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Chapter 7: Problem 42

Change the percent to a decimal. $$62 \frac{1}{5} \%$$

Short Answer

Expert verified
0.622

Step by step solution

01

- Convert the Mixed Fraction to an Improper Fraction

First, convert the mixed number to an improper fraction. For 62 and \( \frac{1}{5} \), the improper fraction is \( \frac{62 \times 5 + 1}{5} = \frac{311}{5} \).
02

- Convert the Improper Fraction to a Decimal

Next, convert the improper fraction to a decimal by dividing the numerator by the denominator. \( \frac{311}{5} = 62.2 \).
03

- Convert the Percent to a Decimal

Finally, convert the decimal from Step 2 to a decimal percent by dividing by 100. \( 62.2 \div 100 = 0.622 \).

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Key Concepts

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

Mixed Fraction
A mixed fraction, or mixed number, combines a whole number and a fraction. For example, in the fraction 62 and \(\frac{1}{5} \), 62 is the whole number, and \( \frac{1}{5} \) is the fractional part. To work with mixed fractions, you often need to convert them into improper fractions. This makes calculations easier.
Improper Fraction
An improper fraction has a numerator larger than or equal to its denominator. To convert a mixed fraction to an improper fraction, follow these steps:
1. Multiply the whole number by the denominator of the fractional part.
2. Add the result to the numerator of the fractional part.
3. Place the total over the original denominator.
    Example: \(\frac{311}{5}\) comes from multiplying 62 by 5 and adding 1 (62*5 + 1 = 311), resulting in \( \frac{311}{5} \).
Decimal Conversion
To change an improper fraction to a decimal, divide the numerator by the denominator. This represents how many parts of the whole you have. For instance, converting the fraction \( \frac{311}{5} \) to a decimal involves dividing 311 by 5, resulting in 62.2. This step helps in changing the fraction to a more manageable decimal form.
Dividing by 100
Finally, converting a percent to a decimal often requires dividing the number by 100. This works because percentages are a ratio out of 100. For example, to convert 62.2% to a decimal, you divide 62.2 by 100, resulting in 0.622. Percent means 鈥榩er hundred鈥�, so you're calculating how many parts per one hundred.

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