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Chapter 10: Problem 48

For Exercises \(33-48,\) convert to scientific notation. $$13,400$$

Short Answer

Expert verified
1.34 脳 10^4

Step by step solution

01

Identify the Significant Figures

Determine the significant figures of the number. In the number 13,400, the significant figures are 1, 3, and 4.
02

Place the Decimal Point

Place the decimal point after the first significant figure. In this case, place the decimal point after 1: 1.3400
03

Determine the Exponent

Count the number of places the decimal point has been moved from its original position to get the number between 1 and 10. The decimal point has been moved 4 places to the left.
04

Write in Scientific Notation

Combine the significant figure identified in step 1 with the exponent determined in step 3: 13,400 = 1.34 脳 10^4 (The trailing zeros can be ignored as they do not affect the significant figures.)

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

significant figures
Significant figures are the digits in a number that carry meaningful information about its precision. These are the non-zero digits as well as any zeros between them or trailing zeros in a decimal number. Understanding significant figures helps you maintain the accuracy of a number when converting it.
In the number 13,400, the significant figures are 1, 3, and 4, because they hold meaningful values.
Knowing which digits are significant is crucial for the next steps in converting a number to scientific notation.
decimal point
A decimal point separates the whole number part from the fractional part of a number. When converting to scientific notation, we need to place the decimal point immediately after the first significant figure.
For example, in 13,400, we place the decimal point after the 1 to get 1.3400.
This helps in creating a new number that is between 1 and 10, which is a key characteristic of scientific notation.
exponent
The exponent in scientific notation represents the number of places the decimal point has moved. This is how we account for the scale of the original number. After placing the decimal point in 1.3400, we count how many places we moved it from its original position in 13,400.
The decimal moved 4 places to the left, so the exponent is 4.
The general format for scientific notation is: significant figure x 10^exponent. Here, it becomes 1.34 x 10^4, simplifying the large original number to a more manageable form.
powers of ten
Powers of ten are a fundamental concept in scientific notation. They allow us to express very large or very small numbers compactly. Each move of the decimal point to the left increases the exponent by 1, while a move to the right decreases it by 1.
When converting 13,400, the decimal point moves 4 places to the left, resulting in the power of ten, 10^4.
Powers of ten help in quickly understanding the scale of a number and make calculations easier.

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