Knowledge Organiser: Integers and Decimals
Part of Integers & Decimals · GCSE GCSE Mathematics revision
This topic summary covers Knowledge Organiser: Integers and Decimals within Integers & Decimals for GCSE Mathematics. Revise Integers & Decimals in Number for GCSE Mathematics with 14 exam-style questions and 22 flashcards. This topic appears regularly enough that it should still be part of a steady revision cycle. It is section 13 of 13 in this topic. Use this topic summary to connect the idea to the wider topic before moving on to questions and flashcards.
Topic position
Section 13 of 13
Practice
14 questions
Recall
22 flashcards
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 two decimals gives a smaller result)
- 4 ÷ 0.5 = 8 (dividing by a decimal less than 1 gives a larger result)
- A fraction 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
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Practice Questions for Integers & Decimals
What is the value of the digit 4 in the number 12.345?
Explain how to multiply two decimal numbers without a calculator.
Quick Recall Flashcards
14 questions on Integers & Decimals — practise free
Instant marking, adaptive difficulty, and 22 spaced repetition flashcards. Free until your GCSEs.
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