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Chapter 6: Problem 356

In the following exercises, convert each fraction to a percent. $$ 3 \frac{5}{8} $$

Short Answer

Expert verified
362.5%

Step by step solution

01

Convert the Mixed Fraction to an Improper Fraction

Convert the mixed fraction to an improper fraction by multiplying the whole number by the denominator, and then adding the numerator. For the fraction \[3 \frac{5}{8}\], this can be done as follows: \[3 \times 8 + 5 = 24 + 5 = 29\]. So, the improper fraction is \[ \frac{29}{8} \].
02

Convert the Improper Fraction to a Decimal

Divide the numerator by the denominator to convert the improper fraction to a decimal. For \[ \frac{29}{8} \], divide 29 by 8 which gives \[ 29 \div 8 = 3.625 \].
03

Convert the Decimal to a Percent

Multiply the decimal by 100 to convert it to a percent. So, \[ 3.625 \times 100 = 362.5 \].

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Key Concepts

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

Mixed Fraction Conversion
A mixed fraction is a combination of a whole number and a fraction, such as 3 \[\frac{5}{8}\]. To work with mixed fractions, you often need to convert them to improper fractions. This makes calculations easier. To convert a mixed fraction to an improper fraction:
  • Multiply the whole number by the denominator.
  • Add the numerator to the product.
Let鈥檚 look at our example: 3 \[\frac{5}{8}\]. Multiply 3 by 8 to get 24. Then add the numerator, 5, to get 29. So, 3 \[\frac{5}{8}\] is equivalent to \[\frac{29}{8}\]. This improper fraction will be useful for the next steps.
Improper Fraction
An improper fraction is one where the numerator (top number) is larger than or equal to the denominator (bottom number). For instance, \[\frac{29}{8}\] is an improper fraction. These fractions may look unusual, but they're simple to work with when converting to decimals or percents.To recall from our first step, we obtained \[\frac{29}{8}\]. Breaking this down, it means we have 29 parts out of 8, making it greater than a whole. Knowing how to handle improper fractions is essential for the following conversions.
Decimal Conversion
The next step is to convert the improper fraction to a decimal. This makes it easier to then convert to a percent. To convert \[\frac{29}{8}\] to a decimal, divide the numerator (29) by the denominator (8).Using a calculator or long division, you get:\[29 \div 8 = 3.625\].So, \[\frac{29}{8}\] equals 3.625 in decimal form. Decimals are a bridge between fractions and percents, making this step crucial.
Percent Calculation
Finally, to convert our decimal to a percent, we multiply by 100. Remember, 'percent' means 'per hundred.' So, we take our decimal, 3.625, and multiply by 100:\[3.625 \times 100 = 362.5\].Thus, 3 \[\frac{5}{8}\] converts to 362.5%.
  • Mixed fraction converted to improper fraction: \[\frac{29}{8}\].
  • Improper fraction converted to decimal: 3.625.
  • Decimal converted to percent: 362.5%.
Knowing each of these steps ensures you can convert any fraction to a percentage accurately and easily!

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