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Chapter 7: Problem 81

Write the percent from the circle graph as a decimal and a fraction. Africa: \(16.2 \%\)

Short Answer

Expert verified
16.2% as a decimal is 0.162 and as a fraction is \(\frac{81}{500}\).

Step by step solution

01

Convert Percent to Decimal

To convert the percent to a decimal, you need to divide the percent value by 100. For Africa's percent, divide 16.2 by 100, which gives the decimal value: \(16.2 \div 100 = 0.162\).
02

Convert Percent to Fraction

To convert the percent to a fraction, write the percent over 100 and then simplify. For 16.2%, it initially becomes \(\frac{16.2}{100}\). To remove the decimal, multiply the numerator and denominator by 10 to get \(\frac{162}{1000}\). Simplify the fraction by dividing both the numerator and the denominator by their greatest common divisor, which is 2, to get \(\frac{81}{500}\).

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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 percentage into a decimal is a common task and is very simple to do. You just need to move the decimal point two places to the left. This is because a percentage signifies how many per hundred, or the fraction of 100. To convert the percentage to a decimal, you basically divide by 100. For example, with Africa's percentage of 16.2%, the decimal conversion is done by dividing 16.2 by 100. Thus, you end up with 0.162 as the decimal equivalent.

This operation can be remembered simply by the rule:
  • Move the decimal point two places to the left.
  • Remove the percent sign (").
So each time you encounter a percentage, just remember to shift that decimal point to the left twice, or divide by 100!
Percent to Fraction Conversion
To convert a percentage to a fraction, start by understanding that a percent is out of 100. This makes the conversion straightforward. Begin by writing the percent as a fraction over 100. For example, 16.2% becomes \( \frac{16.2}{100} \).

If the percentage has a decimal, like 16.2, you need to eliminate it for a cleaner fraction. To do that, multiply both the numerator and denominator by 10 which gives you \( \frac{162}{1000} \). This step ensures that you have whole numbers in your fraction.

A quick tip is to always consider:
  • Write the percent as the numerator over 100.
  • Clear any decimals by scaling up both numerator and denominator appropriately.
From here, you just need to simplify the fraction by finding the greatest common divisor and dividing both parts by it.
Simplifying Fractions
Once you have a fraction, simplification is the next step. Simplifying involves reducing the fraction to its smallest form, where the numerator and denominator have no common factors other than 1.

For the fraction \( \frac{162}{1000} \), check to see if there's a number that can evenly divide both parts of the fraction. In this case, the greatest common divisor is 2. By dividing both the numerator and the denominator by 2, you get \( \frac{81}{500} \). Now, this fraction is in its simplest form.

Here's how you simplify each time:
  • Identify the greatest common divisor (GCD) of the numerator and denominator.
  • Divide both the top and bottom by their GCD.
  • Check your fraction to make sure it's fully simplified.
Simplifying fractions is a crucial skill, making complex expressions much simpler to work with, especially in more advanced math problems.

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