Reach each number to two significant figures and then evaluate $\frac{0.02174 \times 1.2047}{0.023789}$

1. Analyze the question

The task requires two distinct steps:

• Rounding: Convert each of the three numbers in the expression to two significant figures.
• Evaluation: Perform the arithmetic operation (multiplication and division) using these rounded values.

2. Explain the concept

• Significant Figures: When rounding to two significant figures, we start counting from the first non-zero digit. For decimals, leading zeros (zeros before the first non-zero digit) are not significant.
• Rounding Rules: If the digit after the second significant figure is 5 or greater, we round up the second digit. If it is less than 5, we keep the second digit as it is.

3. Show the solution

Step 1: Round each number to two significant figures

• $0.02174$: The first two significant figures are $2$ and $1$. The next digit is $7$ (which is $\geq 5$), so we round up the $1$ to $2$. • Rounded value = $0.022$
• $1.2047$: The first two significant figures are $1$ and $2$. The next digit is $0$ (which is $< 5$), so we keep the $2$ as it is. • Rounded value = $1.2$
• $0.023789$: The first two significant figures are $2$ and $3$. The next digit is $7$ (which is $\geq 5$), so we round up the $3$ to $4$. • Rounded value = $0.024$

Step 2: Evaluate the expression Substitute the rounded values into the expression:

First, multiply the numerator:

Next, divide by the denominator:

To make the division easier, multiply both numerator and denominator by $1000$:

4. Identify the answer

Comparing our result ($1.1$) to the given options: A. 0 B. 0.9 C. 1.1 D. 1.2

The correct option is C.

5. Exam Tip

When dealing with significant figures in JAMB, always remember that leading zeros are never significant. If you are ever confused, write the number in standard form (scientific notation) first; the digits in the coefficient will clearly show you which ones are significant!