Fractions, Decimals, Approximations and Percentages

1. Fractions and Decimals

Fractions represent a part of a whole. They consist of a numerator (top) and a denominator (bottom). Proper fractions have numerators smaller than denominators, while improper fractions have larger numerators. Mixed numbers combine a whole number and a fraction.

• Addition/Subtraction: Find the Lowest Common Multiple (LCM) of the denominators.
• Multiplication: Multiply numerators together and denominators together.
• Division: Multiply by the reciprocal of the divisor.

Decimals are fractions with denominators in powers of 10. Operations follow standard arithmetic rules, ensuring decimal points are aligned for addition and subtraction.

2. Significant Figures (S.F) and Decimal Places (D.P)

Significant figures indicate the precision of a number. Rules include:

• Non-zero digits are always significant.
• Zeros between non-zero digits are significant.
• Leading zeros are not significant.
• Trailing zeros in a decimal are significant.

Decimal places refer to the number of digits to the right of the decimal point.

3. Percentage Error

Percentage error measures the accuracy of an approximation or measurement. The formula is:

Percentage Error = |(Measured Value - Actual Value) / Actual Value| × 100%

4. Commercial Arithmetic

• Simple Interest (I): Calculated using I = (P × R × T) / 100, where P is Principal, R is Rate, and T is Time in years.
• Profit and Loss: Profit = Selling Price (SP) - Cost Price (CP). Percentage Profit = (Profit / CP) × 100%.
• VAT (Value Added Tax): A consumption tax placed on a product whenever value is added at each stage of the supply chain.
• Shares: Units of ownership interest in a corporation. Dividends are profits distributed to shareholders.

5. Ratio, Proportion, and Rate

• Ratio: A comparison of two quantities by division (e.g., a:b).
• Proportion: An equation stating that two ratios are equal. Direct proportion means as one increases, the other increases. Inverse proportion means as one increases, the other decreases.
• Rate: A ratio that compares two different kinds of quantities (e.g., speed in km/h).