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Chapter 1: Problem 35

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. \(1.034 \times 10^{4}\) c. \(1.7992 \times 10^{1}\) d. \(3.37 \times 10^{5}\)

Step by step solution

01

Identify the first three significant digits

In the given number 0.00034159, the first three significant digits are 3, 4, and 1.
02

Round off the number

The next digit (5) is greater than or equal to 5, so we will round up our last significant digit (1) to 2. Thus, the rounded number is 0.000342.
03

Write in standard scientific notation

To write this number in standard scientific notation, we write it in the form \(a \times 10^n\), where \(1 \leq a < 10\) and n is an integer. So, the standard scientific notation will be \(3.42 \times 10^{-4}\). #b. \(103.351 \times 10^{2}\) to four digits#
04

Identify the first four significant digits

In the given number \(103.351 \times 10^2\), the first four significant digits are 1, 0, 3, and 3.
05

Round off the number

The next digit (5) is greater than or equal to 5, so we will round up our last significant digit (3) to 4. Thus, the rounded number is \(103.4 \times 10^2\).
06

Write in standard scientific notation

The resulting number is already in standard scientific notation, so there is no need to make any adjustments. Hence, the answer is \(1.034 \times 10^{4}\). #c. 17.9915 to five digits#
07

Identify the first five significant digits

In the given number 17.9915, the first five significant digits are 1, 7, 9, 9, and 1.
08

Round off the number

The next digit (5) is equal to 5, so we will round up our last significant digit (1) to 2. Thus, the rounded number will be 17.992.
09

Write in standard scientific notation

To write this number in standard scientific notation, we will have \(1.7992 \times 10^{1}\). #d. \(3.365 \times 10^{5}\) to three digits#
10

Identify the first three significant digits

In the given number \(3.365 \times 10^5\), the first three significant digits are 3, 3, and 6.
11

Round off the number

The next digit (5) is equal to 5, so we will round up our last significant digit (6) to 7. Thus, the rounded number will be \(3.37 \times 10^5\).
12

Write in standard scientific notation

The resulting number is already in standard scientific notation, so there is no need to make any adjustments. Hence, the answer is \(3.37 \times 10^{5}\).

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