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 1.47PAE

1.43 Calculate the following to the correct number of significant figures. Assume that all these numbers are measurements.

(a) x = 17.2 + 65.18 2.4

(b) x = 13.0217 / 17.10

(c) x = ( 0.0061020 ) ( 2.0092 ) ( 1200.00 )

(d) x = 0.0034 + ( 0.0034 ) 2 + 4 ( 1.000 ) ( 6.3 × 10 1 ) ( 2 ) ( 1.000 )

(a)

Expert Solution
Check Mark
Interpretation Introduction

To perform: The calculations of 17.2+65.182.4and 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.17.2+65.182.4

17.2+65.182.4=79.98

We must keep only 1 significant figure after the decimal. Round if required79.9880.0

(b)

Expert Solution
Check Mark
Interpretation Introduction

To perform: The calculations of x=13.0217/17.10and 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. Substitute13.0217/17.10

0.7615029

According to the rules, we must keep the number with the least sig. fig. This is 17.10, with only 4 significant figure then0.76150290.7615

(c)

Expert Solution
Check Mark
Interpretation Introduction

To perform: The calculations of (0.0061020)(2.0092)(1200.00)and 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(0.0061020)(2.0092)(1200.00)14.712166

The significant figures are given as:0.006102052.009251200.006

We must keep the smallest amount of sig. fig. for multiplication, therefore, choose 5.14.71216614.712

(d)

Expert Solution
Check Mark
Interpretation Introduction

To perform: The calculations of 0.0034+ (0.0034)2+4(1.000)(6.3x 10 4)(2)(1.000)and 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 calculation0.0034+ (0.0034) 2 +4(1.000)(6.3x 10 4 )(2)(1.000)0.0034+ 0.000012+25.2x 10 4 2.0000.0034+ 0.12x 10 4 +25.2x 10 4 2.000

For the inside addition, keep only 1 significant figure after the digit, since 0.12 has 2 significant figures after the digit and 25.2 has only 1.0.0034+25.32x 10 42.0000.0034+25.3x 10 42.000

When performing the inside of the square root0.0034+0.0502992.0000.0034+0.05032.000

Then, continue with the division. Keep the least amount of significant figures in total.0.0034+0.025150.0034+0.0252

Now, add all.0.0034+0.0252=0.0286

Keep the least amount of significant figures after the decimal point. Which is 4 for both amounts.0.0286

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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