Decimals
Calculators, worked examples and guides — from basic decimal arithmetic through to rounding, significant figures and converting between decimals, fractions and percentages.
Learning about Decimals
The key idea: decimals are just fractions written in base-10 shorthand. 0.5 = ½, 0.25 = ¼, 0.1 = 1/10. The decimal point separates the whole number from the part smaller than one — everything to the right is a fraction of 1.
Adding decimals
"3.47 + 1.8 = ?"
Step 1: Line up decimal points
Step 2: Write 1.8 as 1.80 (match decimal places)
Step 3: Add column by column: 3.47 + 1.80 = 5.27
Shortcut: Always align the decimal points — they must be exactly above each other
Multiplying decimals
"2.4 × 1.5 = ?"
Step 1: Ignore decimals and multiply: 24 × 15 = 360
Step 2: Count decimal places: 2.4 (1dp) × 1.5 (1dp) = 2dp total
Step 3: Place decimal: 3.60 = 3.6
Shortcut: Count decimal places first, then you know where the point goes before you calculate
Dividing decimals
"4.8 ÷ 0.6 = ?"
Step 1: Multiply both by 10 to eliminate the decimal: 48 ÷ 6
Step 2: 48 ÷ 6 = 8
Shortcut: Multiply both numbers by a power of 10 to make the divisor a whole number
Fractions & Decimals Formula Sheet
Need a printable revision sheet? Access rules for converting fractions to terminating and recurring decimals, percentage equivalents, and arithmetic operations with step-by-step worked examples and custom print export.
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Decimal Questions Answered
What is a decimal?
A decimal is a way of writing a number that includes a part smaller than one, separated by a decimal point. 0.5 means five-tenths (½), 0.25 means twenty-five hundredths (¼).
How do I add decimals?
Line up the decimal points vertically, add trailing zeros to match lengths, then add column by column as with whole numbers. 3.4 + 1.25 → write as 3.40 + 1.25 = 4.65.
How do I multiply decimals?
Ignore the decimal points and multiply as whole numbers. Then count the total decimal places in both original numbers and place the point that many places from the right in your answer.
What does rounding to decimal places mean?
Reducing a number to fewer decimal places. Look at the next digit — if it is 5 or above, round up the last kept digit; below 5, leave it unchanged. So 3.47 rounded to 1dp = 3.5.
What is the difference between a decimal and a fraction?
They represent the same values in different notation. 0.25 and ¼ are identical — one uses decimal notation, the other fraction notation. You can convert between them freely.