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Chapter 7: Problem 13

Change the percent to a simplified fraction or mixed number. $$3 \%$$

Short Answer

Expert verified
3% = \( \frac{3}{100} \)

Step by step solution

01

Understand What Percent Means

Percent means 'per hundred'. So, 3% can be written as a fraction with the denominator of 100.
02

Write the Fraction

Convert 3% to a fraction: \[ 3\text{\textpercent} = \frac{3}{100} \]
03

Simplify the Fraction

Check if the fraction \( \frac{3}{100} \) can be simplified. The greatest common divisor (GCD) of 3 and 100 is 1, so this fraction is already in its simplest form.

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Key Concepts

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

simplifying fractions
Simplifying fractions is about expressing them in their simplest form. This means the numerator (top part) and the denominator (bottom part) should have no common factors other than 1. For instance, if you have \( \frac{6}{8} \), you can divide both the numerator and the denominator by their greatest common divisor (GCD), which is 2. Thus, \( \frac{6}{8} \) simplifies to \( \frac{3}{4} \).
In our case, with 3% or \( \frac{3}{100} \), the GCD of 3 and 100 is 1, so the fraction is already in its simplest form. Always check for factors they share to simplify correctly.
understanding percents
Understanding percents is crucial because they are used everywhere - in discounts, interest rates, statistics, and much more. 'Percent' literally means 'per hundred'. So when you see 3%, it means 3 out of 100. To convert a percent to a fraction, place the percent number over 100. For example, 3% becomes \( \frac{3}{100} \).
This understanding allows you to move between percents, fractions, and decimals easily:
  • To convert a percent to a fraction, write it over 100 and simplify if possible.
  • To convert a fraction to a percent, divide the numerator by the denominator and move the decimal point two places to the right.
These skills help you interpret and solve real-life problems effectively.
greatest common divisor (GCD)
The greatest common divisor (GCD) is the largest number that divides two or more numbers without leaving a remainder. It's useful for simplifying fractions. To find the GCD of two numbers, list the factors of each number and choose the largest one they have in common. For example, for 8 and 12:
  • Factors of 8: 1, 2, 4, 8
  • Factors of 12: 1, 2, 3, 4, 6, 12
The GCD is 4, so \( \frac{8}{12} \) simplifies to \( \frac{2}{3} \).
In our original exercise, for 3% or \( \frac{3}{100} \), the factors are:
  • Factors of 3: 1, 3
  • Factors of 100: 1, 2, 4, 5, 10, 20, 25, 50, 100
Since 1 is the only common factor, the GCD is 1, so \( \frac{3}{100} \) is already simplified.

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Most popular questions from this chapter

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Is the number 0.0087 less than or greater than \(1 \% ?\)

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