a fraction and a decimal.
  4. Convert \(0.8\) into a percentage and a reduced fraction.
  5. Convert \( \frac{1}{3} \) into a percentage and a decimal.
  6. Convert \(0.7\) into a percentage and a reduced fraction.
  7. Convert \(210\%\) into a decimal and a reduced fraction.

Answers to the Exercises

  1. \(230\%\)
  2. \(80\%, \; 0.8\)
  3. \(\frac{1}{2}, \; 0.5\)
  4. \(80\%, \; \frac{4}{5}\)
  5. \(33\%, \; 0.33\) (rounded to two decimal places)
  6. \(70\%, \; \frac{35}{50}\)
  7. \(2.1, \; \frac{21}{10}\)

Percent Calculator and Solver

Related topics: Percentages | Fractions