Chapter 3.1, Problem 7SP

a)

Interpretation Introduction

Interpretation : The answers in scientific notation are to be written.

Concept Introduction : A given number is stated as the product of two numbers in scientific notation: a coefficient and 10 raised to a power. Round the number to one significant figure in the measurement.

Answer to Problem 7SP

The answer in scientific notation is $\text{9}\times {\text{10}}^1\text{meters}$ .

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 one significant figure in the measurement.

If the 2^nd digit number is greater than or equal to 5, then the 1^st digit is added up by number 1 while leaving the remaining digit after the 2^nd digit. If the 2^nd digit number is lesser than 5, then the values till the 1^st digit are alone taken up.

The answer obtained is $\text{8}\text{.7}\times {\text{10}}^1\text{ meters}$ .

The scientific notation is given as

  $\text{8}\text{.7}\times {\text{10}}^1\text{ meters}\text{=}\text{9}\times {\text{10}}^1\text{meters}$

b)

Interpretation Introduction

Interpretation : The answers in scientific notation are to be written.

Concept Introduction : A given number is stated as the product of two numbers in scientific notation: a coefficient and 10 raised to a power. Round the number to one significant figure in the measurement.

Answer to Problem 7SP

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

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 one significant figure in the measurement.

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 2^nd digit number is greater than or equal to 5, then the 1^st digit is added up by number 1 while leaving the remaining digit after the 2^nd digit. If the 2^nd digit number is lesser than 5, then the values till the 1^st digit are alone taken up.

The answer obtained is $4.36\times {\text{10}}^8\text{ meters}$ .

The scientific notation is given as

  $4.36\times {\text{10}}^8\text{ meters}\text{=}4\times {\text{10}}^8\text{ meters}$

c)

Interpretation Introduction

Interpretation : The answers in scientific notation are to be written.

Concept Introduction : A given number is stated as the product of two numbers in scientific notation: a coefficient and 10 raised to a power. Round the number to one significant figure in the measurement.

Answer to Problem 7SP

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

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 one significant figure in the measurement.

If the 2^nd digit number is greater than or equal to 5, then the 1^st digit is added up by number 1 while leaving the remaining digit after the 2^nd digit. If the 2^nd digit number is lesser than 5, then the values till the 1^st digit are alone taken up.

The answer obtained is $1.6\times {\text{10}}^{-2}\text{ meters}$ .

The scientific notation is given as

  $1.6\times {\text{10}}^{-2}\text{ meters}\text{=}2\times {\text{10}}^{-2}\text{ meters}$

d)

Interpretation Introduction

Interpretation : The answers in scientific notation are to be written.

Concept Introduction : A given number is stated as the product of two numbers in scientific notation: a coefficient and 10 raised to a power. Round the number to one significant figure in the measurement.

Answer to Problem 7SP

The answer in scientific notation is $9\times {\text{10}}^3\text{ meters}$ .

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 one significant figure in the measurement.

If the 2^nd digit number is greater than or equal to 5, then the 1^st digit is added up by number 1 while leaving the remaining digit after the 2^nd digit. If the 2^nd digit number is lesser than 5, then the values till the 1^st digit are alone taken up.

The answer obtained is $9.01\times {\text{10}}^3\text{ meters}$ .

The scientific notation is given as

  $9.01\times {\text{10}}^3\text{ meters}\text{=}9\times {\text{10}}^3\text{ meters}$

e)

Interpretation Introduction

Interpretation : The answers in scientific notation are to be written.

Concept Introduction : A given number is stated as the product of two numbers in scientific notation: a coefficient and 10 raised to a power. Round the number to one significant figure in the measurement.

Answer to Problem 7SP

The answer in scientific notation is $2\times {\text{10}}^{-3}\text{ meters}$ .

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 one significant figure in the measurement.

If the 2^nd digit number is greater than or equal to 5, then the 1^st digit is added up by number 1 while leaving the remaining digit after the 2^nd digit. If the 2^nd digit number is lesser than 5, then the values till the 1^st digit are alone taken up.

The answer obtained is $1.78\times {\text{10}}^{-3}\text{ meters}$ .

The scientific notation is given as

  $1.78\times {\text{10}}^{-3}\text{ meters}\text{=}2\times {\text{10}}^{-3}\text{ meters}$

f)

Interpretation Introduction

Interpretation : The answers in scientific notation are to be written.

Concept Introduction : A given number is stated as the product of two numbers in scientific notation: a coefficient and 10 raised to a power. Round the number to one significant figure in the measurement.

Answer to Problem 7SP

The answer in scientific notation is $\text{6}\times {\text{10}}^2\text{ meters}$ .

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 one significant figure in the measurement.

If the 2^nd digit number is greater than or equal to 5, then the 1^st digit is added up by number 1 while leaving the remaining digit after the 2^nd digit. If the 2^nd digit number is lesser than 5, then the values till the 1^st digit are alone taken up.

The answer obtained is $6.30\times {\text{10}}^2\text{ meters}$ .

The scientific notation is given as

  $6.30\times {\text{10}}^2\text{ meters}\text{= 6}\times {\text{10}}^2\text{meters}$