Convert 0.04945 to two significant figures

1. Analyze the question

You are asked to round the decimal number 0.04945 to two significant figures.

2. Explain the concept

Significant figures are the digits in a number that carry meaning contributing to its precision. When counting significant figures in a decimal number:

• Leading zeros (zeros to the left of the first non-zero digit) are not significant.
• In 0.04945, the first two zeros are placeholders and are not significant.
• The first significant figure is 4.
• The second significant figure is 9.
• To round to two significant figures, we look at the digit immediately to the right of the second significant figure (the third digit). If it is 5 or greater, we round up; if it is less than 5, we keep the second digit as it is.

3. Show the solution

• Step 1: Identify the first two significant figures in 0.04945. • The first non-zero digit is 4 (this is the 1st significant figure). • The next digit is 9 (this is the 2nd significant figure).
• Step 2: Look at the digit immediately to the right of the 2nd significant figure (which is the digit 4). • The number is 0.04945.
• Step 3: Apply the rounding rule. • Since the digit to the right (4) is less than 5, we do not round up. We simply drop the remaining digits. • The number becomes 0.049.

4. Identify the answer

Comparing our result to the options provided: A. 0.040 B. 0.049 C. 0.050 D. 0.49

The correct option is B.

5. Tip

Always remember: Leading zeros never count. If you are ever confused, write the number in standard form (scientific notation). 0.04945 is $4.945 \times 10^{-2}$. Looking at the digits in the decimal part ($4.945$), it is much easier to see that rounding to two figures gives $4.9 \times 10^{-2}$, which is $0.049$.