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Chapter 1: Problem 33

Round off each of the following numbers to the indicated number of significant digits and write the answer in standard scientific notation. a. \(0.00034159\) to three digits b. \(103.351 \times 10^{2}\) to four digits c. \(17.9915\) to five digits d. \(3.365 \times 10^{5}\) to three digits

Short Answer

Expert verified
a. \(3.42 \times 10^{-4}\) b. \(1.0340 \times 10^{4}\) c. \(1.7992 \times 10^{1}\) d. \(3.37 \times 10^{5}\)

Step by step solution

01

(a) Rounding \(0.00034159\) to three significant digits#

To round \(0.00034159\) to three significant digits, we need to identify the first three significant digits, which are \(3\), \(4\), and \(1\). Now round the number to these three digits. The next digit after the third significant digit is \(5\), so we round up, giving us \(0.000342\). Now, let's convert this into standard scientific notation: \[ 0.000342 = 3.42 \times 10^{-4} \]
02

(b) Rounding \(103.351 \times 10^{2}\) to four significant digits#

First, let's express the number \(103.351 \times 10^{2}\) as a decimal number: \[ 103.351 \times 10^{2} = 10335.1 \] Now, we need to round it to four significant digits. The first four significant digits are \(1\), \(0\), \(3\), and \(3\). Observe that the next digit is \(5\), so we round up, giving us \(10340\). Now, let's express the rounded number in standard scientific notation: \[ 10340 = 1.0340 \times 10^{4} \]
03

(c) Rounding \(17.9915\) to five significant digits#

To round \(17.9915\) to five significant digits, we need to identify the first five significant digits, which are \(1\), \(7\), \(9\), \(9\), and \(1\). Now round the number to these five digits. The next digit after the fifth significant digit is \(5\), so we round up, giving us \(17.992\). Now, let's convert this into standard scientific notation: \[ 17.992 = 1.7992 \times 10^{1} \]
04

(d) Rounding \(3.365 \times 10^{5}\) to three significant digits#

To round \(3.365 \times 10^{5}\) to three significant digits, we need to identify the first three significant digits, which are \(3\), \(3\), and \(6\). Now round the number to these three digits. The next digit after the third significant digit is \(5\), so we round up, giving us \(3.37 \times 10^{5}\). Already in standard scientific notation, the rounded number is: \[ 3.37 \times 10^{5} \]

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