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Chapter 6: Problem 27

In the following exercises, convert each percent to a decimal. $$9 \%$$

Short Answer

Expert verified
0.09

Step by step solution

01

Understand Percent

A percent represents a part per 100. Therefore, 9% means 9 out of 100.
02

Convert Percent to Fraction

To convert 9% to a fraction, write it as \ \( \frac{9}{100} \).
03

Convert Fraction to Decimal

To convert the fraction \ \( \frac{9}{100} \) to a decimal, divide the numerator (9) by the denominator (100). This can be done by moving the decimal point two places to the left. So, \ \( \frac{9}{100} = 0.09 \).

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Key Concepts

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

Percent to Decimal Conversion
Converting a percent to a decimal is an important skill in math. It helps to compare, add, and subtract different values more easily. Here's a simple way to do it:
Percentages represent parts of 100. So, when you have 9%, it means 9 out of 100.
To convert 9% to a decimal, follow these steps:
  • Write the percentage as a fraction: \[ 9\text{\textpercent} = \frac{9}{100} \].
  • Divide the numerator (9) by the denominator (100). This can also be visualized by moving the decimal point two places to the left.
  • So, \[ \frac{9}{100} = 0.09 \].

Now you know that 9% is equal to 0.09 in decimal form. Simple, right?
Basic Arithmetic
Understanding basic arithmetic is crucial for many mathematical operations. This includes addition, subtraction, multiplication, and division.
Let's break down an example using percent to decimal conversion:
  • When converting 9% to a decimal, you write it as a fraction first: \[ \frac{9}{100} \].
  • Next, perform division: Divide 9 by 100.
  • -Or, simplify this by moving the decimal point in 9 (which is 9.0) two places to the left.
  • This gives you \[ 0.09 \].
So, the arithmetic operations you are performing are straightforward division or decimal shifting. This helps in quickly understanding and converting between different numeric forms.
Fraction to Decimal Conversion
Converting fractions to decimals is another key arithmetic skill one must master. This enables easier calculations and comparisons. Here鈥檚 how it works using our example from 9%:
  • Start with your fraction: \[ \frac{9}{100} \]
  • To convert the fraction to a decimal, divide the numerator (9) by the denominator (100).
  • This can be quickly done by moving the decimal point two places to the left, since 100 has two zeros.
  • From \[ 9 \rightarrow 0.09 \]

In summary, knowing how to convert percentages to fractions and then to decimals simplifies solving many math problems. It's practical and widely applicable in everyday situations.
So, remember:
  • Percent to Fraction: \[ 9\text{\textpercent} = \frac{9}{100} \]
  • Fraction to Decimal: \[ \frac{9}{100} = 0.09 \]

With practice, these conversions will become second nature!

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