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Chapter 8: Problem 78

Perform the operations and simplify. Leave answers in exponential form. \((y 3 / 4) 4 / 5\)

Short Answer

Expert verified
The simplified answer in exponential form is \( 4.725 \times 10^{-2} \).

Step by step solution

01

Divide the First Two Numbers

First, divide 93 by 491:\[ \frac{93}{491} \approx 0.189 \]
02

Divide the Result by 4

Now, take the result from step 1 and divide it by 4:\[ \frac{0.189}{4} \approx 0.04725 \]
03

Express in Exponential Form

Since we need to express the answer in exponential form, we convert 0.04725 to an exponential form:\[ 4.725 \times 10^{-2} \]

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Key Concepts

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

Division Operations
Division is a basic arithmetic operation where you split a number into equal parts. In the context of our exercise, we're dividing three numbers in sequence. The key idea is to approach the problem step-by-step. Breaking it down makes it easier to handle and understand.
Here's how you can tackle a complex division problem:
  • Start by dividing the first number by the second number. This reduces the larger problem into a smaller one.
  • Take the result and divide it by the next number. Continue in this way until you've divided by all numbers in sequence.
When dividing, it's important to keep track of precision, especially when you're dealing with decimals. Remember, accuracy in these calculations is crucial because small errors can lead to significantly different results.
Number Conversion
Number conversion is transforming a number from one form to another. In this exercise, we need to convert a decimal number into its exponential form. This is especially useful when dealing with very large or very small numbers.
Exponential notation works by expressing numbers as a product of a number between 1 and 10, and a power of ten. It's a shorthand that makes it easier to write and work with such numbers. For example:
  • Decimal to exponential: To convert 0.04725, we look for a way to express it as a number times a power of ten. Thus, 0.04725 becomes 4.725 multiplied by 10 raised to the power of -2.
This conversion reduces writing complexity and helps you easily compare different magnitudes of numbers.
Problem-Solving Steps
Breaking down complex operations into smaller, manageable steps is key in solving math problems effectively. Let鈥檚 take this exercise as an example:
  • Step 1: Start with dividing the first two numbers. This sets a foundation for the subsequent steps.
  • Step 2: Use the outcome from the first division. Divide this result by the next number (in this case, 4). This allows the problem to be solved incrementally.
  • Step 3: Convert the final division result into exponential form. This conforms to the problem's requirements and ensures the answer is consistent in presentation.
Approaching problems in this step-by-step manner reduces errors and makes tackling difficult problems less intimidating. It ensures that you systematically arrive at the solution with clarity and confidence.

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Most popular questions from this chapter

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