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Chapter 10: Problem 35

For Exercises \(33-48,\) convert to scientific notation. $$8,100,000$$

Short Answer

Expert verified
8.1 脳 10^6

Step by step solution

01

Identify the significant figures

The significant figures in the number 8,100,000 are 8.1. Locate the decimal point to the right of the first significant figure to convert it to a number between 1 and 10.
02

Determine the exponent

Count the number of places the decimal point must move to get from 8,100,000 to 8.1. Here, the decimal point moves 6 places to the left.
03

Write in scientific notation

Combine the significant figure and the exponent to write the number in scientific notation. Since the decimal moved 6 places to the left, the exponent is positive. The scientific notation for 8,100,000 is: \( 8.1 \times 10^6 \)

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Key Concepts

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

Significant Figures
Understanding significant figures is essential when converting numbers to scientific notation. Significant figures are the digits in a number that contribute to its precision. These include all non-zero digits, any zeros between significant digits, and any trailing zeros in the decimal part. For example, in the number 8,100,000, only the digits 8 and 1 are considered significant when written as 8.1 in scientific notation. This simplification makes it easier to understand and work with large numbers. Being precise with significant figures helps raise accuracy and clarity across scientific calculations.
Decimal Point
The position of the decimal point is crucial when converting a number to scientific notation. It requires moving the decimal to a location immediately to the right of the first significant figure, turning the number into a value between 1 and 10. For instance, in converting 8,100,000 to scientific notation, the decimal point is initially absent in the integer form. We mentally place it at the end of the number (8,100,000.), then move it 6 places to the left until we place it just after the 8, creating 8.1. Simplifying the number like this makes it a lot more manageable to work with in calculations.
Exponent
The exponent in scientific notation signifies how many times the base number (between 1 and 10) must be multiplied or divided by 10 to get back to the original number. After finding the significant figures and adjusting the decimal point, count the places you moved the decimal. Each place moved determines the exponent. For 8,100,000, moving the decimal 6 places left, the exponent becomes positive 6. The scientific notation form is then written as \( 8.1 \times 10^6 \). Remember, a positive exponent indicates a large number, while a negative exponent suggests a small number less than one.

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Most popular questions from this chapter

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