Decimals: Place Value, Operations and Examples

A decimal is a number that uses a decimal point to separate the whole part from the fractional part. In 3.75, the 3 is the whole part and the 75 after the point means 75 hundredths. Decimals begin in Year 4 and appear every day in prices, body weight and report-card marks.

Place Value After the Point

This is the heart of the whole topic. Each position after the point is worth one tenth of the one before it.

So 12.345 is read "twelve point three four five", not "twelve point three hundred and forty-five".

Comparing Decimals

Which is larger, 0.7 or 0.25?

Many children answer 0.25 because 25 is bigger than 7. That is wrong. The method: even out the number of digits after the point by adding zeros. 0.7 becomes 0.70. Now 0.70 > 0.25 is obvious.

Adding zeros on the right of a decimal does not change its value. 0.5 = 0.50 = 0.500.

Adding and Subtracting

There is only one requirement: the points must line up vertically.

  12.50
+  3.75
-------
  16.25

If the digit counts differ, pad with zeros. Write 12.5 + 3.75 as 12.50 + 3.75.

Multiplying

Ignore the points, multiply as whole numbers, then count the total number of digits after the point in both original numbers.

Example: 1.2 × 0.5

• 12 × 5 = 60
• Digits after the point: 1 + 1 = 2
• So the answer is 0.60 = 0.6

Dividing

Turn the divisor into a whole number by multiplying both numbers by 10, 100 or 1000.

Example: 4.5 ÷ 0.5

• Multiply both by 10 → 45 ÷ 5 = 9

Converting Between Fractions and Decimals

Fraction to decimal: divide the numerator by the denominator. 3/4 = 3 ÷ 4 = 0.75.

Decimal to fraction: write it by place value and simplify. 0.25 = 25/100 = 1/4.

A few are worth memorising because they recur endlessly:

See also fractions and how to calculate percentages.

The Mistakes That Actually Cost Marks

1. Comparing decimals like whole numbers. Thinking 0.25 is bigger than 0.7. This is the number one error and it signals that place value, not decimals, is the gap.

2. Misaligned points in column addition. Writing 12.5 + 3.75 right-aligned instead of point-aligned throws the answer far off.

3. Miscounting decimal places in multiplication. Placing the point by guesswork once the product is found.

4. Reading 0.45 as "zero point forty-five". That reading encourages a child to treat the decimal part as a whole number, which produces mistake number one directly.

5. Assuming decimals are always less than 1. 12.7 is a decimal and is clearly greater than 1.