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Chapter 5: Problem 90

Evaluate. $$ 10,000(36.94) $$

Short Answer

Expert verified
369,400

Step by step solution

01

Understand the problem

The problem requires calculating the product of two numbers: 10,000 and 36.94.
02

Set up the multiplication

Write out the multiplication operation: \[ 10,000 \times 36.94 \]
03

Perform the multiplication

Multiply the two numbers: \[ 10,000 \times 36.94 = 369,400 \]
04

Verify the result

Check the calculation to ensure accuracy.

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Key Concepts

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

evaluate
To evaluate a multiplication problem, the goal is to find the product of the given numbers.
In this exercise, we're asked to evaluate the expression involving multiplication.
The expression given is \(10,000 \times 36.94 \).
Evaluating an expression essentially means performing the indicated operations to find a numerical answer.
multiplication steps
Understanding the steps to solve a multiplication problem helps break down the process:
  • Step 1: First, identify the numbers involved. Here, it is 10,000 and 36.94.
  • Step 2: Write the multiplication setup clearly as \[10,000 \times 36.94.\]
  • Step 3: Perform the actual multiplication of the two numbers. Ensure to multiply each digit carefully to avoid errors.
  • Step 4: Finally, verify the obtained result for accuracy. This ensures that no mistakes were made during the calculation.
decimal multiplication
Multiplying with decimals involves a few additional steps:
  • Step 1: Ignore the decimal point and treat the numbers as whole numbers. In this example, multiply 10,000 by 3,694.
  • Step 2: Perform the multiplication exactly as you would with whole numbers.
  • Step 3: Count the number of decimal places in the original numbers. Here, 36.94 has two decimal places.
  • Step 4: Place the decimal point in the product so that it has this same number of decimal places. Thus, \(10,000 \times 36.94 = 369,400.00\)
accuracy check
Accuracy is crucial in mathematical calculations.
Verifying your result can save you from errors:
  • Revisit each step: Go back and review each step of your multiplication.
  • Use estimation: Estimating the numbers and their product can help. For instance, 10,000 multiplied by about 37 (close approximation of 36.94) should yield a product of around 370,000, which confirms our answer's accuracy.
  • Alternative calculation methods: Use different methods like breaking down the multiplication into simpler parts to cross-check.
Consistently practicing these verification strategies enhances accuracy in your mathematical computations.

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