Problem 59 - Prealgebra

Question

Write each fraction or mixed number as a decimal. Use a bar to show a repeating decimal. $$-7 \frac{4}{5}$$

Step-by-Step Solution

Answer

The number \( -7 \frac{4}{5} \) as a decimal is \( -7.8 \), which is a terminating decimal.

Step 1: Convert the Fraction to a Decimal

Take the fraction \( \frac{4}{5} \) and convert it to a decimal by dividing 4 by 5. Perform the division: \( 4 \div 5 = 0.8 \). Thus, the fraction \( \frac{4}{5} \) is equivalent to the decimal 0.8.

Step 2: Combine with the Whole Number

Now combine the whole number part of the mixed number with the decimal found from the fraction in Step 1. So, \( -7 \frac{4}{5} \) becomes \( -7 + 0.8 = -7.8 \).

Step 3: Identify Non-Repeating Decimals

Check whether the decimal found in Step 2 has any repeating digits. Since 0.8 does not repeat any digits, it is considered as a terminating decimal. Therefore, there is no need to use a bar over any digit.

Key Concepts

Understanding Mixed Numbers

Mixed numbers can initially seem a bit daunting, but they are quite simple once you get the hang of them. A mixed number is a whole number combined with a fraction, sitting side by side.
For example, in the mixed number \(-7 \frac{4}{5}\), \(-7\) is the whole number and \(\frac{4}{5}\) is the fraction. When you want to convert a mixed number into a decimal, you first need to break it down into its parts.
The fraction is converted to a decimal separately from the whole number. Then, the decimal version of the fraction and the whole number are combined to get the decimal representation of the whole mixed number. Understanding this helps simplify the process of converting mixed numbers into decimals.

What are Terminating Decimals?

Decimals can be classified broadly into two categories: terminating and repeating. A terminating decimal is one that has an end. It does not go on forever. An example is 0.8, which stops after the first decimal place.
This is different from repeating decimals, which continue infinitely. Repeating decimals usually have a sequence of one or more digits that repeat endlessly.
In the conversion process of fractions or mixed numbers, recognizing a terminating decimal is vital. It means the decimal representation is complete and does not need any additional notation, like a bar, that is used for repeating decimals.

Steps to Convert Fractions to Decimals

Converting fractions to decimals is an essential skill in mathematics that is easier than it may seem. When you have a fraction like \(\frac{4}{5}\), converting it involves only a simple division.
Here's how to do it successfully:

• Take the numerator (the top number of the fraction) and divide it by the denominator (the bottom number).
• For \(\frac{4}{5}\), you would divide 4 by 5.
• This division gives you 0.8, a straightforward piece in the process.

Breaking down these steps can make what seems like a challenging task into something much more manageable.
So each time you see a fraction, remember it's just an opportunity to practice simple division!