Question

What will be the number of significant figures in the summation of \(0.153,\; 153.2\) and \(153.2\)?

• A. \(3\)
• B. \(4\)
• C. \(5\)
• D. \(6\)

Hint:

For addition and subtraction:

Look at \textbf{decimal places}, not significant figures
Final answer has the same decimal places as the least precise number

Answer 1

The Correct Option is B

To determine the number of significant figures in the summation of three numbers \(0.153\), \(153.2\), and \(153.2\), we need to follow these steps:

1.  Identify the number of significant figures in each number:
   • \(0.153\) has three significant figures.
   • \(153.2\) has four significant figures.
   • \(153.2\) again has four significant figures.
2. Compute the summation:
   • Adding these values gives \(0.153 + 153.2 + 153.2 = 306.553\).
3. Determine the number of significant figures in the result:
   • When adding or subtracting, the result should be reported with the same number of decimal places as the measurement with the smallest number of decimal places.
   • \(153.2\) and \(153.2\) each have one decimal place.
   • \(0.153\) has three decimal places.
   • The result should be rounded to one decimal place (the smallest number of decimal places among the numbers). Thus, \(306.6\) is the appropriate rounding.
4. Count the significant figures in the rounded sum:
   • The number \(306.6\) has four significant figures.

The correct answer is therefore \(4\) significant figures.