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Chapter 2: Problem 11

Convert the percent notation in each sentence to decimal notation. Of those who play Guitar Hero and Rock Band but do not currently play an actual musical instrument, 67% indicated that they are likely to begin playing an actual instrument.

Short Answer

Expert verified
0.67

Step by step solution

01

Identify the Percentage

In the given sentence, the percentage that needs to be converted to a decimal is 67%.
02

Convert Percentage to Decimal

To convert a percentage to a decimal, divide the percentage by 100. This conversion follows the formula: \[ \text{Decimal} = \frac{\text{Percentage}}{100} \] Applying this formula: \[ \text{Decimal} = \frac{67}{100} \]
03

Simplify the Division

Perform the division to convert the percentage to a decimal: \[ \frac{67}{100} = 0.67 \]

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Key Concepts

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

percentage to decimal conversion
Converting percentages to decimals is a fundamental concept in mathematics. To start, it's important to understand that a percentage is a part of a whole, expressed out of 100.
For example, 67% means 67 out of 100. To convert this percentage into a decimal, we simply divide it by 100. This is because the term 'percent' literally means 'per hundred'.
So, whenever you see a percentage, you can transform it into a decimal by using the formula:
\[ \text{Decimal} = \frac{\text{Percentage}}{100} \]
For the given exercise:
Let's convert 67% to a decimal:
\[ \text{Decimal} = \frac{67}{100} \]
Step-by-step, this means:
\[ \frac{67}{100} = 0.67 \]
Therefore, 67% as a decimal is 0.67.
elementary algebra
Elementary algebra involves the basics of arithmetic as well as the introduction to algebra. When dealing with percentages, being familiar with fractions and division is crucial.
In algebra, we're often transforming percentages into decimals or fractions to simplify calculations. For example, converting 67% to its decimal form (0.67) allows for easier manipulation in equations or real-world math problems.
Here's a simple process:
  • Identify the percentage.
  • Convert it to a decimal or fraction to fit the problem context.
This helps in tackling more complex algebraic problems where percentages might be used.
Remember, the ability to move between these forms easily is a cornerstone of elementary algebra.
mathematical notation
Mathematical notation is like the language of math; it includes symbols and formulas used to convey mathematical ideas clearly and efficiently.
In the context of converting percentages to decimals, the key notation to understand is the division symbol and percentage sign.
Here鈥檚 the notation breakdown:
  • \text{Percentage Sign} (%): Indicates a number out of 100.
  • Fraction Bar (/): Represents division.
So, for converting 67% to a decimal, we use the '%' symbol and the division process. The formula becomes:
\[ \frac{67}{100} = 0.67 \]
Understanding these symbols and how to use them helps streamline solving such problems and makes the math appear universal and consistent across different problems.
fractions to decimals
Converting fractions to decimals is another essential skill in math. For percentages like 67%, we usually see it written as 67/100.
To convert this fraction into a decimal, we perform division. 67 divided by 100 gives us 0.67.
Here鈥檚 a step-by-step guide:
  • First, write the percentage as a fraction. For example, 67% becomes 67/100.
  • Next, divide the numerator (top number) by the denominator (bottom number).
  • Finally, the result of the division is the decimal form.
This method can be used for any percentage to quickly and easily convert it to a decimal.
For example, if you have 50%, write it as 50/100 and divide: 50 梅 100 = 0.50 or simply 0.5.
Remember, every percentage can be turned into a fraction and then a decimal, which is essential for solving various math problems efficiently.

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Most popular questions from this chapter

Wedding costs. The Arnold Inn offers two plans for wedding parties. Under plan A, the inn charges \(\$ 30\) for each person in attendance. Under plan \(\mathrm{B}\), the inn charges \(\$ 1300\) plus \(\$ 20\) for each person in excess of the first 25 who attend. For what size parties will plan \(\mathrm{B}\) cost less? (Assume that more than 25 guests will attend.)

Use an inequality and the five-step process to solve each problem. The formula \(R=-0.0026 t+4.0807\) can be used to predict the world record, in minutes, for the 1500 -m run tyears after \(1900 .\) Determine (in terms of an inequality) those years for which the world record will be less than \(3.8 \mathrm{min}\)

Translate to an inequality. A number is less than \(10 .\)

Match the sentence with one of the following: $$ a

To prepare for Section \(2.6,\) review inequalities. Write a second inequality with the same meaning. $$x<5$$
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