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Chapter 7: Problem 49

Do your computation using scientific notation. $$(0.004)(250)$$

Short Answer

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Step by step solution

01

- Convert to Scientific Notation

Convert each number to scientific notation.\(0.004 = 4 \times 10^{-3}\)\(250 = 2.5 \times 10^2\)
02

- Multiply the Coefficients

Multiply the coefficients of the numbers:\(4 \times 2.5 = 10\)
03

- Add the Exponents

Add the exponents of the powers of 10:\((-3) + 2 = -1\)
04

- Combine the Results

Combine the results from steps 2 and 3 to get the final answer in scientific notation:\(10 \times 10^{-1} = 1.0\)

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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 conveniently. It consists of two main components:
  • A coefficient: a number between 1 and 10.
  • An exponent: a power of 10.
For example, instead of writing 0.004, you can use scientific notation to write it as \(4 \times 10^{-3}\). This method is especially useful in fields like science and engineering, where you often deal with extremely large or small values.
coefficients multiplication
When multiplying numbers in scientific notation, the first step is to multiply their coefficients.
For example, consider the problem \((0.004)(250)\). Both numbers need to be converted into scientific notation:
  • \( 0.004 = 4 \times 10^{-3}\)
  • \(250 = 2.5 \times 10^2 \)
Now, multiply the coefficients:
\[ 4 \times 2.5 = 10\] This simplifies the process and keeps you on the path to the final answer.
exponents addition
Once you've multiplied the coefficients, the next step is to handle the powers of 10 by adding their exponents.
Continuing with our example, you have:
  • \(4 \times 10^{-3}\)
  • \(2.5 \times 10^2\)
After multiplying the coefficients:
\[4 \times 2.5 = 10\] you need to add the exponents:
\[ -3 + 2 = -1 \] This step helps you maintain the integrity of scientific notation by adjusting the power of 10 correctly.
elementary algebra
Combining coefficients and exponents in scientific notation relies on elementary algebra concepts.
From our example:
After multiplying \(4 \times 2.5 = 10\) and adding exponents \(-3 + 2 = -1\), you finally combine these results:
\[ 10 \times 10^{-1} = 1.0 \] Elementary algebra principles help you simplify and combine the terms efficiently, ensuring you reach the correct answer.

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