Fractions, Decimals, and Percentages: A Comprehensive Guide

Fractions, decimals, and percentages are three different ways of expressing the same value. This article provides a comprehensive guide to understanding and converting between these three representations.

Key Facts

1. Equivalents: Fractions, decimals, and percentages are different ways of expressing the same value. For example, 1/2 is equivalent to 0.5 as a decimal and 50% as a percentage.
2. Converting Percentages to Decimals: To convert a percentage to a decimal, divide by 100 and remove the percent sign. For example, 75% is equivalent to 0.75 as a decimal.
3. Converting Decimals to Percentages: To convert a decimal to a percentage, multiply by 100 and add the percent sign. For example, 0.25 is equivalent to 25%.
4. Converting Fractions to Decimals: To convert a fraction to a decimal, divide the numerator (top number) by the denominator (bottom number). For example, 3/4 is equal to 0.75 as a decimal.
5. Converting Decimals to Fractions: To convert a decimal to a fraction, write the decimal as the numerator and 1 as the denominator. Then, simplify the fraction if possible. For example, 0.5 is equal to 1/2.
6. Converting Fractions to Percentages: To convert a fraction to a percentage, divide the numerator by the denominator, then multiply by 100 and add the percent sign. For example, 3/8 is equal to 37.5%.
7. Converting Percentages to Fractions: To convert a percentage to a fraction, divide the percentage by 100 and simplify the fraction if possible. For example, 80% is equal to 4/5.

Equivalents

Fractions, decimals, and percentages are equivalent to each other. This means that they represent the same quantity, just in different forms. For example, the fraction 1/2 is equivalent to the decimal 0.5 and the percentage 50%.

Converting Percentages to Decimals

To convert a percentage to a decimal, divide the percentage by 100 and remove the percent sign. For instance, 75% is equivalent to 0.75 as a decimal.

Converting Decimals to Percentages

To convert a decimal to a percentage, multiply the decimal by 100 and add the percent sign. For instance, 0.25 is equivalent to 25% as a percentage.

Converting Fractions to Decimals

To convert a fraction to a decimal, divide the numerator (top number) by the denominator (bottom number). For instance, 3/4 is equal to 0.75 as a decimal.

Converting Decimals to Fractions

To convert a decimal to a fraction, write the decimal as the numerator and 1 as the denominator. Then, simplify the fraction if possible. For instance, 0.5 is equal to 1/2.

Converting Fractions to Percentages

To convert a fraction to a percentage, divide the numerator by the denominator, then multiply by 100 and add the percent sign. For instance, 3/8 is equal to 37.5% as a percentage.

Converting Percentages to Fractions

To convert a percentage to a fraction, divide the percentage by 100 and simplify the fraction if possible. For instance, 80% is equal to 4/5 as a fraction.

Conclusion

Fractions, decimals, and percentages are all valid representations of quantities. Understanding how to convert between these representations is essential for various mathematical and scientific applications.

FAQs

What are fractions, decimals, and percentages?

Fractions, decimals, and percentages are different ways of expressing the same value. A fraction is a part of a whole, a decimal is a number written using a decimal point, and a percentage is a value expressed as a fraction of 100.

How do I convert a fraction to a decimal?

To convert a fraction to a decimal, divide the numerator (top number) by the denominator (bottom number). For example, to convert 3/4 to a decimal, divide 3 by 4, which gives you 0.75.

How do I convert a decimal to a percentage?

To convert a decimal to a percentage, multiply the decimal by 100 and add the percent sign. For example, to convert 0.25 to a percentage, multiply 0.25 by 100, which gives you 25%.

How do I convert a percentage to a fraction?

To convert a percentage to a fraction, divide the percentage by 100 and simplify the fraction if possible. For example, to convert 75% to a fraction, divide 75 by 100, which gives you 3/4.

How do I convert a fraction to a percentage?

To convert a fraction to a percentage, divide the numerator by the denominator, then multiply by 100 and add the percent sign. For example, to convert 3/8 to a percentage, divide 3 by 8, which gives you 0.375. Then, multiply 0.375 by 100, which gives you 37.5%.

How do I simplify a fraction?

To simplify a fraction, divide both the numerator and the denominator by their greatest common factor (GCF). For example, to simplify 6/12, divide both 6 and 12 by 6, which gives you 1/2.

What is the difference between a proper fraction and an improper fraction?

A proper fraction is a fraction where the numerator is smaller than the denominator. An improper fraction is a fraction where the numerator is greater than or equal to the denominator.

What is a mixed number?

A mixed number is a number that consists of a whole number and a fraction. For example, 2 1/2 is a mixed number.