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Chapter 0: Problem 79

$$ \text { Find } 125 \% \text { of } 45 . $$

Short Answer

Expert verified
56.25

Step by step solution

01

- Convert Percentage to Decimal

Convert 125% to a decimal by dividing by 100. \[ 125\text{%} = \frac{125}{100} = 1.25 \]
02

- Multiply by the Given Number

Multiply the decimal form of the percentage by 45. \[ 1.25 \times 45 \]
03

- Perform the Multiplication

Calculate the multiplication to find the result. \[ 1.25 \times 45 = 56.25 \]

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Key Concepts

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

conversion of percentages
Understanding how to convert a percentage to a decimal is crucial for solving many math problems. Here's how you do it:
Percentages are parts of 100. Thus, to convert a percentage to a decimal, you divide by 100.
For example, to convert 125% to a decimal:
125% is the same as \(\frac{125}{100}\) which equals 1.25.
By dividing by 100, you move the decimal point two places to the left.
This conversion makes it easier to use the percentage in mathematical operations like multiplication or division.
Key steps:
  • Take the percentage value.
  • Divide by 100.
  • Note the result is now a decimal, ready for further calculations.
multiplication
Multiplication is one of the basic arithmetic operations, essential for various calculations like finding percentages of numbers.
After converting a percentage to a decimal, you use multiplication to find the specified part of a number.
For instance, once we have 1.25 (the decimal form of 125%), we multiply it by 45 to find 125% of 45:
\(\text{1.25} \times \text{45}\).
The methodology is straightforward:
  • Write down the decimal.
  • Write down the number you want to find the percentage of.
  • Multiply the two numbers.
  • The product gives you the desired percentage of the original number.
This step of multiplying the values directly gives us the answer.
decimal representation
Decimals represent fractions or parts of whole numbers, crucial for precision in mathematical calculations.
When you convert a percentage to a decimal, you effectively turn it into a format that鈥檚 easy to multiply, divide, and use in equations.
For example, in converting 125% to 1.25, you have prepared it for direct arithmetic operations.
The decimal system is based on powers of 10, making it very straightforward to handle moves of digits.
Important Points:
  • A single decimal place represents tenths (1/10), two decimal places represent hundredths (1/100), and so on.
  • Decimals are used throughout mathematics, from basic calculations to advanced topics.
  • Knowing how to convert percentages to decimals helps in clearer, more precise computations.

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Most popular questions from this chapter

For exercises \(85-108\), write \(>\) or \(<\) between the numbers to make a true statement. $$ \frac{3}{11} \quad \frac{2}{7} $$

For exercises \(85-108\), write \(>\) or \(<\) between the numbers to make a true statement. $$ \frac{3}{4} \quad \frac{5}{9} $$

For exercises 1-12, rewrite the decimal number as a fraction. Simplify the fraction to lowest terms. $$ 0.002 $$

For exercises \(47-58\), rewrite the percent as a decimal number. $$ 8.4 \% $$

For exercises 97-114, evaluate. $$ -\frac{1}{3}(11-7)-\frac{1}{9}(14-6) $$
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