# Express each of the following numbers in scientific notation: a. 19,570,261 (population of New York state) b. 7,190,900,000 (world population) c. 0.00000000007461 m (length of a hydrogen- hydrogen chemical bond) d. 0.000015 m (diameter of a human hair)

### 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 16E
Textbook Problem
302 views

## Express each of the following numbers in scientific notation:a. 19,570,261 (population of New York state)b. 7,190,900,000 (world population)c. 0.00000000007461 m (length of a hydrogen- hydrogen chemical bond)d. 0.000015 m (diameter of a human hair)

Interpretation Introduction

Interpretation:

Each number is to be expressed in the scientific notation.

Concept introduction:

Scientific notations are used to express a large number in a compact form.

Scientific notation consists of two parts, a decimal part (a number between 1 to 10) and an exponential part (10 raised to an exponent).

Following steps should be considered to express any number in scientific notation:

The decimal point is moved in order to obtain the number between 1 and 10.

The exponent can either be positive or negative based on the direction of movement of decimal.

If the direction of movement of the decimal is to the right, the exponent will be negative and the direction of movement of decimal is to the left, the exponent will be positive.

### Explanation of Solution

a) 19,570,261 (population of New York state)

The number is 19,570,261. For obtaining a number between 1 and 10, move the decimal point to the left by 7 decimal places. Thus, the exponent is 7 and its sign will be positive as the decimal point is moved to the left. Hence, scientific notation for 19,570,261 is 1.9570261×107 .

b) 7,190,900,000 (world population)

The number is 7,190,900,000. For obtaining a number between 1 and 10, move the decimal point to the left by 9 decimal places. Thus, the exponent is 9 and its sign will be positive as the decimal point is moved to the left. Hence, scientific notation for 7,190,900,000 is 7.190900000×109

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