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Chapter 5: Problem 203

Convert each fraction to a decimal. \(-\frac{3}{8}\)

Short Answer

Expert verified
-0.375

Step by step solution

01

Understand the Fraction

The fraction given is \(-\frac{3}{8}\). This means you need to divide -3 (the numerator) by 8 (the denominator).
02

Perform the Division

Divide 3 by 8. To do this, you can set up the division 3 梅 8. Since the division won't result in a whole number, add decimal points and zeroes to perform the long division.
03

Execute Long Division

3 divided by 8 gives 0.375. Since we were dividing a negative number to start with (\(-3/8\)), the result of the division should be negative. Therefore, \(-\frac{3}{8} = -0.375\).

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Key Concepts

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

Fraction to Decimal Conversion
Converting fractions to decimals is a fundamental skill in mathematics. A fraction represents a division of two numbers. For example, \(\frac{1}{2}\) means dividing 1 by 2.
To convert a fraction to a decimal, you perform the division operation of the numerator (top number) by the denominator (bottom number).
Here鈥檚 a simple way to do it:
  • Identify the numerator and the denominator.
  • Set up the division problem (numerator 梅 denominator).
  • If the result isn't a whole number, continue by adding decimal points and zeroes as needed to find the decimal representation.
Remember, the outcome of this process is a decimal number that is equivalent to the initial fraction.
For our example, \(\frac{3}{8}\), dividing 3 by 8 yields 0.375.
Negative Fractions
Negative fractions occur when either the numerator or the denominator is negative (or both).
To handle negative fractions, follow these steps:
  • Convert the fraction to a decimal as you would with a positive fraction.
  • Apply the negative sign to the final result based on the original fraction鈥檚 sign.
In our example, \(-\frac{3}{8}\), the numerator is -3. When we convert this fraction to a decimal, we get 0.375 from dividing 3 by 8.
Since the fraction was negative, the final decimal should also be negative, thus \(-0.375\).
Long Division
Long division is an essential technique for converting fractions to decimals, especially when the division does not result in a whole number.
Here鈥檚 how to perform long division for converting fractions to decimals:
  • Set up the division by placing the numerator (3) inside the division bracket and the denominator (8) outside.
  • Since 8 cannot go into 3, we add a decimal point and zero to 3 to make it 30.
  • Determine how many times 8 fits into 30 (which is 3 times, yielding 24 when multiplied).
  • Subtract 24 from 30 to get a remainder of 6. Bring down another 0 to make it 60.
  • Repeat the process: 8 goes into 60 seven times (56 when multiplied), leaving a remainder of 4. Bring down another 0 to get 40.
  • Finally, 8 goes into 40 exactly five times without a remainder.
Thus, 3 divided by 8 is 0.375.
Don't forget to place the negative sign in front when starting with a negative fraction, giving us \(-0.375\) in this case.

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Most popular questions from this chapter

Mollie had a 16 -ounce cappuccino at her neighborhood coffee shop. The cappuccino had 110 calories. If Mollie walks for one hour, she burns 246 calories. For how many minutes must Mollie walk to burn off the calories in the cappuccino? Explain your reasoning.

In the following exercises, round each number to the nearest tenth. $$0.67$$

In the following exercises, convert each decimal to a fraction or mixed number. $$20.375$$

In the following exercises, find each unit price and then identify the better buy. Round to three decimal places. Breakfast Cereal, 10.7 ounces for \(\$ 2.69\) or 14.8 ounces for \(\$ 3.69\)

New Car Purchase Selena's new car cost \(\$ 23,795.95 .\) Round this number to the nearest: (a) dollar (b) thousand dollars (c) ten thousand dollars.
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