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Chapter 2: Problem 158

Round each number to three significant digits and express the answer in scientific notation: (a) \(0.592861\) (b) 438932 (c) \(0.000073978\) (d) \(0.235469\) (e) \(82.550\) (f) \(529.8\)

Short Answer

Expert verified
The rounded numbers in scientific notation are: (a) \(5.93 \times 10^{-1}\) (b) \(4.39 \times 10^5\) (c) \(7.40 \times 10^{-5}\) (d) \(2.35 \times 10^{-1}\) (e) \(8.25 \times 10^1\) (f) \(5.30 \times 10^2\)

Step by step solution

01

(a) Identify the three most significant digits in \(0.592861\)

The three most significant digits in \(0.592861\) are \(5, 9,\) and \(2\). Since the next digit after \(2\), which is \(8\), is greater than or equal to \(5\), we should round up to get \(0.593\).
02

(a) Express \(0.593\) in scientific notation

Put \(0.593\) in the form \(a \times 10^b\), where \(1 \leq a < 10\) and \(b\) is an integer. Here, we have \(5.93 \times 10^{-1}\).
03

(b) Identify the three most significant digits in \(438932\)

The three most significant digits in \(438932\) are \(4, 3,\) and \(8\). Since the next digit after \(8\), which is \(9\), is greater than or equal to \(5\), we should round up to get \(439000\).
04

(b) Express \(439000\) in scientific notation

Put \(439000\) in the form \(a \times 10^b\), where \(1 \leq a < 10\) and \(b\) is an integer. Here, we have \(4.39 \times 10^5\).
05

(c) Identify the three most significant digits in \(0.000073978\)

The three most significant digits in \(0.000073978\) are \(7, 3,\) and \(9\). Since the next digit after \(9\), which is \(7\), is greater than or equal to \(5\), we should round up to get \(0.0000740\).
06

(c) Express \(0.0000740\) in scientific notation

Put \(0.0000740\) in the form \(a \times 10^b\), where \(1 \leq a < 10\) and \(b\) is an integer. Here, we have \(7.40 \times 10^{-5}\).
07

(d) Identify the three most significant digits in \(0.235469\)

The three most significant digits in \(0.235469\) are \(2, 3,\) and \(5\). Since the next digit after \(5\), which is \(4\), is less than \(5\), we do not need to round. The number remains \(0.235\).
08

(d) Express \(0.235\) in scientific notation

Put \(0.235\) in the form \(a \times 10^b\), where \(1 \leq a < 10\) and \(b\) is an integer. Here, we have \(2.35 \times 10^{-1}\).
09

(e) Identify the three most significant digits in \(82.550\)

The three most significant digits in \(82.550\) are \(8, 2,\) and \(5\). Since the next digit after \(5\), which is \(5\), is equal to \(5\), we need to look at the following digit, which is \(0\) and less than \(5\). Thus, we don't need to round. The number remains \(82.5\).
10

(e) Express \(82.5\) in scientific notation

Put \(82.5\) in the form \(a \times 10^b\), where \(1 \leq a < 10\) and \(b\) is an integer. Here, we have \(8.25 \times 10^1\).
11

(f) Identify the three most significant digits in \(529.8\)

The three most significant digits in \(529.8\) are \(5, 2,\) and \(9\). Since the next digit after \(9\), which is \(8\), is greater than or equal to \(5\), we should round up to get \(530\).
12

(f) Express \(530\) in scientific notation

Put \(530\) in the form \(a \times 10^b\), where \(1 \leq a < 10\) and \(b\) is an integer. Here, we have \(5.30 \times 10^2\).

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