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Chapter 6: Problem 563

Convert each number to decimal form. $$3.8 \times 10^{-2}$$

Short Answer

Expert verified
0.038

Step by step solution

01

Understand the Scientific Notation

The number is given in scientific notation: $$3.8 \times 10^{-2}$$. In this form, the number consists of a coefficient (3.8) and an exponent (-2) applied to the base 10.
02

Interpret the Exponent

The exponent (-2) indicates that the decimal point in the coefficient (3.8) should be moved 2 places to the left.
03

Move the Decimal Point

Start with the number 3.8. Moving the decimal point 2 places to the left gives us: $$0.038$$.

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Key Concepts

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

Decimal Conversion
In many mathematical and scientific problems, numbers are often represented in scientific notation for simplicity. However, to better understand and utilize these numbers in practical applications, converting them to decimal form is beneficial.
When you are given a number like 3.8 in scientific notation, it typically includes a coefficient (3.8) and an exponent that specifies the power of 10. The goal of decimal conversion is to transform this representation into a standard decimal number. In our example, the exponent is -2.
Here鈥檚 a quick guide:
  • Identify the coefficient.
  • Understand the exponent and its impact on the decimal point.
  • Properly adjust the position of the decimal point.
By following these steps, you can simplify the expression and make calculations much easier.
Exponent Interpretation
The exponent in scientific notation plays a crucial role in determining the position of the decimal point. In our example, \(3.8 \times 10^{-2}\), the exponent is -2. Here are the steps to interpret it:
  • If the exponent is positive, it indicates how many places to move the decimal point to the right.
  • If the exponent is negative, it indicates how many places to move the decimal point to the left.

In this case, since the exponent is -2, you need to move the decimal point two places to the left. For positive exponents, the number gets larger, and for negative exponents, the number gets smaller. Understanding this is key to correctly converting scientific notation to decimal form.
Moving Decimal Points
Accurately moving the decimal point is the final step in converting scientific notation to a decimal number. Let's look at our example of \(3.8 \times 10^{-2}\). You should:
  • Start with the coefficient (3.8).
  • Account for the negative exponent (-2) by moving the decimal point two places to the left.
  • If there aren鈥檛 enough digits, add zeroes to fill the required spaces.

So, starting from 3.8, moving the decimal points two places to the left gives you 0.038. It鈥檚 helpful to remember that anytime you shift the decimal leftward, for each move left, you make the number smaller by a factor of 10.
This method ensures you precisely translate scientific notation into its corresponding decimal value, simplifying further calculations and interpretations.

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Most popular questions from this chapter

Divide each polynomial by the monomial. $$\frac{20 y^{2}+12 y-1}{-4 y}$$

Simplify. (a) \(b^{-5}\) (b) \(\left(k^{2}\right)^{-5}\)

Simplify. (a) \(\left(\frac{7}{2}\right)^{-3}\) (b) \(\left(-\frac{3}{x y^{2}}\right)^{-3}\)

Divide each polynomial by the binomial. $$\left(y^{2}-3 y-15\right) \div(y-8)$$

Divide each polynomial by the binomial. $$\left(x^{2}-14 x+49\right) \div(x-7)$$
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