Decimals, Fractions, Percentages

Understanding Decimals, Fractions, and Percentages

Decimals, fractions, and percentages are different ways of expressing proportions and quantities.
A fraction expresses a part of a whole and is expressed as a/b where a is the numerator (part) and b is the denominator (whole).
A decimal is a number based on the number 10 and is expressed with a decimal point (.).
A percentage is a way of expressing a number as a fraction of 100 and is expressed by the % symbol.

To convert a decimal to a fraction, consider the place value of the decimal, make it the numerator and make the corresponding multiple of 10 (depending on how many decimal places) the denominator. Simplify if possible.
To convert a fraction to a decimal, divide the numerator by the denominator using long or short division.
To convert a decimal to a percentage, multiply the decimal by 100 and add the % symbol.
To convert a percentage to a decimal, remove the % symbol and divide by 100.
To convert a fraction to a percentage, first convert the fraction to a decimal, and then convert the decimal to a percentage.
To convert a percentage to a fraction, crate a fraction with the percentage as the numerator and 100 as the denominator, then simplify if possible.

A common mistake when dealing with decimals and fractions is misunderstanding the place value of the number. For example, 0.5 is not the same as 0.05.
Another frequent error is incorrect conversion between percentages and fractions. For example, 50% is not equivalent to 50/100 but rather to 1/2 or 0.5.
Ordering fractions and decimals can often cause problems. Remember to convert all values to the same form to compare and order correctly.

Continually practicing conversions between the three forms can help to instil a deeper understanding of the relationship between decimals, fractions, and percentages.
When comparing and ordering these numbers, it’s usually easier to convert everything to decimals.
Regularly apply what you learn to real-world settings. For example, use percentages when figuring out discounts or markups, fractions for splitting items, and decimals in measurements.