Number and Place Value

OCR

GCSE

The domain of Number and Place Value constitutes the axiomatic foundation of mathematics, governing the representation, ordering, and manipulation of real numbers including integers, decimals, and rational forms. Candidates must demonstrate fluency in the hierarchy of operations (BIDMAS), the decomposition of integers into prime factors to derive Highest Common Factors (HCF) and Lowest Common Multiples (LCM), and the efficient handling of very large or small quantities using standard form. Furthermore, this topic demands rigorous precision in approximation, requiring the application of rounding to specified significant figures and the calculation of error intervals to define the limits of accuracy in measurement.

Objectives

Exam Tips

Pitfalls

Key Terms

Mark Points

Subtopics in this area

Number and Place Value

What You Need to Demonstrate

Key skills and knowledge for this topic

Award B1 for correct rounding to the specified number of significant figures, ignoring subsequent incorrect working
Award M1 for a complete method to convert standard form to ordinary numbers before calculation if required
Credit responses that correctly apply the laws of indices, specifically subtracting indices for division
Award A1 for the final answer presented in correct standard form notation A × 10^n where 1 ≤ A < 10
Award M1 for identifying the correct upper and lower bounds before attempting the calculation in error interval questions
Award B1 for correct conversion of numbers to standard form, ensuring the coefficient A satisfies 1 ≤ A < 10
Award M1 for showing the explicit rounding of values to 1 significant figure before calculation in estimation questions
Award B1 for the correct evaluation of negative indices, specifically recognizing the reciprocal relationship (e.g., 5^-2 = 1/25)

Example Examiner Feedback

Real feedback patterns examiners use when marking

"You have correctly identified the place value, but check your rounding direction for the final significant figure"
"Good use of index laws. To improve, ensure you handle negative indices by creating the reciprocal before evaluating"
"This is a common error: remember that an estimate requires rounding *before* calculation, not after"
"Excellent work on the bounds. For full marks, ensure your inequality signs correctly distinguish between inclusive and exclusive bounds"

Marking Points

Key points examiners look for in your answers

Award B1 for correct rounding to the specified number of significant figures, ignoring subsequent incorrect working
Award M1 for a complete method to convert standard form to ordinary numbers before calculation if required
Credit responses that correctly apply the laws of indices, specifically subtracting indices for division
Award A1 for the final answer presented in correct standard form notation A × 10^n where 1 ≤ A < 10
Award M1 for identifying the correct upper and lower bounds before attempting the calculation in error interval questions
Award B1 for correct conversion of numbers to standard form, ensuring the coefficient A satisfies 1 ≤ A < 10
Award M1 for showing the explicit rounding of values to 1 significant figure before calculation in estimation questions
Award B1 for the correct evaluation of negative indices, specifically recognizing the reciprocal relationship (e.g., 5^-2 = 1/25)
Award M1 for correct application of BIDMAS, particularly ensuring multiplication/division precedes addition/subtraction in mixed operation strings

Examiner Tips

Expert advice for maximising your marks

💡When asked to 'Estimate', you must round every number to 1 significant figure before performing any calculation; exact answers often score zero
💡For standard form calculations on a calculator, use the 'EXP' or 'x10^x' button to avoid order of operation errors
💡In error interval questions, clearly state the inequality notation; remember that the upper bound is strictly 'less than' (<) while the lower bound is 'less than or equal to' (≤)
💡Check your answers for standard form constraints: the leading number must be between 1 and 10
💡In estimation questions, you must write down the rounded values (e.g., 'approx 50', 'approx 0.2') to secure method marks even if the final calculation is wrong
💡When ordering decimals, add placeholder zeros so all numbers have the same number of decimal places; this prevents treating '0.4' as smaller than '0.35'
💡For standard form calculations on non-calculator papers, handle the coefficients and powers of 10 separately, then adjust the final result to ensure valid standard form

Common Mistakes

Pitfalls to avoid in your exam answers

Confusing significant figures with decimal places, particularly when zeros are involved at the end of a number (e.g., rounding 0.0456 to 2 s.f. as 0.05)
Incorrectly applying index laws, specifically multiplying bases rather than adding indices (e.g., 3^2 × 3^3 = 9^5 instead of 3^5)
Failing to identify the correct upper bound in error intervals, often treating the bound as inclusive rather than exclusive
In estimation questions, performing the exact calculation first and then rounding the answer, which results in zero marks
Confusing the magnitude of negative numbers, for example, stating that -0.5 is smaller than -0.8 due to ignoring the negative sign's effect on value
In estimation questions, performing the exact calculation first and then rounding the answer, rather than rounding components to 1 significant figure first as required
Incorrectly manipulating indices, such as multiplying bases together when powers differ, or treating a negative power as a negative number (e.g., 2^-3 = -8)

Study Guide Available

Comprehensive revision notes & examples

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Key Terminology

Essential terms to know

Structure of the number system and place value

Prime factorisation, HCF and LCM

Standard form (scientific notation)

Approximation, rounding, and error intervals

Order of operations (BIDMAS/BODMAS)

Place value ordering (Integers and Decimals)

Approximation, Estimation, and Error Intervals

Prime Factorisation, HCF, and LCM

Standard Form and Index Laws

Rational and Irrational Numbers (Surds)

Likely Command Words

How questions on this topic are typically asked

Calculate

Estimate

Write

Work out

Order

Show that

Evaluate

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