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Introduction to General, Organic a...

11th Edition
Frederick A. Bettelheim + 4 others
Publisher: Cengage Learning
ISBN: 9781285869759

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Chapter
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BuyFindarrow_forward

Introduction to General, Organic a...

11th Edition
Frederick A. Bettelheim + 4 others
Publisher: Cengage Learning
ISBN: 9781285869759
Chapter 1.3, Problem 1.1P
Textbook Problem
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Problem 1-1

Multiply:

(a) ( 6.49 × 10 7 ) ( 7.22 × 10 3 )

(b) ( 3.4 × 10 5 ) ( 8.2 × 10 11 )

Divide:

(a) 6.02 × 10 23 3.10 × 10 5

(b) 3.14 2.30 × 10 5

(a)

Interpretation Introduction

Interpretation:

Multiply the given numbers.

Concept Introduction:

Multiplication is an arithmetic operation of mathematics; the multiplication of a number is the repeated addition of that number.

Answer to Problem 1.1P

The product of the given multiply is 4.69×105 .

Explanation of Solution

Significant figures are the numbers which are reported by estimating a measurement.

The following are the rules that decide whether a zero is significant or not:

1. The zeroes present between two non-zero digits is significant.

2. A trailing zero within the decimal is significant.

3. Zeroes at the starting of a decimal number are not significant.

Some general rules for rounding data are as follows:

If the last digit, which needs to be rounded off precedes a number which is equal to or greater than 5, then add +1 to the last digit and report the resulting value.

If the last digit, which needs to be rounded off precedes a number which is lesser than 5 then, the last digit is left unchanged and the resulting value is reported.

For example; 0.000 012 58 L  contains 4 significant numbers, when it rounds off into three significant number then we add +1 in 5. Thus, the number is 0.000 012 6 L  which contains 3 significant numbers.

The given numbers can be multiplied as follows:

  (6.49×107)(7.22×103)=64900000×0.00722=468578=4.69×105

The answer has the minimum number of significant digits which is 3.

(b)

Interpretation Introduction

Interpretation:

Multiply the given numbers.

Concept Introduction:

Multiplication is an arithmetic operation of mathematics; the multiplication of a number is the repeated addition of that number.

Answer to Problem 1.1P

The product of the given multiply is 2.8×1015 .

Explanation of Solution

Significant figures are the numbers which are reported by estimating a measurement.

The following are the rules that decide whether a zero is significant or not:

1. The zeroes present between two non-zero digits is significant.

2. A trailing zero within the decimal is significant.

3. Zeroes at the starting of a decimal number are not significant.

Some general rules for rounding data are as follows:

If the last digit, which needs to be rounded off precedes a number which is equal to or greater than 5, then add +1 to the last digit and report the resulting value.

If the last digit, which needs to be rounded off precedes a number which is lesser than 5 then, the last digit is left unchanged and the resulting value is reported.

For example; 0.000 012 58 L  contains 4 significant numbers, when it rounds off into three significant number then we add +1 in 5. Thus, the number is 0.000 012 6 L  which contains 3 significant numbers.

The given numbers can be multiplied as follows:

  (3.4×105)(8.2×1011)=0.000034×0.000000000082=0.000000000000002788=2.788×1015=2.8×1015

The answer has the minimum number of significant digits which is 2.

Divide

(a)

Interpretation Introduction

Interpretation:

Divide the given numbers

Concept Introduction:

The numbers which are divided is known as dividend.

The number that is divides is called the divisor.

The answer of division is the quotient.

Multiply and division is reverse to each other.

Answer to Problem 1.1P

The quotient of the given division is 1.8×1018 .

Explanation of Solution

Significant figures are the numbers which are reported by estimating a measurement.

The following are the rules that decide whether a zero is significant or not:

1. The zeroes present between two non-zero digits is significant.

2. A trailing zero within the decimal is significant.

3. Zeroes at the starting of a decimal number are not significant.

Some general rules for rounding data are as follows:

If the last digit, which needs to be rounded off precedes a number which is equal to or greater than 5, then add +1 to the last digit and report the resulting value.

If the last digit, which needs to be rounded off precedes a number which is lesser than 5 then, the last digit is left unchanged and the resulting value is reported.

For example; 0.000 012 58 L  contains 4 significant numbers, when it rounds off into three significant number then we add +1 in 5. Thus, the number is 0.000 012 6 L  which contains 3 significant numbers.

The given numbers can be divided as follows:

  6.02×10233.1×105=6.02×102353.1=1.77×10181.8×1018

The answer has the minimum number of significant digits which is 2.

(b)

Interpretation Introduction

Interpretation:

Divide the given numbers

Concept Introduction:

The numbers which are divided is known as dividend.

The number that is divides is called the divisor.

The answer of division is the quotient.

Multiply and division is reverse to each other.

Answer to Problem 1.1P

The quotient of the given division is 1.37×105 .

Explanation of Solution

Significant figures are the numbers which are reported by estimating a measurement.

The following are the rules that decide whether a zero is significant or not:

1. The zeroes present between two non-zero digits is significant.

2. A trailing zero within the decimal is significant.

3. Zeroes at the starting of a decimal number are not significant.

Some general rules for rounding data are as follows:

If the last digit, which needs to be rounded off precedes a number which is equal to or greater than 5, then add +1 to the last digit and report the resulting value.

If the last digit, which needs to be rounded off precedes a number which is lesser than 5 then, the last digit is left unchanged and the resulting value is reported.

For example; 0.000 012 58 L  contains 4 significant numbers, when it rounds off into three significant number then we add +1 in 5. Thus, the number is 0.000 012 6 L  which contains 3 significant numbers.

The given numbers can be divided as follows:

  3.142.30×105=3.14×1052.30=136521.71.37×105

The answer has the minimum number of significant digits which is 3.

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Chapter 1 Solutions

Introduction to General, Organic and Biochemistry
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