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Chapter 8: Problem 85

Express the given number in scientific notation. $$28,700$$

Short Answer

Expert verified
2.87 脳 10^4

Step by step solution

01

- Identify the Coefficient and the Base

First, find a number between 1 and 10 by moving the decimal point in the original number 28,700. This gives 2.87.
02

- Determine the Exponent

Count the number of places the decimal point has been moved. From 28,700, the decimal was moved 4 places to the left. Thus, the exponent is 4.
03

- Write in Scientific Notation

Combine the coefficient (2.87) with the base 10 raised to the power of the exponent (4). Thus, 28,700 in scientific notation is written as \(2.87 \times 10^4\).

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Key Concepts

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

Coefficient
In scientific notation, the coefficient is a crucial part. It is the number that is multiplied by 10 raised to an exponent power. The coefficient must be a number between 1 and 10. For example, in the number 28,700, after moving the decimal point, we get 2.87 as the coefficient.
  • The coefficient tells us how many significant digits are in the number.
  • It ensures that the notation is in its simplest form.
You determine the coefficient by placing the decimal point after the first non-zero digit. This simplifies larger numbers, making them easier to work with.
Exponent
The exponent in scientific notation tells us how many times the base (10) is multiplied by itself. It is a positive or negative integer. For the number 28,700, the exponent is found by counting the places the decimal point was moved to get the coefficient.
Since we moved the decimal point 4 places to the left, the exponent is 4.
  • If the decimal is moved to the left, the exponent is positive.
  • If moved to the right, the exponent is negative.
Exponents help in expressing very large or very small numbers compactly.
Decimal Point
The position of the decimal point is a key element in converting a number to scientific notation. By moving the decimal point, you create the coefficient that falls between 1 and 10. In the example of 28,700, moving the decimal point 4 places to the left forms the coefficient 2.87.
  • Moving the point adjusts the scale of the number.
  • This shift is balanced by the exponent, which keeps the number's value unchanged.
Understanding decimal point adjustments is vital for mastering scientific notation.

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Most popular questions from this chapter

Explain how you would generalize the long division process to handle $$\frac{5 x^{4}-8 x^{3}+7 x^{2}-2 x+1}{x^{2}+x-1}$$

Simplify the expression and express your final answer with positive exponents only. $$\left(x^{3}\right)^{4}$$

Divide each of the following. Use the long division process where necessary. $$\frac{4 t^{3}-33 t+24}{2 t-5}$$

Perform the indicated operations and simplify. $$\left(5 x^{2} y\right)^{2}$$

Factor each of the following expressions as completely as possible. If an expression is not factorable, say so. $$10 x^{2}-40 x y-120 y^{2}$$
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