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Chapter 4: Problem 41

Express answers in standard notation. $$ \frac{20,000 \times 0.018}{300 \times 0.0004} $$

Short Answer

Expert verified
3000

Step by step solution

01

- Simplify the Numerator

Calculate the value of the numerator: \(20,000 \times 0.018\).Perform the multiplication: \(20,000 \times 0.018 = 360\).
02

- Simplify the Denominator

Calculate the value of the denominator: \(300 \times 0.0004\).Perform the multiplication: \(300 \times 0.0004 = 0.12\).
03

- Divide the Results

Divide the simplified numerator by the simplified denominator: \( \frac{360}{0.12} \).Perform the division: \(360 \div 0.12 = 3000\).

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Key Concepts

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

Understanding the Numerator
The numerator is the top part of a fraction. It represents the number of parts we have out of the whole. In our exercise, the numerator is initially given as \(20,000 \times 0.018\). To simplify the fraction, we calculate the numerator first. By performing the multiplication, we get: \(20,000 \times 0.018 = 360\). Summarizing:
  • Numerator: Top part of a fraction.
  • Represents parts of the whole in a fraction.
  • Calculation for the exercise: \(20,000 \times 0.018 = 360\).
Breaking it down helps us understand the part-to-whole relationship better.
Decoding the Denominator
The denominator is the bottom part of a fraction. It indicates the total number of parts that make up a whole. For our exercise, the given denominator is \(300 \times 0.0004\). Simplifying this involves calculating it step-by-step. Performing the multiplication, we get: \(300 \times 0.0004 = 0.12\). So, in summary:
  • Denominator: Bottom part of a fraction.
  • Indicates total parts in the whole.
  • Calculation for the exercise: \(300 \times 0.0004 = 0.12\).
This helps to understand the structure of the fraction better.
Mastering Division in Fractions
Division is the operation of splitting into equal parts or groups. It tells us how many equal parts fit into the whole. In our simplified exercise, after calculating the numerator (360) and the denominator (0.12), we proceed to divide: \( \frac{360}{0.12} \). Performing the division, we get \(360 \div 0.12 = 3000\).To summarize:
  • Division: Splits numbers into equal parts or groups.
  • In fractions: Determines how many times the denominator fits into the numerator.
  • Calculation for the exercise: \( 360 \div 0.12 = 3000 \).
Understanding these steps ensures clarity in solving and simplifying fractions.

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