BECE Mathematics 2017 Paper

Concept:Standard form expresses a number as a value between $1$ and $10$ multiplied by a power of $10$.To divide decimals easily, first convert them into powers of $10$.Explanation:Write each decimal as a whole number multiplied by a power of $10$.Moving the decimal point to the right gives a negative power of $10$.$64.5 = 645 \times 10^{-1}$$0.015 = 15 \times 10^{-3}$Now divide:$\frac{64.5}{0.015} = \frac{645 \times 10^{-1}}{15 \times 10^{-3}}$Simplify the whole numbers:$\frac{645}{15} = 43$Apply the index law $\frac{a^m}{a^n} = a^{m-n}$:$\frac{10^{-1}}{10^{-3}} = 10^{-1-(-3)} = 10^{2}$So the product is $43 \times 10^{2}$.Convert $43$ to standard form by moving the decimal point one place left:$43 = 4.3 \times 10^{1}$Combine using $a^m \times a^n = a^{m+n}$:$4.3 \times 10^{1} \times 10^{2} = 4.3 \times 10^{3}$Answer:$64.5 \div 0.015 = 4.3 \times 10^{3}$The correct option is B. $4.3 \times 10^{3}$.