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Chapter 5: Problem 85

Convert to decimal notation. $$ 8.02 \times 10^{-3} $$

Short Answer

Expert verified
0.00802

Step by step solution

01

Identify the Scientific Notation Components

Recognize the components of the scientific notation. Here, the number is written as \(8.02 \times 10^{-3}\).The number consists of a coefficient (8.02) and a power of 10 (-3).
02

Understand the Meaning of the Negative Exponent

A negative exponent indicates that the decimal point in the coefficient (8.02) needs to be moved to the left. The exponent tells us how many places to move the decimal point.
03

Move the Decimal Point

Shift the decimal point in the coefficient, 8.02, three places to the left. Since there are fewer than three digits to the left of the decimal point, use zeros to fill in the empty spaces: \(8.02 \rightarrow 0.00802\).

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Key Concepts

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

Coefficient
When working with scientific notation, the first number you see is called the coefficient. In the given problem, the number 8.02 is the coefficient. The coefficient represents a number between 1 and 10. It's essential because it helps normalize the size of any number. The coefficient tells us how many times we multiply or divide by 10 to get our original number. This straightforward format makes it much easier to handle very large or small numbers in calculations.
Negative Exponent
A negative exponent indicates that the number should be divided by 10 multiple times. For example, in the problem, we have an exponent of -3. This negative sign means we need to divide 8.02 by 10 three times. In scientific notation, negative exponents shift the decimal point to the left. Each shift to the left decreases the number's value, making it a small fraction. So, a negative exponent helps in transforming large or decimal numbers into a more manageable form.
Move the Decimal Point
To convert from scientific notation to decimal form, you need to move the decimal point in the coefficient as many places as indicated by the exponent. In our example, the coefficient is 8.02, and the exponent is -3. The negative exponent tells us to move the decimal point three places to the left. Since 8.02 only has one digit before the decimal point, we add zeros to create space: After moving the decimal point, the number becomes 0.00802. This process helps in visualizing and converting the numbers easily.

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