Chapter 0, Problem 0.49SP

(a)

Interpretation Introduction

Interpretation:

Answer for the given problem with correct number of significant figures has to be performed.

Concept Introduction:

Significant figures:

The total number of digits that are recorded for a measurement is named as measurements of number of significant figures.

Rules for significant figures:

• Zero present in the middle of number are always significant
  • Example: The number of significant figures in $\text{4}\text{.803 cm}$ is four.
• Zero present at the starting of a number are non-significant, they act to find the decimal point.
  • Example: The number of significant figures in $\text{0}\text{.0061g}$ is three.
• Zero present at the end of the number and after a decimal point are significant.
  • Example: The number of significant figures in $\text{55}\text{.220 K}$ is five.
• Zero present at the end of the number and before a decimal point are non-significant.
  • Example: The number of significant figures in $\text{34,200}$ m may be three, four or five.

Rounding off the significant figures:

• If the first digit is less than five, round down by dropping it and all succeeding digits
• If the first digit is greater than or equal to five, remove five and add one to the digit on the left.

Rounding off by calculations:

• On performing multiplications or divisions, answers could not have more significant figures than either of the original numbers.
• On performing addition or subtractions, answers could not have more digits to the right side of the decimal point than either of the original numbers.

(b)

Interpretation Introduction

Interpretation:

Answer for the given problem with correct number of significant figures has to be performed.

Concept Introduction:

Significant figures:

The total number of digits that are recorded for a measurement is named as measurements of number of significant figures.

Rules for significant figures:

• Zero present in the middle of number are always significant
  • Example: The number of significant figures in $\text{4}\text{.803 cm}$ is four.
• Zero present at the starting of a number are non-significant, they act to find the decimal point.
  • Example: The number of significant figures in $\text{0}\text{.0061g}$ is three.
• Zero present at the end of the number and after a decimal point are significant.
  • Example: The number of significant figures in $\text{55}\text{.220 K}$ is five.
• Zero present at the end of the number and before a decimal point are non-significant.
  • Example: The number of significant figures in $\text{34,200}$ m may be three, four or five.

Rounding off the significant figures:

• If the first digit is less than five, round down by dropping it and all succeeding digits
• If the first digit is greater than or equal to five, remove five and add one to the digit on the left.

Rounding off by calculations:

• On performing multiplications or divisions, answers could not have more significant figures than either of the original numbers.
• On performing addition or subtractions, answers could not have more digits to the right side of the decimal point than either of the original numbers.