Number: fluency, estimation and accuracy
What the Number strand tests
Number underpins every other strand. Foundation Level questions ask you to order and calculate with integers, fractions, decimals and percentages; use powers and roots; apply HCF and LCM; write numbers in scientific notation; and round to a required degree of accuracy. You must also decide whether an exact answer or an estimate is appropriate and show enough method to earn full marks.
Core rules
- A fraction is a division: a/b = a ÷ b. Equivalent fractions are made by multiplying or dividing top and bottom by the same non-zero number.
- To add or subtract fractions, use a common denominator. To multiply, multiply numerators and denominators. To divide, multiply by the reciprocal.
- A percentage is a fraction out of 100. An increase of p% uses the multiplier 1 + p/100; a decrease uses 1 - p/100.
- Scientific notation is a × 10^n, where 1 ≤ a < 10 and n is an integer.
- The HCF is the largest number that divides exactly into each of the given numbers. The LCM is the smallest number that each of the given numbers divides into.
- Round only at the end of a calculation, and state the required accuracy.
Worked example
A jacket costs €80 before VAT. VAT is charged at 23%. Find the total price.
The VAT multiplier is 1 + 0.23 = 1.23. Total = 80 × 1.23 = €98.40. Check the VAT separately: 0.23 × 80 = €18.40, and 80 + 18.40 = €98.40. Answer: €98.40.
Traps that cost marks
- Finding a percentage of a number but forgetting to add it back for an increase.
- Rounding a calculator display too early and losing accuracy in later steps.
- Treating (-3)^2 and -3^2 as the same: the first is 9, the second is -9.
- Mixing cent and euro amounts within one calculation.