/*! 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 78 Convert \(11 / 9\) to a percent,... [FREE SOLUTION] | 91影视

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Chapter 7: Problem 78

Convert \(11 / 9\) to a percent, and round your answer to the nearest tenth of a percent.

Short Answer

Expert verified
\(11/9\) as a percent is \(122.2\%\).

Step by step solution

01

Divide the Fraction

First, convert the fraction \(\frac{11}{9}\) to a decimal by dividing 11 by 9. Perform the division: \(11 \div 9 = 1.2222...\) which is a repeating decimal.
02

Convert Decimal to Percent

To convert the decimal to a percentage, multiply the result from Step 1 by 100. So, \(1.2222... \times 100 = 122.222...\).
03

Round to Nearest Tenth

Round the decimal 122.222... to the nearest tenth. Look at the hundredths place, which is 2, and since it's less than 5, the tenths place stays the same. Thus, \(122.2\%\) is the rounded value.

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Key Concepts

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

Fractions to Decimals
Turning a fraction into a decimal involves a simple division. When you're asked to convert a fraction like \( \frac{11}{9} \) into its decimal form, you'll need to divide the numerator (11) by the denominator (9).
In this case, performing the division \( 11 \div 9 \) gives you \( 1.2222... \), which is a repeating decimal as the digit "2" repeats endlessly.
  • Start by placing the numerator inside the division and the denominator outside.
  • If the division doesn't end, you often encounter repeating decimals, where the same number or group of numbers repeats again and again.
Understanding how to perform this process is crucial as it forms the foundation for further calculations and conversions.
Rounding Decimals
Once you have a decimal number, sometimes it's necessary to round it to make it simpler or more practical for use.
Let's take the decimal \( 122.222... \) from our previous calculation.
To round a number to the nearest tenth, you'll look at the digit in the hundredths place, which in this case is 2.
  • If the digit is 5 or more, you'll round the tenths place up.
  • If it's less than 5, as in our example, you'll keep the tenths place as is.
So, \( 122.222... \) rounded to the nearest tenth becomes \( 122.2 \).
Rounding helps in simplifying too detailed figures into more manageable and usable numbers.
Decimal Representation
Decimals are an alternative way of expressing fractions and help provide a clear visual representation of numbers on a number line.
In this context, the decimal representation of \( \frac{11}{9} \) is \( 1.2222... \), showcasing a repeating cycle after the decimal point.
  • Non-repeating decimals are straightforward where the decimals end after a few digits.
  • Repeating decimals, like in our example, are usually represented with a bar over the repeating digits (e.g., \( 1.\overline{22} \)).
These representations are crucial for comparing, adding, subtracting, multiplying, and dividing different numbers.
Understanding them also enables you to work with percentages and makes complex problems more approachable.

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