Decimals are everywhere — from prices and measurements to scientific data. This guide walks through the four basic operations with decimals, plus rounding and converting to fractions and percentages.
A decimal is a way of writing numbers that fall between whole numbers. The decimal point separates the whole-number part on the left from the fractional part on the right. Each position to the right of the decimal point represents a place value that is one-tenth of the place before it: tenths, hundredths, thousandths, and so on.
For example, in 4.73, the 4 is in the ones place, the 7 is in the tenths place (7/10), and the 3 is in the hundredths place (3/100). Together, 4.73 means 4 + 7/10 + 3/100.
The key rule for adding or subtracting decimals is to line up the decimal points vertically. Once the points are aligned, fill in any empty spaces with zeros so each number has the same number of decimal places. Then add or subtract column by column, just as you would with whole numbers. Bring the decimal point straight down into your answer.
Example: 3.25 + 1.7
Rewrite 1.7 as 1.70 so both numbers have two decimal places. Line them up:
3.25 + 1.70 = 4.95
Result: 4.95
Example: 10.0 − 4.63
Rewrite 10.0 as 10.00 to match the two decimal places in 4.63. Subtract column by column, borrowing where needed:
10.00 − 4.63 = 5.37
Result: 5.37
To multiply decimals, ignore the decimal points at first and multiply the numbers as if they were whole numbers. Then count the total number of decimal places in both original numbers and place the decimal point that many positions from the right in your answer.
Example: 2.5 × 1.4
Multiply as whole numbers: 25 × 14 = 350.
Count decimal places: 2.5 has 1 place, 1.4 has 1 place → total of 2 places.
Place the decimal: 350 → 3.50
Result: 3.5
Example: 0.03 × 0.6
Multiply as whole numbers: 3 × 6 = 18.
Count decimal places: 0.03 has 2 places, 0.6 has 1 place → total of 3 places.
Place the decimal: 18 → 0.018
Result: 0.018
When dividing by a decimal, the goal is to make the divisor a whole number. Move the decimal point in the divisor to the right until it becomes a whole number, and move the decimal point in the dividend the same number of places. Then divide normally and place the decimal point directly above its new position in the dividend.
Example: 7.5 ÷ 2.5
Move the decimal one place right in both numbers: 7.5 → 75 and 2.5 → 25.
Divide: 75 ÷ 25 = 3
Result: 3
Example: 0.84 ÷ 0.4
Move the decimal one place right in both numbers: 0.84 → 8.4 and 0.4 → 4.
Divide: 8.4 ÷ 4 = 2.1
Result: 2.1
Rounding a decimal means shortening it to a specific place value. Look at the digit one place to the right of where you want to round. If that digit is 5 or greater, round up; if it is less than 5, round down (keep the digit the same). Drop all digits after the rounded place.
Example: Round 3.847 to the nearest tenth
The tenths digit is 8. The digit to its right is 4 (less than 5), so round down.
Result: 3.8
Example: Round 12.065 to the nearest hundredth
The hundredths digit is 6. The digit to its right is 5 (5 or greater), so round up.
Result: 12.07
Decimal to fraction: Write the decimal over its place value and simplify. For example, 0.75 = 75/100 = 3/4.
Decimal to percentage: Multiply by 100 and add the percent sign. For example, 0.45 × 100 = 45%.
Example: Convert 0.125 to a fraction
0.125 = 125/1000. Divide numerator and denominator by 125: 125/1000 = 1/8.
Result: 1/8
For more on switching between fractions, decimals, and percentages, see our conversions guide.
Ready to practice?