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Chapter 1: Problem 22

Write each number in decimal form. \(8.67 \times 10^{2}\)

Short Answer

Expert verified
The decimal form of the number is 867.

Step by step solution

01

Identify the Base Number

The base number here is 8.67. This number is what's going to be adjusted based on the exponent provided.
02

Understand the Exponent

The exponent in this problem is 2, which indicates how many places the decimal point should move. Since it is positive, the decimal point will move to the right.
03

Move the Decimal Point

Starting with 8.67, move the decimal point 2 places to the right to account for the exponent 2. This transforms the number to 867. If the exponent were negative, we would move the decimal point to the left instead.
04

Write the Final Result

After moving the decimal point, the number in decimal form is 867. This is the original number adjusted according to the given exponent.

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Key Concepts

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

Decimal Representation
When we talk about decimal representation, we essentially refer to expressing numbers in their base-10 form. This is the common way we write numbers every day. In the original exercise, you have a number represented as a product involving a base number and a power of ten, specifically in the form of scientific notation. For example, the decimal form of the scientific notation \(8.67 \times 10^{2}\) involves adjusting the base number 8.67 by moving its decimal point. To convert it into a straightforward or decimal number, you follow the instructions given by the exponent, which helps in deciding how and where to shift the decimal point.
Exponent Rules
Understanding exponent rules is key to mastering scientific notation. An exponent tells you how many times a base number is used as a factor. In this exercise, the exponent is 2. This means you multiply the base number, 8.67, by
  • 10 once (\(10^1\)), leading to 86.7,
  • then multiply 86.7 by 10 again (\(10^2\)), arriving at 867.

In essence, each step multiplies your answer from the last by 10. Remember:
  • A positive exponent tells you to move the decimal to the right.
  • A negative exponent would mean moving the decimal to the left, dividing by powers of ten instead.
Multiplying by Powers of Ten
The multiplication by powers of ten is essential in transforming a base number in scientific notation into its decimal form. The base number is 8.67 and it is multiplied by \(10^2\) which influences the movement of the decimal. Each increase by 1 in the exponent shifts the decimal one place to the right, effectively multiplying by 10.
  • In our example, \(10^2\) means moving the decimal two places to the right, making the number larger.
  • The original place of the decimal point is after the '8', as in 8.67. After moving it two places right, it becomes 867.

This simple operation allows for easy transitions between small and large numbers, making calculations and estimations more manageable.

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Most popular questions from this chapter

Use the rules for addition of measurements to add each set of measurements. $$ 12 \mathrm{~s} ; 1.004 \mathrm{~s} ; 0.040 \mathrm{~s} ; 3.9 \mathrm{~s} ; 0.87 \mathrm{~s} $$

Use the rules for division of measurements to divide. $$ 185 \mathrm{mi} \div 4.5 \mathrm{~h} $$

Determine the accuracy (the number of significant digits) of each measurement. \(7 \mathrm{~N}\)

Use the rules for subtraction of measurements to subtract each second measurement from the first. $$ \begin{array}{r} 14.73 \mathrm{~m} \\ 9.378 \mathrm{~m} \\ \hline \end{array} $$

Use the rules for multiplication and division of measurements to find the value of each of the following. $$ \frac{(45.2 \mathrm{~kg})(13.7 \mathrm{~m})}{(2.65 \mathrm{~s})^{2}} $$
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