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Chapter 2: Problem 82

Convert each percent to a decimal. $$ 174 \% $$

Short Answer

Expert verified
1.74

Step by step solution

01

Understand the Percent

Recognize that a percent means per hundred. So, 174% means 174 out of 100.
02

Convert Percent to Fraction

Convert the percent to a fraction by placing the number over 100. Thus, 174% becomes \( \frac{174}{100} \).
03

Simplify the Fraction (if needed)

Check if the fraction can be simplified. In this case, \( \frac{174}{100} \) is already in its simplest form.
04

Convert Fraction to Decimal

Divide the numerator by the denominator to convert the fraction to a decimal. So, \( \frac{174}{100} = 1.74 \).

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Key Concepts

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

Percent
In mathematics, a percent represents a part of a whole divided into 100 equal parts. The term 'percent' comes from the Latin 'per centum,' meaning 'by the hundred.'
For instance, 174% means 174 out of 100 or 1.74 times the original value.
It's important to understand this because converting a percent to other forms, like fractions or decimals, relies on this definition.
It's also helpful beyond math class. You'll see percents in everyday life:
  • Sales tax rates
  • Discounts
  • Interest rates
Fraction to Decimal Conversion
Converting a fraction to a decimal is a fundamental math skill.
The basic idea is to divide the top number (numerator) by the bottom number (denominator).
For example, to convert the fraction \( \frac{174}{100} \) to a decimal, you perform division: 174 梅 100 = 1.74.
This division operation is straightforward and gives you the decimal form directly.
Decimal representation is particularly useful for calculations and comparisons.
You may encounter larger or unwieldy fractions; knowing that you can always convert them to decimals simplifies many math problems.
Basic Arithmetic
Basic arithmetic, including addition, subtraction, multiplication, and division, is foundational. Knowing how percentages, fractions, and decimals interact relies on these basic skills.
For instance, converting 174% to a decimal involves:
  • Understanding that percent means per hundred
  • Writing 174% as \( \frac{174}{100} \)
  • Performing the division 174 梅 100
  • Getting the result 1.74
Each step involves basic arithmetic operations that are crucial.
Being comfortable with these basics ensures success in more complex math topics.

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