Chapter 5.2, Problem 6RQ

(a)

Interpretation Introduction

Interpretation: The number of significant figures needs to be determined.

Concept Introduction : Significant figures of a number are termed as digits which contribute to the precision of that number. Any measurement involves an estimate and thus is uncertain to some extent. A reliably identified digit used to find a decimal point is known as significant figure.

Answer to Problem 6RQ

The significant figure in $1.8+1.80+1.800$ = $\text{2}\text{sig}\text{fig}\text{.}$

Explanation of Solution

The number of meaningful digits in a calculated quantity is known as significant figures. All non- zero digits are significant and leading zeros are never count as significant but captive zeros are significant.

If in any number the zero present between the non-zeros numbers so it is considered as significant.

When zeros are present left of all non-zero numbers then zero is considered as not significant.

If a decimal is present with non-zeros number and zero is present to the right of all non-zero numbers then zero is considered as significant.

The given calculation can be performed as follows:

  $1.8+1.80+1.800$

  $=5.4=\text{2}\text{sig}\text{fig}\text{.}$

(b)

Interpretation Introduction

Interpretation: The number of significant figures needs to be determined.

Concept Introduction : Significant figures of a number are termed as digits which contribute to the precision of that number.Any measurement involves an estimate and thus is uncertain to some extent. A reliably identified digit used to find a decimal point is known as significant figure.

Answer to Problem 6RQ

The significant figure in $100+0.08640$

  $=1\text{sig}\text{fig}\text{.}$

Explanation of Solution

The number of meaningful digits in a calculated quantity is known as significant figures. All non- zero digits are significant and leading zeros are never count as significant but captive zeros are significant.

If in any number the zero present between the non-zeros numbers so it is considered as significant.

When zeros are present left of all non-zero numbers then zero is considered as not significant.

If a decimal is present with non-zeros number and zero is present to the right of all non-zero numbers then zero is considered assignificant.

  $100+0.08640$

  $=100.0864$

  $=1\times {10}^2$

  $=1\text{sig}\text{fig}\text{.}$

(c)

Interpretation Introduction

Interpretation: The number of significant figures needs to be determined.

Concept Introduction : Significant figures of a number are termed as digits which contribute to the precision of that number.Any measurement involves an estimate and thus is uncertain to some extent. A reliably identified digit used to find a decimal point is known as significant figure.

Answer to Problem 6RQ

The significant figure in $7342\times 6800$

  $=2\text{sig}\text{fig}\text{.}$

Explanation of Solution

The number of meaningful digits in a calculated quantity is known as significant figures. All non- zero digits are significant and leading zeros are never count as significant but captive zeros are significant.

If in any number the zero present between the non-zeros numbers so it is considered as significant.

When zeros are present left of all non-zero numbers then zero is considered as not significant.

If a decimal is present with non-zeros number and zero is present to the right of all non-zero numbers then zero is considered as significant.

The given calculation is as follows:

  $7342\times 6800$

  $=49,925,600$

The given number is rounded as follows:

  $=5.0\times {10}^7$

  $=2\text{sig}\text{fig}\text{.}$

(d)

Interpretation Introduction

Interpretation: The number of significant figures needs to be determined.

Concept Introduction : Significant figures of a number are termed as digits which contribute to the precision of that number.Any measurement involves an estimate and thus is uncertain to some extent. A reliably identified digit used to find a decimal point is known as significant figure.

Answer to Problem 6RQ

The significant figure in $4.00\times {10}^5\times 3.14÷14.2$

  $\text{=3sig}\text{fig}$

Explanation of Solution

The number of meaningful digits in a calculated quantity is known as significant figures. All non- zero digits are significant and leading zeros are never count as significant but captive zeros are significant.

If in any number the zero present between the non-zeros numbers so it is considered as significant.

When zeros are present left of all non-zero numbers then zero is considered as not significant.

If a decimal is present with non-zeros number and zero is present to the right of all non-zero numbers then zero is considered as significant.

The given measurement is as follows:

  $4.00\times {10}^5\times 3.14÷14.2$

  $=88,450.7042$

The above number can be rounded as follows:

  $=8.84\times {10}^4$

  $\text{=3sig}\text{fig}$