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Chapter 1: Problem 32

Use exponential notation to express the number 385,500 to a. one significant figure. b. two significant figures. c. three significant figures. d. five significant figures.

Short Answer

Expert verified
a. The number 385,500 expressed to one significant figure in exponential notation is \(4 \times 10^5\). b. The number 385,500 expressed to two significant figures in exponential notation is \(3.9 \times 10^5\). c. The number 385,500 expressed to three significant figures in exponential notation is \(3.86 \times 10^5\). d. The number 385,500 expressed to five significant figures in exponential notation is \(3.8550 \times 10^5\).

Step by step solution

01

Find the largest power of 10

For one significant figure, the largest power of 10 is \(10^5\), because \(385,500 \approx 4 \times 10^5\).
02

Round the number

Round 385,500 to the nearest multiple of \(10^5\). The closest multiple is 400,000.
03

Write in exponential notation

Express 400,000 in exponential notation: \[4 \times 10^5\] #b. two significant figures#
04

Find the largest power of 10

For two significant figures, the largest power of 10 is \(10^4\), because \(385,500 \approx 39 \times 10^4\).
05

Round the number

Round 385,500 to the nearest multiple of \(10^4\). The closest multiple is 390,000.
06

Write in exponential notation

Express 390,000 in exponential notation: \[3.9 \times 10^5\] #c. three significant figures#
07

Find the largest power of 10

For three significant figures, the largest power of 10 is \(10^3\), because \(385,500 \approx 386 \times 10^3\).
08

Round the number

Round 385,500 to the nearest multiple of \(10^3\). The closest multiple is 386,000.
09

Write in exponential notation

Express 386,000 in exponential notation: \[3.86 \times 10^5\] #d. five significant figures#
10

Count the number of significant figures

The given number, 385,500, has five significant figures.
11

Write in exponential notation

Since the given number already has five significant figures, write it in exponential notation: \[3.8550 \times 10^5\]

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