Problem 21 Convert to decimal notation. $... [FREE SOLUTION]

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Basic College Mathematics

Marvin L. Bittinger, Judith A. Beecher, Barbara L. Johnson

$Math Studyset 91影视 Explanations$ Math

13 Edition

Chapter 10: Problem 21

Convert to decimal notation. $$ -8 \frac{7}{25} $$

Short Answer

Expert verified

-8.28

Step by step solution

- Convert Mixed Number to Improper Fraction

First, convert the mixed number $-8 \frac{7}{25}$ to an improper fraction. Multiply the whole number part ($-8$) by the denominator ($25$) and add the numerator ($7$). Keep the negative sign outside. \[ -8 \frac{7}{25} = - \left( 8 \times 25 + 7 \right) / 25 = - \left( 200 + 7 \right) / 25 = - 207 / 25 \]

- Divide the Numerator by the Denominator

Now, divide the numerator ($-207$) by the denominator ($25$) to convert the fraction to a decimal. \[ -\frac{207}{25} = -8.28 \]

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Key Concepts

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

mixed number

A mixed number is a combination of a whole number and a fraction. In our exercise, the mixed number is \-8 $ \frac{7}{25} $.
Mixed numbers can be tricky to work with in calculations, so they are often converted to improper fractions first.
Why do we use mixed numbers? They are useful for representing quantities that are more than a whole, like when measuring ingredients in cooking.

For example, if you have 3 and a half apples, you are really talking about 3 whole apples and another half of an apple.

improper fraction

An improper fraction has a numerator (the top number) that is larger than the denominator (the bottom number).
In our exercise, the improper fraction resulting from the mixed number \-8 $ \frac{7}{25} $ is \-$ \frac{207}{25} $.
How do you convert a mixed number to an improper fraction? It's simple!

First, multiply the whole number by the denominator.
Second, add that result to the numerator.
Finally, place the new value over the original denominator.

So, for \-8 $ \frac{7}{25} $, we multiply 8 by 25 and then add 7. This gives us \-$ 207 $/25.

division

Division is the final step to convert an improper fraction to a decimal.
For our fraction \-$ \frac{207}{25} $, we need to divide 207 by 25.
Division tells us how many times a number fits into another number. For instance, 25 fits into 207 about 8.28 times.
When we include our negative sign, the decimal becomes \鈥�8.28.

Steps to divide:

Write down the division problem as a fraction.
Divide the numerator by the denominator.
Add the negative sign if necessary.

So, for \-$ \frac{207}{25} $, it鈥檚 \鈥�8.28. Easy!

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91影视

Convert to decimal notation. $$ -8 \frac{7}{25} $$

Short Answer

Step by step solution

- Convert Mixed Number to Improper Fraction

- Divide the Numerator by the Denominator

Key Concepts

mixed number

improper fraction

division

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