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Chapter 7: Problem 68

Write each fraction as a percent. Round to the nearest hundredth percent. $$ \frac{10}{11} $$

Short Answer

Expert verified
\( \frac{10}{11} \approx 90.91\% \)

Step by step solution

01

Understand the Problem

To convert the fraction \( \frac{10}{11} \) to a percent, we must multiply the fraction by 100.
02

Perform the Division

Divide the numerator by the denominator: \( \frac{10}{11} \approx 0.9091 \).
03

Convert to Percent

Multiply the decimal by 100 to convert to a percentage: \( 0.9091 \times 100 = 90.91 \).
04

Round to Nearest Hundredth

The calculated percentage is \( 90.91 \), which is already rounded to the nearest hundredth.

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Key Concepts

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

Fractions
A fraction consists of two numbers, the numerator and the denominator. Fractions represent parts of a whole.

In the fraction \( \frac{10}{11} \), '10' is the numerator, while '11' is the denominator. The numerator indicates how many parts we have, and the denominator shows how many equal parts the whole is divided into.

To better understand fractions, here are some quick tips:
  • Fractions can be converted to decimals and percentages for easier interpretation.
  • Fractions can represent numbers less than one, exactly one, or greater than one.
  • Fractions can be simplified if both the numerator and denominator share a common factor.
Understanding fractions is fundamental to performing conversions into decimal and percentage forms.
Decimal Conversion
Decimal conversion involves changing a fraction into its decimal form. This is done by dividing the numerator by the denominator using division.

For example, to convert \( \frac{10}{11} \) into a decimal, you divide 10 by 11, which gives the approximation \( 0.9091 \). This value is a result of performing a long division, where the numerator is divided into the denominator.

Here are some helpful points about decimal conversion:
  • Decimal numbers can show a more clear representation of fractions, making them easier to use in calculations.
  • Decimals can be terminating or non-terminating; for \( \frac{10}{11} \), it is non-terminating.
  • To ensure accuracy, decimals can be rounded to a certain number of decimal places.
Decimals help in visualizing and operating on fractions in real-world problems.
Rounding Decimals
Rounding decimals makes numbers easier to work with by reducing them to a specific place value, such as the nearest tenth, hundredth, or thousandth.

For instance, if you have the decimal \( 0.9091 \), and you're asked to round to the nearest hundredth, look at the third decimal place (9 in this case). Since this number is 5 or greater, you'll round up the second decimal (0). Thus, \( 0.91 \) is the rounded form.

Here are a few things to remember when rounding decimals:
  • Identify which place value you will round to (e.g., nearest hundredth).
  • Look at the digit immediately after the place value to decide whether to round up or stay (5 or more rounds up).
  • Rounding simplifies numbers, which helps in estimation and making decisions.
Rounding ensures that your decimals are manageable and precise in contexts where exact numbers aren't possible or needed.

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