Question

For each of the following numbers, if the number is rewritten in standard scientific notation, what will be the value of the exponent (for the power of 10)? a. $0.000067$ b. $9,331,442$ c. $1 / 10,000$ d. $163.1 \times 10^{2}$

Name: Problem 4, Chapter 5: World of Chemistry
Uploaded: 2023-08-31T08:54:52-08:00
Duration: 1 min 48 s
Channel: Lijeesh Krishnan
Description: For each of the following numbers, if the number is rewritten in standard scientific notation, what will be the value of the exponent (for the power of 10)? a. 0.000067 b. 9,331,442 c. 1 / 10,000 d. 163.1 ×10^2

   For each of the following numbers, if the number is rewritten in standard scientific notation, what will be the value of the exponent (for the power of 10)?
a. $0.000067$
b. $9,331,442$
c. $1 / 10,000$
d. $163.1 \times 10^{2}$

World of Chemistry

Steven S.Zumdahl,… 1st Edition

Chapter 5, Problem 4

Instant Answer

Solved by Expert Lijeesh Krishnan

08/31/2023

Step 1

Scientific notation is a way of expressing numbers that are too big or too small to be conveniently written in decimal form. It is commonly used by scientists, mathematicians and engineers. The format for writing a number in scientific notation is $a \times Show more…

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For each of the following numbers, if the number is rewritten in standard scientific notation, what will be the value of the exponent (for the power of 10)? a. $0.000067$ b. $9,331,442$ c. $1 / 10,000$ d. $163.1 \times 10^{2}$

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Key Concepts

Normalization

Normalization is the process of transforming a given number into standard scientific notation by adjusting its decimal point so that the coefficient is within the range of 1 to 10. The number of places the decimal shifts directly determines the power of 10, which is represented by the exponent.

Scientific Notation

Scientific notation is a compact way of writing numbers, especially very large or very small ones, as the product of a coefficient (between 1 and 10) and a power of 10. This method simplifies calculations and comparisons by standardizing the representation of numbers.

Exponent in Scientific Notation

The exponent indicates the number of places the decimal point must be moved to normalize the number's coefficient between 1 and 10. A positive exponent means the decimal point is moved to the left, while a negative exponent shows movement to the right, thereby representing the scale of the number.

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