# Express each of the following in decimal notation: a. 6.022 × 10 23 (number of carbon atoms in 12.01 grams of carbon) b. 3.00 × 10 8 m/s (speed of light) c. 450 × 10 − 9 m (wavelength of blue light) d. 13.7 × 10 9 yr (approximate age of the universe)

### Chemistry In Focus

7th Edition
Tro + 1 other
Publisher: Cengage Learning,
ISBN: 9781337399692

Chapter
Section

### Chemistry In Focus

7th Edition
Tro + 1 other
Publisher: Cengage Learning,
ISBN: 9781337399692
Chapter 2, Problem 18E
Textbook Problem
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## Express each of the following in decimal notation:a. 6.022 × 10 23 (number of carbon atoms in 12.01 grams of carbon)b. 3.00 × 10 8 m/s (speed of light)c. 450 × 10 − 9 m (wavelength of blue light)d. 13.7 × 10 9 yr (approximate age of the universe)

Interpretation Introduction

Interpretation:

Each number is to be expressed in decimal notation.

Concept introduction:

Decimal notation is a system in which the numbers expressed in the scientific notation are written in the form of large or small numbers containing many zeros.

If the exponent is positive, the decimal is shifted to the right to many places and zeros are written, if there are not enough digits.

If the exponent is negative, the decimal is shifted to the left to many places and zeros are written, if there are not enough digits.

### Explanation of Solution

a) 6.022×1023 (number of carbon atoms in 12.01 grams of carbon)

To convert 6.022×1023 into decimal notation, multiply 6.022 by 1000,000,000,000,000,000,000,00 because the exponent is positive in this case. The expression for 6.022×1023 in decimal notation is written as follows:

6.022×100000000000000000000000=602,200,000,000,000,000,000,000

Thus, the decimal notation for 6.022×1023 is 602,200,000,000,000,000,000,000.

b) 3.00×108m/s (speed of light)

To convert 3.00×108m/s into decimal notation, multiply 3.00 by 100000000 because the exponent is positive in this case. The expression for 3.00×108m/s in decimal notation is written as follows:

3.00×100000000=300,000,000 m/s

Thus, decimal notation for 3.00×108m/s is 300,000,000 m/s

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