Chapter 5, Problem 6Q

Interpretation Introduction

(a)

Interpretation:

The value of $x$ in the following expression is to be calculated.

  $x=6.0246+2.01-5093.1$

Concept introduction:

Eachdigit of the number that isused to express it to desired degree of accuracy from initial first non-zero digit is called significant figure.The digit at rightmost place of quantity is most uncertain digit. The number of certain and uncertain digit in a quantity is considered as significant figures. Digits with more significant figures have more certainty in measurement.

The rules for the significant figures are as follows:

• All digits, except for zero are generally considered significant. For example, there are 2 significant figures (1 and 7) in 71.
• Zeros that are present between two digits, other than zero are always significant. Example 103.1403 has seven significant figures.
• Zeros present to the left of significant figures are not significant. For example, 0.00086 has only two significant figures (8 and 6).
• Trailing zeroes are used to set one decimal point are non-significant figures. For example, in7800 has 3 significant figures.
There are 3 significant figures in $7.80\times {10}^3$ .

Rules for calculation of significant figures are as follows:

• Operations such as addition and subtraction, result containsthe same number of decimal places as operand or measurement with minimum decimal places.
• In multiplication and division operations, result carries same number of significant figures as operand or measurement with minimum significant figures. While exact numbers have noeffect on number of significant digits in the final answer.

Interpretation Introduction

(b)

Interpretation:

The value of $y$ in the following expression is to be determined.

  $y=0.0046\times 3.9870\times 456.9$

Concept introduction:

Each digit of the number that is used to express it to desired degree of accuracy from initial first non-zero digit is called significant figure. The digit at rightmost place of quantity is most uncertain digit. The number of certain and uncertain digit in a quantity is considered as significant figures. Digits with more significant figures have more certainty in measurement.

The rules for the significant figures are as follows:

• All digits, except for zero are generally considered significant. For example, there are 2 significant figures (1 and 7) in 71.
• Zeros that are present between two digits, other than zero are always significant. Example 103.1403 has seven significant figures.
• Zeros present to the left of significant figures are not significant. For example, 0.00086 has only two significant figures (8 and 6).
• Trailing zeroes are used to set one decimal point are non-significant figures. For example, in7800 has 3 significant figures.
There are 3 significant figures in $7.80\times {10}^3$ .

Rules for calculation of significant figures are as follows:

• Operations such as addition and subtraction,the result contains the same number of decimal places as operand or measurement with minimum decimal places.
• In multiplication and division operations, the result carries the same number of significant figures as operand or measurement with minimum significant figures. While exact numbers have noeffect on number of significant digits in final answer.