Decimal Calculator

How to Add and Subtract Decimals

To add or subtract decimals by hand, align the decimal points vertically and add zeros as placeholders so all numbers have the same number of decimal places. Then add or subtract as with whole numbers, keeping the decimal in the same column.

Example — Addition: 3.75 + 1.5. Write as 3.75 + 1.50. Align decimal points. Add: 3.75 + 1.50 = 5.25.

Example — Subtraction: 8.3 − 2.75. Write as 8.30 − 2.75. Subtract: 8.30 − 2.75 = 5.55.

How to Multiply Decimals

Multiply decimals as if they were whole numbers, ignoring the decimal points. Then count the total number of decimal places in both factors and place the decimal point that many places from the right in the product.

Example: 3.75 × 1.5. Multiply 375 × 15 = 5,625. Count decimal places: 3.75 has 2, and 1.5 has 1, total = 3. Place decimal 3 places from right: 5.625.

How to Divide Decimals

To divide decimals, convert the divisor (the number you're dividing by) to a whole number by moving its decimal point to the right. Move the dividend's decimal the same number of places. Then divide normally.

Example: 3.75 ÷ 1.5. Multiply both by 10: 37.5 ÷ 15. Divide: 37.5 ÷ 15 = 2.5.

Converting Decimals to Fractions

• Terminating decimals: Write the decimal over its place value and simplify. 0.75 = 75/100 = 3/4. 0.125 = 125/1000 = 1/8.
• Repeating decimals: For 0.333... set x = 0.333..., then 10x = 3.333..., subtract: 9x = 3, x = 1/3. For 0.272727...: 99x = 27, x = 27/99 = 3/11.

Converting Decimals to Percentages

Multiply the decimal by 100 (or move the decimal point two places to the right). 0.75 = 75%. 0.033 = 3.3%. 1.5 = 150%. To go the other direction: divide the percentage by 100. 45% = 0.45. 7.5% = 0.075.

Rounding Decimals

To round to a specific decimal place: look at the digit one place to the right of where you're rounding. If it's 5 or greater, round up. If it's 4 or less, round down (keep the digit as is). Example: Round 3.7461 to 2 decimal places. Look at the third decimal place: 6 ≥ 5, so round up. Answer: 3.75. Round to 1 decimal place: look at second decimal 4 < 5, round down: 3.7.

Common Decimal-Fraction Equivalents

• 1/2 = 0.5
• 1/3 = 0.333...
• 1/4 = 0.25
• 1/5 = 0.2
• 1/6 = 0.1666...
• 1/8 = 0.125
• 3/4 = 0.75
• 2/3 = 0.666...
• 1/10 = 0.1
• 3/8 = 0.375
• 5/8 = 0.625
• 7/8 = 0.875