Chemistry & Chemical Reactivity
Chemistry & Chemical Reactivity
9th Edition
ISBN: 9781305176461
Author: Kotz
Publisher: Cengage
Question
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Chapter L, Problem 25PS

(a)

Interpretation Introduction

Interpretation: The correct number of significant figure for 1.52 and 9.44×103 has to be provided.

Concept Introduction:

Significant of zeroes:

  • Zeroes between two other significant digits are significant.
  • Zeroes to the right of a nonzero number, and also to the right of decimal place, are significant.
  • Zeroes that are placeholders are not significant.

Rules used for significant figures in calculations:

Rule 1: When adding or subtracting numbers, the number of decimal places in the answer is equal to the number of decimal places in the number with fewest digits after the decimal.

Rule 2: In multiplication or division, the number of significant figures in the answer is determined by the quantity with the fewest significant figures.

Rule 3: When a number is rounded off, the last digit to be retained is increased by one only if the following digit is 5 or greater.

(a)

Expert Solution
Check Mark

Answer to Problem 25PS

9.44×103; The number of significant figures is three.

Explanation of Solution

In 1.52, the decimal numbers with no zeroes and has only the significant numbers.  So, the significant number is 3.

In 6.21×103, the decimal numbers with no zeroes and has only the significant numbers. So, the significant number is 3.

The multiplication of 1.52 and 9.44×103:

  × 1.52      significantfigure3(6.21×103)significantfigure3_=9.4392×103 _

The number of significant figures should the answer contain is the fewest number of significant figures of the given quantity.  Both the quantity possesses same significant figures.  Hence, the answer should be written as 9.44×103.  The significant figure is three.

(b)

Interpretation Introduction

Interpretation: The correct number of significant figure for 6.217×1035.23×102 has to be provided.

Concept Introduction:

Significant of zeroes:

  • Zeroes between two other significant digits are significant.
  • Zeroes to the right of a nonzero number, and also to the right of decimal place, are significant.
  • Zeroes that are placeholders are not significant.

Rules used for significant figures in calculations:

Rule 1: When adding or subtracting numbers, the number of decimal places in the answer is equal to the number of decimal places in the number with fewest digits after the decimal.

Rule 2: In multiplication or division, the number of significant figures in the answer is determined by the quantity with the fewest significant figures.

Rule 3: When a number is rounded off, the last digit to be retained is increased by one only if the following digit is 5 or greater.

(b)

Expert Solution
Check Mark

Answer to Problem 25PS

5694; The number of significant figures is four.

Explanation of Solution

In 6.217×103, written as 6217 no decimal numbers; has only the significant numbers.  So, the significant number is 4.

In 5.23×102, written as 523 no decimal numbers and has only the significant numbers.  So, the significant number is 3.

The subtraction of 6217 and 523:

  -   6217 decimal places0523      decimal places 0_=5694    decimal places 0 _

The number of decimal places should the answer contain is the fewest decimal places of the given quantity.  Both the quantity possesses zero decimal places.  Hence, the answer should be written as 5694.  The significant figure is four.

(c)

Interpretation Introduction

Interpretation: The correct number of significant figure for 6.217×103÷5.23×102 has to be provided.

Concept Introduction:

Significant of zeroes:

  • Zeroes between two other significant digits are significant.
  • Zeroes to the right of a nonzero number, and also to the right of decimal place, are significant.
  • Zeroes that are placeholders are not significant.

Rules used for significant figures in calculations:

Rule 1: When adding or subtracting numbers, the number of decimal places in the answer is equal to the number of decimal places in the number with fewest digits after the decimal.

Rule 2: In multiplication or division, the number of significant figures in the answer is determined by the quantity with the fewest significant figures.

Rule 3: When a number is rounded off, the last digit to be retained is increased by one only if the following digit is 5 or greater.

(c)

Expert Solution
Check Mark

Answer to Problem 25PS

11.9; The number of significant figures is three.

Explanation of Solution

In 6.217×103, writes as 6217 has no decimal numbers with no zeroes and has only the significant numbers.  So, the significant number is 4.

In 5.23×102, written as 523 has no decimal numbers with no zeroes and has only the significant numbers.  So, the significant number is 3.

The division of 6217 and 523:

  ÷ 6217  significantfigure4 523 significantfigure3_=11.887  _

The number of significant figures should the answer contain is the fewest number of significant figures of the given quantity.  Out of both the quantity 523 possesses 3 significant figures.  Hence, the answer should be written as 11.9 (rounding off).  The significant figure is three.

(d)

Interpretation Introduction

Interpretation: The correct number of significant figure for (0.0546)(16.0000)[7.77955.85]  has to be provided.

Concept Introduction:

Significant of zeroes:

  • Zeroes between two other significant digits are significant.
  • Zeroes to the right of a nonzero number, and also to the right of decimal place, are significant.
  • Zeroes that are placeholders are not significant.

Rules used for significant figures in calculations:

Rule 1: When adding or subtracting numbers, the number of decimal places in the answer is equal to the number of decimal places in the number with fewest digits after the decimal.

Rule 2: In multiplication or division, the number of significant figures in the answer is determined by the quantity with the fewest significant figures.

Rule 3: When a number is rounded off, the last digit to be retained is increased by one only if the following digit is 5 or greater.

(d)

Expert Solution
Check Mark

Answer to Problem 25PS

0.122; The number of significant figures is three.

Explanation of Solution

The division and multiplication of:

  (0.0546)(16.0000)[7.77955.85] Multiplication of 0.0546 and 16.0000:_× 0.0546   significantfigure316.0000    significantfigure6_=0.874      significantfigure_Division of 7.779 and 55.85:_÷ 7.779    significantfigure4 55.85 significantfigure4_=0.1393 significantfigure_Finally,Mutiplication of 0.874 and 0.1393:_× 0.874   significantfigure30.1393   significantfigure4_=0.12174       _

Finally, on the multiplication of 0.874 and 0.1393 gives the value 0.12174.  Out of the two obtained quantity 0.874 possesses 3 significant figures.  Hence, the answer should be written as 0.122 (rounding off).  The significant figure is three.

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Chapter L Solutions

Chemistry & Chemical Reactivity

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