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Chapter 2: Problem 91

Solve each problem. \(18 \%\) of 780 is what number?

Short Answer

Expert verified
140.4

Step by step solution

01

Understand the Problem

Determine what needs to be found. We are looking for 18% of 780.
02

Convert Percentage to Decimal

Convert 18% to a decimal by dividing by 100. \[ 18\text{%} = \frac{18}{100} = 0.18 \]
03

Multiply by the Number

Multiply 0.18 by 780. \[ 0.18 \times 780 = 140.4 \]

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Key Concepts

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

Convert Percentage to Decimal
When you see a percentage, you are actually looking at a number out of 100. To convert a percentage to a decimal, you need to divide it by 100. This is because 'percent' literally means 'per hundred'. For example, if you have 18%, you can convert it to a decimal by performing the division:
ewline ewline ewline ewline ewline \[ 18\text{%} = \frac{18}{100} = 0.18 \]
ewline ewline
  • Always remember to move the decimal point two places to the left as you divide by 100.
  • This step is crucial for further calculations.
It's a straightforward process once you get the hang of it.
Multiplication
Once you have your decimal, you are halfway there. The next part involves multiplication. To find a percentage of a number, you simply multiply the decimal by the number in question. ewline ewline In our problem, after converting 18% to 0.18, you would multiply it by 780 as follows:
ewline ewline \[ 0.18 \times 780 = 140.4 \]
ewline ewline
  • Ensure you line up the decimal points correctly if you're doing it by hand.
  • Use a calculator if you're uncertain, to avoid small mistakes.
Multiplication helps determine the exact number that represents 18% of 780.
Problem-Solving Steps
Solving percentage problems is simple if you follow clear steps. Here's a brief rundown:
  • Step 1: Understand the Problem
    Determine what you need to find. Identify the percentage and the whole number.
  • Step 2: Convert Percentage to Decimal
    Rewrite the percentage as a decimal by dividing by 100. Move the decimal point two places to the left.
  • Step 3: Multiply by the Number
    Take the decimal and multiply it by the whole number. This gives you the portion of the number you're looking at.
By following these steps, you can solve similar problems more easily. Remember: Breaking down a problem into smaller steps makes it more manageable.

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