Chapter 5.2, Problem 5RQ

(a)

Interpretation Introduction

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

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 5RQ

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 is as follows:

  $1.8+1.80+1.800$

When addition is performed, the final number will have minimum number of digits after decimals. Here, minimum number of digits after decimal is 1 that is in 1.8.

. Thus, there will be 1 digit after decimal. Thus, there will be 2 significant figures.

(b)

Interpretation Introduction

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

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 5RQ

The significant figure in $100+0.08640$ is 1.

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:

  $100+0.08640$

When addition is performed, the final number will have minimum number of digits after decimals. Here, minimum number of digits after decimal is in 100 that is zero.

Thus, final number has 0 digits after decimal like 100. Thus, total number of significant figures will be 1.

(c)

Interpretation Introduction

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

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 5RQ

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.

When multiplication is performed, the final number will have number of significant figures equal to the minimum number of significant figures in the number involved in calculation. Here, 7342 has 4 significant figures and 6800 has 2 significant figures thus,

  $7342\times 6800$

  $=2\text{sig}\text{fig}\text{.}$

(d)

Interpretation Introduction

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

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 5RQ

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.

When multiplication is performed, the final number will have number of significant figures equal to the minimum number of significant figures in the number involved in calculation. Here, $4.00\times {10}^5$ has 3 significant figures, $3.14$ has 3 significant figures and $14.2$ has 3 significant figures thus,

  $4.00\times {10}^5\times 3.14÷14.2$

  $\text{=3sig}\text{fig}$ .