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Chapter 7: Problem 66

Convert the fraction to a percent. $$1 \frac{1}{6}$$

Short Answer

Expert verified
116.67\%

Step by step solution

01

Convert the mixed number to an improper fraction

First, convert the mixed number \(1 \frac{1}{6}\) to an improper fraction. Multiply the whole number 1 by the denominator 6, then add the numerator 1. Place this result over the original denominator:\[1 \frac{1}{6} = \frac{6 \times 1 + 1}{6} = \frac{7}{6}\]
02

Divide the numerator by the denominator

Now, divide the numerator 7 by the denominator 6 to convert the fraction to a decimal:\[\frac{7}{6} = 1.1667\]
03

Convert the decimal to a percent

Multiply the decimal 1.1667 by 100 to convert it to a percentage:\[1.1667 \times 100 = 116.67\%\]

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Key Concepts

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

Mixed Number to Improper Fraction
To tackle this, we first need to change the mixed number into an improper fraction. A mixed number has a whole number and a fraction combined, like \(1 \frac{1}{6}\). To convert it to an improper fraction:
  • Multiply the whole number (1) by the denominator of the fraction (6). This gives us 6.
  • Then, we add the numerator (1) to that product. Now we have 7.
  • Finally, place this result over the original denominator (6). So, \(1 \frac{1}{6} = \frac{7}{6}\).
This process ensures that you have a single fraction which is easier to work with in further calculations.
Decimal Conversion
Next, we need to convert the improper fraction to a decimal. For the fraction \(\frac{7}{6}\), divide the numerator (7) by the denominator (6). This division can be done as follows:
  • 7 divided by 6 equals approximately 1.1667.
So, \(\frac{7}{6} = 1.1667\) as a decimal. Always remember that converting fractions to decimals simplifies further steps in calculations, particularly when moving to percentages.
Percentage Conversion
Finally, we convert the decimal to a percentage. This step is straightforward:
  • Take the decimal value (1.1667).
  • Multiply it by 100.
So, \(1.1667 \times 100 = 116.67\text{\text{%}} \).
This multiplication shifts the decimal point two places to the right, converting your decimal into a percentage. Therefore, the fraction \(1 \frac{1}{6}\) equals 116.67\text{%} when converted to a percentage. Converting to percentages is a great way to understand proportions in real-world contexts, making the numbers more relatable.

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Most popular questions from this chapter

Yellowstone National Park has \(3366 \mathrm{mi}^{2}\) of undeveloped land. If this represents \(99 \%\) of the total area, find the total area of the park.

Carson had 600 dollar and spent \(44 \%\) of it on clothes. Then he spent \(20 \%\) of the remaining money on dinner. How much did he spend altogether?

Forty-four percent of Americans use online travel sites to book hotel or airline reservations. If 400 people need to make airline or hotel reservations, how many would be expected to use online travel sites?

Mr. Asher made \(\$ 49,000\) as a teacher in Virginia in \(2007,\) and he spent \(\$ 8,800\) on food that year. In \(2008,\) he received a \(4 \%\) increase in his salary, but his food costs increased by \(6.2 \%\) a. How much money was left from Mr. Asher's 2007 salary after subtracting the cost of food? b. How much money was left from his 2008 salary after subtracting the cost of food? Round to the nearest dollar.

Write the fraction in percent notation to the nearest tenth of a percent. $$\frac{13}{15}$$
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