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Chapter 6: Problem 31

In the following exercises, convert each percent to a decimal. $$40 \%$$

Short Answer

Expert verified
0.4

Step by step solution

01

- Understand Percent

Percent means per hundred. So, 40% means 40 per hundred.
02

- Convert Percent to Fraction

Convert the percent to a fraction by placing the percent number over 100. Therefore, 40% becomes \( \frac{40}{100} \).
03

- Simplify the Fraction

Simplify the fraction if possible. \( \frac{40}{100} \) simplifies to \( \frac{2}{5} \), but this step is not necessary for conversion to decimal.
04

- Divide to Get Decimal

Divide the numerator by the denominator to get the decimal form. Performing the division \( \frac{40}{100} = 0.40 \).
05

- Remove Extra Zeros (if necessary)

While 0.40 is correct, it's usual to simplify to \( 0.4 \) for neatness.

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Key Concepts

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

Understanding Percent
The word 'percent' comes from the Latin phrase 'per centum,' which means 'by the hundred.'
When we say 40%, we are really talking about 40 parts out of 100. This means percent values represent a part of a whole, where the whole is always 100.
For example, if you score 40% on a test, it means you got 40 out of every 100 questions right.
Understanding percents is crucial because they are used frequently in everyday life, such as in discounts, interest rates, and statistics.
Fraction to Decimal Conversion
Converting a percent to a decimal involves converting it to a fraction and then to a decimal.
Here鈥檚 how you can do it step-by-step:
  • First, take the percent value. In this example, it's 40%.
  • Next, convert the percent to a fraction by placing the percent number over 100. Therefore, 40% becomes \( \frac{40}{100} \).
  • To convert the fraction \( \frac{40}{100} \) to a decimal, you divide the numerator (40) by the denominator (100). So, \( \frac{40}{100} = 0.40 \).
As you can see, the decimal equivalent of 40% is 0.40.
Notice that it can be simplified further by removing the extra zero, making it 0.4.
Simplifying Fractions
Simplifying fractions can make them easier to understand or use in calculations.
Here's a quick rundown of how to simplify:
  • Look at the numerator (the top number) and the denominator (the bottom number) of your fraction.
  • Find the greatest common divisor (GCD) of these two numbers. The GCD is the largest number that divides both the numerator and the denominator without leaving a remainder.
  • Divide both the numerator and the denominator by the GCD to simplify the fraction.
Using our earlier example, \( \frac{40}{100} \), the GCD of 40 and 100 is 20.
Dividing both the numerator and the denominator by 20 gives us \( \frac{2}{5} \).
While simplifying isn't necessary for converting percents to decimals, it is a helpful skill to know for other types of math problems.

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Most popular questions from this chapter

In the following exercises, solve. Elsa gets paid \(\$ 4,600\) per month. Her car payment is \(\$ 253\) . What percent of her monthly pay goes to her car payment?

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The nutrition fact sheet at a fast food restaurant says a small portion of chicken nuggets has 190 calories, and 114 calories are from fat. What percent of the total calories is from fat?

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In the following exercises, convert each percent to (a) a decimal (b) a simplified fraction. $$ 24 \% $$
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