Knowledge Organiser: Integers and Decimals
Key Terms
- Integer: A whole number (positive, negative, or zero)
- Decimal: A number containing a decimal point showing parts of a whole
- Tenths: First decimal place (0.1); hundredths: second (0.01)
- Terminating decimal: Stops after a finite number of decimal places
- Recurring decimal: A decimal that repeats forever (e.g. 0.333…)
Must-Know Facts
- When adding/subtracting decimals: always align decimal points
- When multiplying: count total decimal places in both numbers, place in answer
- 6.3 ÷ 0.7: multiply both by 10 → 63 ÷ 7 = 9 (remove decimal from divisor)
- 0.5 × 0.2 = 0.1 (multiplying by a number between 0 and 1 gives a smaller result)
- 4 ÷ 0.5 = 8 (dividing by a decimal less than 1 gives a larger result)
- A fraction in simplest form terminates only if its denominator has factors of 2 and 5 only
Key Methods
- Adding decimals: line up decimal points, fill gaps with zeros, add column by column
- Multiplying decimals: multiply as integers, count decimal places, insert point
- Dividing by a decimal: multiply both numbers by 10/100 to make divisor whole
- Decimal to fraction: write digits over matching power of 10, then simplify
Common Mistakes
- Not lining up decimal points: When adding or subtracting decimals, always align the decimal points: misalignment shifts digits into the wrong column
- Comparing decimal lengths: 0.75 is not bigger than 0.8: pad with zeros to compare: 0.80 vs 0.75, so 0.80 is bigger
- Multiplying decimals: Multiply as whole numbers first, then count total decimal places and reinsert the point: forgetting the count shifts the answer by a factor of 10
- Dividing by a decimal: Multiply both numbers by a power of 10 to make the divisor a whole number before dividing