Chapter 3.1, Problem 6SP

Interpretation Introduction

Interpretation : The round of given measurement to three significant figures is to be calculated.

Concept Introduction : The known digits plus the last, estimated digit make up the significant figures in a measurement. Round the number to three significant figures in the measurement.

Answer to Problem 6SP

The answer in scientific notation is $8.71\times {10}^1\text{meters}$ .

Explanation of Solution

The known digits plus the last, estimated digit make up the significant figures in a measurement.

There is a set of rules to detect the digits in a significant measured value.

Round the number to three significant figures in the measurement.

If the 4^th digit number is greater than or equal to 5, then the 3^rd digit is added up by number 1 while leaving the remaining digit after the 4^th digit. If the 4^th digit number is lesser than 5, then the values till the 3^rd digit are alone taken up.

The given question is $\text{87}\text{.073 meters}$ .

The scientific notation is given as:

  $\begin{array}{c}\text{87}\text{.073 meters}\text{=}\text{87}\text{.1 meters}\\ \text{= 8}\text{.71}\times {\text{10}}^{-1}\text{meters}\end{array}$

Interpretation Introduction

Interpretation : The round of given measurement to three significant figures is to be calculated.

Concept Introduction : The known digits plus the last, estimated digit make up the significant figures in a measurement. Round the number to three significant figures in the measurement.

Answer to Problem 6SP

The answer in scientific notation is $\text{4}\text{.36}\times {\text{10}}^8\text{ meters}$ .

Explanation of Solution

The known digits plus the last, estimated digit make up the significant figures in a measurement.

There is a set of rules to detect the digits in a significant measured value.

Round the number to three significant figures in the measurement.

If the 4^th digit number is greater than or equal to 5, then the 3^rd digit is added up by number 1 while leaving the remaining digit after the 4^th digit is simply dropped. If the 4^th digit number is lesser than 5, then the values till the 3^rd digit are alone taken up.

The given question is $\text{4}\text{.3621}\times {\text{10}}^8\text{ meters}$ .

The scientific notation is given as

  $\text{4}\text{.3621}\times {\text{10}}^8\text{ meters}\text{=}\text{4}\text{.36}\times {\text{10}}^8\text{ meters}$

Interpretation Introduction

Interpretation : The round of given measurement to three significant figures is to be calculated.

Concept Introduction : The known digits plus the last, estimated digit make up the significant figures in a measurement. Round the number to three significant figures in the measurement.

Answer to Problem 6SP

The answer in scientific notation is $\text{1}\text{.5}\times {\text{10}}^{-2}\text{meter}$ .

Explanation of Solution

The known digits plus the last, estimated digit make up the significant figures in a measurement.

There is a set of rules to detect the digits in a significant measured value.

Round the number to three significant figures in the measurement.

If the 4^th digit number is greater than or equal to 5, then the 3^rd digit is added up by number 1 while leaving the remaining digit after the 4^th digit is simply dropped. If the 4^th digit number is lesser than 5, then the values till the 3^rd digit are alone taken up.

The given question is $0.01522\text{meter}$ .

The scientific notation is given as:

  $\begin{array}{c}0.01522\text{meter}\text{=}0.015\text{ meter}\\ \text{= 1}\text{.5}\times {\text{10}}^{-2}\text{meter}\end{array}$

Interpretation Introduction

Interpretation : The round of given measurement to three significant figures is to be calculated.

Concept Introduction : The known digits plus the last estimated digit make up the significant figures in a measurement. Round the number to three significant figures in the measurement.

Answer to Problem 6SP

The answer in scientific notation is $9.01\times {10}^3\text{meters}$ .

Explanation of Solution

The known digits plus the last, estimated digit make up the significant figures in a measurement.

There is a set of rules to detect the digits in a significant measured value.

Round the number to three significant figures in the measurement.

If the 4^th digit number is greater than or equal to 5, then the 3^rd digit is added up by number 1 while leaving the remaining digit after the 4^th digit is simply dropped. If the 4^th digit number is lesser than 5, then the values till the 3^rd digit are alone taken up.

The given question is $9009\text{meters}$ .

The scientific notation is given as:

  $\begin{array}{c}9009\text{meters}\text{=}9010\text{ meters}\\ \text{= 9}\text{.010}\times {\text{10}}^3\text{meters}\end{array}$

Interpretation Introduction

Interpretation : The round of given measurement to three significant figures is to be calculated.

Concept Introduction : The known digits plus the last estimated digit make up the significant figures in a measurement. Round the number to three significant figures in the measurement.

Answer to Problem 6SP

The answer in scientific notation is $1.78\times {10}^{-3}\text{meter}$ .

Explanation of Solution

The known digits plus the last, estimated digit make up the significant figures in a measurement.

There is a set of rules to detect the digits in a significant measured value.

Round the number to three significant figures in the measurement.

If the 4^th digit number is greater than or equal to 5, then the 3^rd digit is added up by number 1 while leaving the remaining digit after the 4^th digit is simply dropped. If the 4^th digit number is lesser than 5, then the values till the 3^rd digit are alone taken up.

The given question is $1.7777\times {10}^{-3}\text{meter}$ .

The scientific notation is given as:

  $1.7777\times {10}^{-3}\text{meter}\text{=}1.78\times {10}^{-3}\text{ meters}$

Interpretation Introduction

Interpretation : The round of given measurement to three significant figures is to be calculated.

Concept Introduction : The known digits plus the last, estimated digit make up the significant figures in a measurement. Round the number to three significant figures in the measurement.

Answer to Problem 6SP

The answer in scientific notation is $6.30\times {10}^2\text{meters}$ .

Explanation of Solution

The known digits plus the last, estimated digit make up the significant figures in a measurement.

There is a set of rules to detect the digits in a significant measured value.

Round the number to three significant figures in the measurement.

If the 4^th digit number is greater than or equal to 5, then the 3^rd digit is added up by number 1 while leaving the remaining digit after the 4^th digit is simply dropped. If the 4^th digit number is lesser than 5, then the values till the 3^rd digit are alone taken up.

The given question is $\text{629}\text{.55 meters}$ .

The scientific notation is given as

  $\begin{array}{c}\text{629}\text{.55 meters}\text{=}630\text{ meters}\\ \text{= 6}\text{.30}\times {\text{10}}^2\text{meters}\end{array}$