Number and Quantity
Number and Quantity
The Number and Quantity domain tests fluency with real numbers and the ways quantities are represented, compared, and converted. Expect operations with integers, fractions, decimals, percentages, ratios, rates, powers, roots, and scientific notation, often embedded in short contexts.
Core rules
- Fractions, decimals, and percentages are interchangeable: 3/8 = 0.375 = 37.5%.
- Percentage change is (new - old)/old × 100%, and successive changes multiply rather than add.
- Ratios compare like quantities; rates compare different units. Match units before setting up a proportion.
- For powers: a^m a^n = a^(m+n), a^m/a^n = a^(m-n), (a^m)^n = a^(mn), and a^(-n) = 1/a^n.
- Scientific notation writes a number as k × 10^n with 1 ≤ |k| < 10.
- Estimate before computing to catch place-value and unit errors.
Worked example
A jacket costs $80. Its price is increased by 25%, then reduced by 20% in a sale. What is the final price? Increase: 80 × 1.25 = 100. Reduction: 100 × 0.80 = 80. Final price is $80. The two changes do not generally cancel: the multiplier product 1.25 × 0.80 = 1.00 decides the result.
Traps
- Adding percentages instead of multiplying successive multipliers.
- Mixing percent of the original amount with percent of the new amount.
- Forgetting that a ratio such as 2:3 has 5 parts in total.
- Rounding too early; carry exact values until the final step.
- Treating a negative exponent as a negative result.