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Chapter 6: Problem 50

Convert each fraction to a decimal. $$ 8 \frac{5}{16} $$

Short Answer

Expert verified
The decimal equivalent of \(8 \frac{5}{16}\) is 8.3125.

Step by step solution

01

Convert the Mixed Number to an Improper Fraction

First, we need to convert the mixed number \(8 \frac{5}{16}\) into an improper fraction. A mixed number is composed of a whole number and a fraction. To convert it, multiply the whole number (8) by the denominator (16) and then add the numerator (5). This gives us \(8 \times 16 + 5 = 128 + 5 = 133\). So the improper fraction is \(\frac{133}{16}\).
02

Divide the Numerator by the Denominator

To convert a fraction into a decimal, divide the numerator by the denominator. Here, divide 133 by 16. When you do the division, you obtain \(133 \div 16 = 8.3125\). Thus, \(\frac{133}{16}\) as a decimal is 8.3125.

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Key Concepts

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

Understanding Mixed Numbers
Mixed numbers are a combination of a whole number and a fraction. For instance, in the mixed number \(8 \frac{5}{16}\), the number 8 is the whole number, and \(\frac{5}{16}\) is the fraction. Mixed numbers are useful because they can express quantities that are more than one whole but not quite another whole. They are commonly used in real-life situations, like measuring ingredients in cooking.
  • To work with mixed numbers mathematically, it is often necessary to convert them into improper fractions.
  • This simplifies calculations, particularly when you need to perform division, multiplication, or conversion into decimals.
What are Improper Fractions?
An improper fraction occurs when the numerator (the top number) is larger than the denominator (the bottom number). An example can be seen with \(\frac{133}{16}\). Here, 133 is greater than 16 making the fraction improper.
  • Improper fractions represent a value greater than or equal to one whole.
  • They can often appear confusing at first glance, but they are straightforward once you understand that the numbers above and below the line represent division.
To convert a mixed number like \(8 \frac{5}{16}\) into an improper fraction, follow these steps:
  • Multiply the whole number by the denominator of the fractional part.
  • Add the numerator of the fractional part to this product.
  • This sum becomes the new numerator, while the denominator remains unchanged.
So \(8 \times 16 + 5 = 133\) and you get the improper fraction \(\frac{133}{16}\). Working with them can make arithmetic much more compact and manageable.
Understanding Division in Mathematics
Division is a fundamental operation in mathematics that is used to find out how many times one number is contained within another. It is crucial when converting fractions to decimals. For example, to convert the improper fraction \(\frac{133}{16}\) into a decimal, you simply need to divide 133 by 16.
  • The division tells us how many whole units of 16 fit into 133 and what the remaining fraction is.
  • This is executed as long division starting from the left, digit by digit.
The result of dividing 133 by 16 gives us 8.3125, meaning the improper fraction \(\frac{133}{16}\) is equivalent to the decimal 8.3125. This highlights how division can untangle fractions into a more familiar decimal form, making numbers easier to interpret and use in calculations.

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