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Chapter 1: Problem 47

Round each of the following numbers to three significant figures and express the result in standard exponential notation: $(\mathbf{a}) 2048732.23(\mathbf{b}) 0.000292945(\mathbf{c})-82454.09$ (d) \(942.057024(\mathbf{e})-0.00000324683 .\)

Short Answer

Expert verified
The rounded numbers in standard exponential notation are: (a) \(2.05 \times 10^6\), (b) \(2.93 \times 10^{-4}\), (c) \(-8.25 \times 10^4\), (d) \(9.42 \times 10^2\), and (e) \(-3.25 \times 10^{-6}\).

Step by step solution

01

Part a: 2048732.23

First, identify the first three significant figures, which are 2, 0, and 4. Since the fourth significant digit (8) is greater than or equal to 5, round up the last significant digit. The rounded number is 2050000. Now, express the result in standard exponential notation: \(2.05 \times 10^6\).
02

Part b: 0.000292945

Identify the first three significant figures (2, 9, and 2). Since the fourth significant digit (9) is greater than or equal to 5, round up the last significant digit. The rounded number is 0.000293. Express the result in standard exponential notation: \(2.93 \times 10^{-4}\).
03

Part c: -82454.09

First, ignore the negative sign. Then find the first three significant figures, which are 8, 2, and 4. Since the fourth significant digit (5) is greater than or equal to 5, round up the last significant digit. The rounded number is 82500, and with the negative sign, it's -82500. Now, express the result in standard exponential notation: \(-8.25 \times 10^4\).
04

Part d: 942.057024

First, identify the first three significant figures (9, 4, and 2). Since the fourth significant digit (0) is less than 5, do not round up the last significant digit. The rounded number is 942. Now, express the result in standard exponential notation: \(9.42 \times 10^2\).
05

Part e: -0.00000324683

First, ignore the negative sign. Then find the first three significant figures (3, 2, and 4). Since the fourth significant digit (6) is greater than or equal to 5, round up the last significant digit. The rounded number is 0.00000325, and with the negative sign, it's -0.00000325. Now, express the result in standard exponential notation: \(-3.25 \times 10^{-6}\).

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