Chemistry for Engineering Students
Chemistry for Engineering Students
3rd Edition
ISBN: 9781285199023
Author: Lawrence S. Brown, Tom Holme
Publisher: Cengage Learning
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Chapter 1, Problem 1.46PAE

Perform these calculations and express the result with the proper number of significant figures.

(a) ( 4.850  g 2 .34 g ) / 1.3  mL

(b) V = π r 3 , where r = 4.112  cm

(c) ( 4.66 × 10 3 ) × 4.666

(d) 0.003400/65.2

Expert Solution
Check Mark
Interpretation Introduction

(a)

To perform:

The calculations of (4.850g2.34g)1.3mLand express the result in proper number of significant figure.

Explanation of Solution

First, set the rules for “significant numbers”

  • zeroes to the left are not significant.
  • zeroes to the right are not significant if not specified as “exact” zeroes.
  • all other digits other than zero are significant.
  • zeroes between non-zero numbers are significant.

Second, define the addition/subtraction and multiplication/division rules for significant numbers.

  • Addition/Subtraction ( Always keep the least significant number after the decimal point.
  • Multiplication/Division ( Always keep the least significant number of the whole number.
  • If addition/subtraction and Multiplication/division are included, separate the operation to simple operations and keep following the rules.

Now, for the given operation.(4.850g2.34g)1.3mL

Perform subtraction.2.510g1.3mL

Since there are only two significant digits after the decimal, keep only 2 significant figures in the product.2.51g1.3mL

Now, for multiplication, perform total operation.

1.9307gmL

According to sig. fig. rules, we must keep only 2 sig. fig. since that is the least amount of sig. fig. for 1.3 mL. Round if required.

1.93gmL

Rounding is required. Report:

1.9gmL.

Expert Solution
Check Mark
Interpretation Introduction

(b)

To perform:

The calculations of V=πr3;r = 4.112 cmand express the result in proper number of significant figure.

Explanation of Solution

First, set the rules for “significant numbers”

  • zeroes to the left are not significant.
  • zeroes to the right are not significant if not specified as “exact” zeroes.
  • all other digits other than zero are significant.
  • zeroes between non-zero numbers are significant.

Second, define the addition/subtraction and multiplication/division rules for significant numbers.

  • Addition/Subtraction ( Always keep the least significant number after the decimal point.
  • Multiplication/Division ( Always keep the least significant number of the whole number.
  • If addition/subtraction and Multiplication/division are included, separate the operation to simple operations and keep following the rules.

Now, for the given operation. SubstituteV=πr3;r=4.112cm

V=πx(4.112cm)3

Assume that pi is actually an exact number, i.e. has infinite amount of significant figures.

V=218.42839cm3

According to sig. fig. rules, we must keep only 4 sig. fig. since that is the least amount of significant figures for 4.112. Round if requiredV=218.4cm3

Expert Solution
Check Mark
Interpretation Introduction

(c)

To perform:

The calculations of (4.66x10-3)x4.666and express the result in proper number of significant figure.

Explanation of Solution

First, set the rules for “significant numbers”

  • zeroes to the left are not significant.
  • zeroes to the right are not significant if not specified as “exact” zeroes.
  • all other digits other than zero are significant.
  • zeroes between non-zero numbers are significant

Second, define the addition/subtraction and multiplication/division rules for significant numbers.

  • Addition/Subtraction ( Always keep the least significant number after the decimal point.
  • Multiplication/Division ( Always keep the least significant number of the whole number.
  • If addition/subtraction and Multiplication/division are included, separate the operation to simple operations and keep following the rules.

Now, for the given operation. Perform calculation(4.66x103)x4.66621743.56

Total sig. fig. reported are 3, for 4.66.

Round if required21743.5621400

It can also be reported in scientific notation.2.14x104.

Expert Solution
Check Mark
Interpretation Introduction

(d)

To perform:

The calculations of 0.00340065.2and express the result in proper number of significant figure.

Explanation of Solution

First, set the rules for “significant numbers”.

  • zeroes to the left are not significant.
  • zeroes to the right are not significant if not specified as “exact” zeroes.
  • all other digits other than zero are significant.
  • zeroes between non-zero numbers are significant.

Second, define the addition/subtraction and multiplication/division rules for significant numbers.

  • Addition/Subtraction ( Always keep the least significant number after the decimal point.
  • Multiplication/Division ( Always keep the least significant number of the whole number.
  • If addition/subtraction and Multiplication/division are included, separate the operation to simple operations and keep following the rules.

Now, for the given operation. Perform calculation0.00340065.2=0.000052147

Total sig. fig. are 4 for 0.003400 and 3 for 65.2. Choose 3 significant figures in total.

Round if required 0.000052140.0000521

Conclusion

Always ensure to keep the correct significant numbers when performing addition, subtraction, multiplication and division. It is relevant to keep track of accuracy in the measurements.

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Chapter 1 Solutions

Chemistry for Engineering Students

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