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Chapter 7: Problem 5

Convert the percent to a decimal and a fraction. $$0.02 \%$$

Short Answer

Expert verified
0.02% is 0.0002 as a decimal and 1/5000 as a fraction.

Step by step solution

01

- Convert Percent to Decimal

To convert a percent to a decimal, divide the percent by 100. For 0.02%, divide 0.02 by 100: \( \frac{0.02}{100} = 0.0002 \)
02

- Convert Decimal to Fraction

To convert the decimal 0.0002 to a fraction, recognize that 0.0002 is equivalent to \( \frac{2}{10000} \). Simplify the fraction by dividing both the numerator and the denominator by their greatest common divisor, which is 2: \( \frac{2 \text{ (num.)}}{10000 \text{ (den.)}} = \frac{1}{5000} \)

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Key Concepts

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

convert percent to decimal
To convert a percent to a decimal, we need to divide the percentage value by 100. This is because 'percent' means 'per hundred'. So, for instance, if you have 0.02%, you divide it by 100 like this: \[0.02 \div 100 = 0.0002\] This conversion method works with any percentage. Always remember to divide by 100 to move from a percent to a decimal. This simple step is crucial for many math problems, so practice it often.
convert decimal to fraction
Converting a decimal to a fraction involves a few easy steps. First, know the place value of the decimal. For example, 0.0002 is in the ten-thousandth place. This means 0.0002 can be written as: \[0.0002 = \frac{2}{10000}\] To further simplify the fraction, find the greatest common divisor (GCD) of the numerator and the denominator. For 2 and 10,000, the GCD is 2. Divide both the numerator and the denominator by this GCD: \[\frac{2}{10000} = \frac{2 \div 2}{10000 \div 2} = \frac{1}{5000}\] Now, you have successfully converted the decimal 0.0002 to the simplified fraction \( \frac{1}{5000} \). This process is always the same, regardless of the decimal number you're given.
simplifying fractions
Simplifying fractions makes them easier to read and work with. To simplify a fraction, look for the greatest number that divides both the numerator and the denominator without a remainder, known as the greatest common divisor (GCD). For our fraction \( \frac{2}{10000} \), the GCD is 2. Divide both the top and bottom by this number: \[\frac{2}{10000} = \frac{2 \div 2}{10000 \div 2} = \frac{1}{5000}\] This leaves you with the simplest form of the fraction. Always simplify fractions when possible as it makes subsequent calculations more manageable. Practice finding the GCD and simplifying fractions regularly to get comfortable with the process.

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Most popular questions from this chapter

Solve the problem using a percent proportion. \(0.5 \%\) of what number is \(44 ?\)

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Convert the fraction to a percent. $$\frac{71}{100}$$

Write the fraction in percent notation to the nearest tenth of a percent. $$\frac{1}{15}$$

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