Decimals

Decimal Place Value

Digits after the decimal point have the following place values:

• First digit after decimal → tenths (÷10)
• Second digit → hundredths (÷100)
• Third digit → thousandths (÷1000)

Example: 4.237 = 4 + 2/10 + 3/100 + 7/1000

Comparing Decimals

Line up the decimal points, then compare digit by digit from left to right.

Example: Compare 0.45 and 0.405 → both have 4 tenths, but 5 hundredths vs 0 hundredths → 0.45 > 0.405

Rounding Decimals

Same rule as whole numbers — look at the digit immediately to the right of where you are rounding.

Example: Round 3.678 to 1 decimal place → look at hundredths digit (7 ≥ 5) → round up → 3.7

Adding and Subtracting Decimals

Line up the decimal points. Fill empty places with zeros if needed.

Example: 12.5 + 3.75 = 12.50 + 3.75 = 16.25

Multiplying Decimals

Multiply as whole numbers, then count total decimal places in both numbers and place the decimal point in the answer.

Example: 2.4 × 1.3 → 24 × 13 = 312 → 2 decimal places → 3.12

Dividing Decimals

If dividing by a decimal, multiply both numbers by a power of 10 to make the divisor a whole number.

Example: 4.5 ÷ 0.3 → multiply both by 10 → 45 ÷ 3 = 15

Converting Fractions to Decimals

Divide the numerator by the denominator.

3/4 = 3 ÷ 4 = 0.75   |   1/3 = 0.333… (recurring)

Key Tips

• Remember: 0.1 = 10%, 0.01 = 1%, 0.5 = 50%, 0.25 = 25%, 0.75 = 75%
• Use estimation to check your answers make sense