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Chapter 1: Problem 117

How many significant numbers are there in \((2.30 \pm 4.70) \times 10^{5} ?\) (a) 3 (b) 4 (c) 2 (d) 5

Short Answer

Expert verified
The total number of significant numbers in the given value \((2.30 \pm 4.70) \times 10^{5}\) is 3. Thus, the correct answer is (a) 3.

Step by step solution

01

Identify the value and uncertainty

The given value is \((2.30 \pm 4.70) \times 10^{5}\). Here, \(2.30\times 10^{5}\) is the value, and \(\pm 4.70\times 10^{5}\) is the uncertainty.
02

Identify significant numbers in the value

In the value \(2.30\times 10^{5}\), there are three significant numbers: 2, 3, and 0 (the 2 and 3 are non-zero digits, and the 0 is a trailing zero in a decimal number which is also significant).
03

Identify significant numbers in the uncertainty

In the uncertainty \(\pm 4.70\times 10^{5}\), there are also three significant numbers: 4, 7, and 0 (the 4 and 7 are non-zero digits, and the 0 is a trailing zero in a decimal number which is also significant).
04

Determine the least number of significant numbers

As per the rules of significant numbers, when adding or subtracting values, the result must have the same number of decimal places as that of the number with the least decimal places. Here, both the value and the uncertainty have the same number of decimal places (two), so this rule does not affect the significant numbers in this case.
05

Identify the total number of significant numbers

Since the value and uncertainty both have the same number of significant numbers (three), there are a total of 3 significant numbers in the given value \((2.30 \pm 4.70) \times 10^{5}\). The correct answer is (a) 3.

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