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Chemistry & Chemical Reactivity

10th Edition
John C. Kotz + 3 others
ISBN: 9781337399074

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BuyFindarrow_forward

Chemistry & Chemical Reactivity

10th Edition
John C. Kotz + 3 others
ISBN: 9781337399074
Textbook Problem

Carry out the following operations. Provide the answer with the correct number of significant figures.

  1. (a) (1.52)(6.21 × 10_3)
  2. (b) (6.217 ×103)—(5.23 × 102)
  3. (c) (6.217 × 103) ÷ (5.23 × 102)
  4. (d) ( 0.0546 ) ( 160000 ) [ 7.779 55.85 ]

(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.

Explanation

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

(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.

(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.

(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.

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