Q: What does IP Maths Notes (Lower Sec, Year 1-2): 01) Number Systems & Indices cover? A: Master integer, fractional, and decimal conversions, index laws, and significant figure rounding for Year 1 IP maths.
Number sense underpins every algebraic manipulation you will meet from Year 2 onward. This guide cleans up conversion fluency, index laws, surds, and estimation so you never lose calculator-free marks.
Learning targets
Convert between fractions, decimals, and percentages without a calculator.
Apply the five index laws, including negative and fractional indices.
Standardise answers to the correct number of significant figures.
Present surds in rationalised form.
1. Number systems refresher
1.1 Fraction-decimal-percentage triad
Fractions express parts of a whole. Simplify by dividing numerator and denominator by their highest common factor.
Decimals express fractions in base-ten. For terminating decimals, use place value; for recurring decimals, note the repeating block.
Percentages compare against 100. Use the identity value=base×100percentage
.
Example: Convert 0.375 into fraction and percentage.
0.375=1000375=83,0.375=37.5%.
1.2 Ordering rational and irrational numbers
Place numbers on a single number line by converting to decimals. Surds such as 5≈2.236 give context for comparisons against rationals like 49=2.25.
2. Index laws
The five core laws hold for any non-zero base a and integers m,n:
Product: am×an=am+n
Quotient: anam=am−n
Power of a power: (am)n=amn
Zero index: a0=1
Negative index: a−n=an1
Extend to fractional indices via roots: anm=(am)n1.
