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Chapter 7: Problem 82

Write the percent from the circle graph as a decimal and a fraction. Asia: \(59.8 \%\)

Short Answer

Expert verified
Decimal: 0.598, Fraction: \(\frac{299}{500}\).

Step by step solution

01

Convert Percent to Decimal

To convert a percentage to a decimal, divide the percentage by 100. Here, we have 59.8%. Therefore, the decimal form is \( \frac{59.8}{100} = 0.598 \).
02

Convert Percent to Fraction

To convert a percentage to a fraction, write the percentage as a fraction over 100 and then simplify. So, 59.8% becomes \( \frac{59.8}{100} \). Multiplying the numerator and denominator by 10 to eliminate the decimal gives \( \frac{598}{1000} \). Simplify the fraction by dividing both the numerator and the denominator by 2: \( \frac{598 \div 2}{1000 \div 2} = \frac{299}{500} \).

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Key Concepts

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

Convert Percent to Decimal
Converting a percent to a decimal is a straightforward process. Percent means "per hundred," so to change it to a decimal, you simply divide by 100. This moves the decimal point two places left. For example:

* For 59.8%, divide 59.8 by 100. * Move the decimal point two places to the left: 59.8 becomes 0.598.

And voil脿, you have your decimal form! This method works universally, no matter the percentage. It's a solid trick that helps with rapid calculations and simplifications in math.
Convert Percent to Fraction
Transforming a percent into a fraction is another useful skill. You start by writing the percentage over 100, since a percent is out of 100. Take 59.8% as an example:

* Write as a fraction: 59.8% becomes \( \frac{59.8}{100} \).* To clear the decimal, multiply the numerator and denominator by 10, converting \( \frac{59.8}{100} \) into \( \frac{598}{1000} \).

Now you have converted the percent into a fraction, but we're not quite done yet. There's one more step: simplification.
Simplifying Fractions
Simplifying fractions makes them easier to understand and work with. The goal is to find the smallest possible numbers that maintain the same ratio. For our fraction \( \frac{598}{1000} \), do the following steps:

* Check if both the numerator and the denominator can be divided by the same number. In this case, both 598 and 1000 can be divided by 2.* Divide the numerator and the denominator by 2: \( \frac{598 \div 2}{1000 \div 2} = \frac{299}{500} \).

Now, \( \frac{299}{500} \) is in its simplest form, as 299 is a prime number. Always aim to simplify the fractions you encounter to make your results cleaner and calculations easier.

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