/*! This file is auto-generated */ .wp-block-button__link{color:#fff;background-color:#32373c;border-radius:9999px;box-shadow:none;text-decoration:none;padding:calc(.667em + 2px) calc(1.333em + 2px);font-size:1.125em}.wp-block-file__button{background:#32373c;color:#fff;text-decoration:none} Problem 76 In the following exercises, conv... [FREE SOLUTION] | 91影视

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Chapter 6: Problem 76

In the following exercises, convert each fraction to a percent. $$1 \frac{2}{3}$$

Short Answer

Expert verified
166.67\text{\textpercent}

Step by step solution

01

Convert the Mixed Number to an Improper Fraction

First, convert the mixed number to an improper fraction. For the mixed number \(1 \frac{2}{3}\), multiply the whole number part (1) by the denominator (3) and add the numerator (2). This gives: \(1 \times 3 + 2 = 5\). So, \(1 \frac{2}{3} = \frac{5}{3}\).
02

Divide the Numerator by the Denominator

Next, divide the numerator (5) by the denominator (3) to convert the fraction to a decimal. This gives: \(\frac{5}{3} \rightarrow 5 \textdiv 3 \thickapprox 1.6667\).
03

Convert the Decimal to a Percent

Finally, multiply the decimal by 100 to convert it to a percent. So, \(1.6667 \times 100 = 166.67\text{\textpercent}\).

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Key Concepts

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

Mixed Number Conversion
To convert a mixed number to an improper fraction, follow this simple method:
First, let's understand what a mixed number is. A mixed number consists of a whole number and a fraction, like this: 1 2/3.
Here's how to convert it:
  • Multiply the whole number by the denominator of the fraction. For 1 2/3, multiply the whole number 1 by the denominator 3. This gives: 1 x 3 = 3.
  • Add the numerator to this result. So, take the 3 you got from the multiplication, and add the numerator, which is 2. This gives: 3 + 2 = 5.
  • Place this result over the original denominator. So, 1 2/3 becomes 5/3.
Mixed number converted! Now 1 2/3 is the improper fraction 5/3.
Improper Fraction
An improper fraction has a numerator larger than its denominator. For example, 5/3 is improper because 5 > 3.
Although improper fractions may look unusual, they are perfectly normal in math and are often used in calculations.
In the conversion process, we typically start by turning mixed numbers into improper fractions like we just discussed. Once you have an improper fraction, the next step is to convert it into a decimal.
To recap:
  • A mixed number (like 1 2/3) is first converted into an improper fraction (like 5/3).
Now, let's move to the next step.
Fraction to Decimal Conversion
Converting a fraction to a decimal is straightforward. You need to divide the numerator by the denominator.
Here鈥檚 how you do it:
  • Take the improper fraction 5/3.
  • Divide the numerator (5) by the denominator (3).
Using division, 5 divided by 3 equals approximately 1.6667.
So, \(\frac{5}{3} = 1.6667\).
This step transforms the fraction into a more usable form for the final conversion to a percent.
Decimal to Percent Conversion
Converting a decimal to a percent is simple. You multiply the decimal by 100. This shows how many parts out of 100 the decimal represents.
Here's the procedure:
  • Start with the decimal from the previous step, 1.6667.
  • Multiply this decimal by 100.
  • So, 1.6667 x 100 = 166.67.
That鈥檚 it! Now, the decimal 1.6667 is 166.67%.
Remember, multiplying by 100 shifts the decimal point two places to the right, converting it to a percentage.
To wrap up, we converted 1 2/3 to an improper fraction (5/3), then to a decimal (1.6667), and finally to a percent (166.67%).

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