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Chapter 7: Problem 66

Write each fraction as a percent. Round to the nearest hundredth percent. $$ \frac{11}{12} $$

Short Answer

Expert verified
\(\frac{11}{12}\) is approximately \(91.67\%\).

Step by step solution

01

Understand the Fraction

The fraction given is \( \frac{11}{12} \). This means 11 parts out of 12 equal parts make the whole. To express this fraction as a percent, we'll convert it using division followed by multiplication.
02

Convert the Fraction to Decimal

Divide the numerator by the denominator to convert the fraction to a decimal. Using a calculator or long division, divide 11 by 12, obtaining \( 0.91666\ldots \).
03

Convert Decimal to Percent

To convert the decimal \( 0.91666\ldots \) to a percent, multiply by 100. This gives \( 91.666\ldots \% \).
04

Round to the Nearest Hundredth Percent

Look at the third decimal place to determine if the second should be rounded. Since the decimal is \( 91.666\ldots \% \), you round up to \( 91.67\% \).

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Key Concepts

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

Fractions to Decimals
Fractions and decimals are just two different ways to represent numbers. A fraction like \(\frac{11}{12}\) means you have 11 parts out of 12 total equal parts. To change a fraction into a decimal, you simply divide the top number by the bottom number. In this case, dividing 11 by 12 gives \(0.91666\ldots\). This process might require a calculator or long division. Here's a simple way to think of it: Like slicing a cake into 12 equal pieces and taking 11, you're checking how much of the cake you are using in decimal form.
Rounding Decimals
When you get a decimal with many digits like \(0.91666\ldots\), it might seem overwhelming. Part of what makes numbers easier to handle is rounding them off. When rounding decimals, focus on the first few digits after the decimal point, as it helps in keeping calculations manageable. The rule for rounding is straightforward:
  • Look at the digit two places after the decimal if rounding to the nearest hundredth.
  • If this digit is 5 or more, increase the second decimal place by one.
  • If it's less than 5, keep the second decimal place as it is.
For example, in \(0.91666\ldots\), the third decimal is 6. So, you round the second decimal up, resulting in \(0.92\).
Basic Arithmetic Operations
Arithmetic operations are the foundation of working with numbers. They include addition, subtraction, multiplication, and division. Let's focus on division, as it's crucial for converting fractions to decimals. Division helps us break a whole into smaller parts, which is what we do when converting fractions.
You can visualize division by thinking of it as sharing an amount evenly. For instance:
  • If you divide 11 candies among 12 friends, each friend gets about \(0.91666\ldots\) pieces of candy.
  • Here, division gives us insight into how much each part (a decimal) is of the whole (the fraction \(\frac{11}{12}\)).
Using a calculator helps, but practicing with long division builds an understanding of how these numbers work together.

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