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Chapter 9: Problem 23

Use a calculator to find each of the following to four decimal places. $$ 10^{-2.9523} $$

Short Answer

Expert verified
0.0011

Step by step solution

01

Understand the Expression

The expression to evaluate is given as an exponent with a base of 10. The task is to find the value of this expression.
02

Use a Calculator

Input the expression into a calculator. On most scientific calculators, you can input the expression as follows: 10 ^ (-2.9523).
03

Compute the Result

After entering 10 raised to the power of -2.9523 into the calculator, press the '=' or 'enter' button to compute.
04

Rounding the Result

The calculator provides a result. Round this result to four decimal places as required by the exercise.

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Key Concepts

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

Scientific Notation
Scientific notation is a way to express very large or very small numbers. It simplifies numbers using powers of 10. For instance, instead of writing 0.0001, you can write it as 1 x 10^{-4}. Scientific notation is helpful in many fields such as science and engineering.
When you encounter an expression like 10^{-2.9523}, it means that you are dealing with a power of 10. Here, 10 is the base, and -2.9523 is the exponent. This tells us that we are working with a small number.
To handle such expressions easily, you can use a calculator, as it simplifies the process of computation.
Calculator Usage
Calculators are a great tool for computing complex mathematical expressions, including exponentiation. Here is how you can use a scientific calculator to solve the expression 10^{-2.9523}:
  • First, turn on your calculator.
  • Then, find the exponentiation function, which is often denoted as '^' or sometimes as '**'.
  • Input the base value, which is 10 in this case.
  • Next, enter the exponent, which is -2.9523.
  • Finally, press the '=' or 'enter' button to get the result.
Following these steps should give you the computed value. Calculators can quickly and accurately solve these kinds of problems, saving you time and effort.
Rounding Numbers
Rounding numbers is an important skill, especially when you need to present data or results concisely. To round a number to a certain number of decimal places, follow these easy steps:
  • Identify the decimal place to which you need to round the number.
  • Look at the digit immediately following this place.
  • If this digit is 5 or higher, round up. If it is 4 or lower, round down.
For example, let鈥檚 say your calculator gives you the answer 0.00112256 for 10^{-2.9523}.
To round this to four decimal places, you would:
  • Identify the fourth decimal place: 0.0011
  • Look at the next digit, which is 2.
  • Since 2 is less than 5, you keep the fourth decimal place as is.
Therefore, the rounded result is 0.0011. Rounding makes numbers easier to read and work with, especially when dealing with precise data.

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Most popular questions from this chapter

Let \(c(w)\) represent the cost of mailing a package that weighs \(w\) pounds. Let \(f(n)\) represent the weight, in pounds, of \(n\) copies of a certain book. Explain what \((c \circ f)(n)\) represents.

The net amount of e-book sales, in millions of dollars, can be estimated by $$ S(t)=2.05(1.8)^{t} $$ where \(t\) is the number of years after 2002 Data: Association of American Publishers a) In what year was there 8 billion dollars in e-book net sales? b) Find the doubling time.

Students in an English class took a final exam. They took equivalent forms of the exam at monthly intervals thereafter. The average score \(S(t),\) in percent, after \(t\) months was found to be $$ S(t)=78-20 \log (t+1), \quad t \geq 0 $$ a) What was the average score when they initially took the test, \(t=0 ?\) b) What was the average score after 4 months? after 24 months? c) Graph the function. d) After what time \(t\) was the average score \(60 \% ?\)

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Solve $$ \log _{x} 9=\frac{1}{2} $$
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