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Chapter 7: Problem 104

Which of the numbers represent \(60 \% ?\) a. 6.0 b. \(0.60 \%\) c. 0.6 d. \(\frac{3}{5}\)

Short Answer

Expert verified
Options c (0.6) and d (\[ \frac{3}{5} \])

Step by step solution

01

Understand 60%

60% means 60 out of 100 or 60/100. Convert this to its simplest form.
02

Simplify 60%

Simplify \[ \frac{60}{100} = \frac{3}{5} \]. This shows that 60% is equivalent to \[ \frac{3}{5} \].
03

Convert Other Options

Convert the remaining options to decimal or percentage form and compare them to 60%. \ \ a. 6.0 = 600% (multiply by 100) \ \ b. 0.60% = 0.006 (divide by 100) \ \ c. 0.6 = 60% (0.6 * 100) \ \ d. \[ \frac{3}{5} \] = 60% (from Step 2)
04

Compare the Results

From the above calculations, options c (0.6) and d (\[ \frac{3}{5} \]) represent 60%.

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Key Concepts

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

Understanding Percentage Conversion
Percentage conversion is a useful skill in mathematics that allows you to understand how a part relates to a whole.

For example, 60% means 60 parts out of 100. We can express this as the fraction \(\frac{60}{100}\).

To simplify, we divide both the numerator and the denominator by their greatest common divisor, which for 60 and 100 is 20.

Hence, \(\frac{60}{100} = \frac{3}{5}\).

This tells us that 60% is equivalent to \(\frac{3}{5}\). Understanding this concept allows us to convert percentages into simpler forms and compare them easily with other numbers.
Simplifying Fractions
When working with percentages, it鈥檚 often necessary to simplify fractions.

Simplifying a fraction involves reducing it to its simplest form.
For instance, if we start with \(\frac{60}{100}\), we need to identify the greatest common divisor (GCD) of the numerator (60) and the denominator (100). In this case, the GCD is 20.

Therefore, we divide both the numerator and the denominator by 20: \(\frac{60}{100} = \frac{60 \div 20}{100 \div 20} = \frac{3}{5}\).

This process helps us see that fractions can be simplified to make calculations and comparisons easier.
Decimal to Percentage Conversion
Converting a decimal to a percentage is straightforward.

Remember that a percentage is just a way of expressing a number as a fraction of 100.

To convert a decimal into a percentage, we simply multiply it by 100.

For example, converting 0.6 to a percentage:

\(0.6 \times 100 = 60\%\)

Hence, 0.6 is the same as 60%.

It鈥檚 important to note that this conversion works both ways:

if given a percentage like 60%, we can convert it back to a decimal by dividing by 100:

\(60\% = \frac{60}{100} = 0.6\).

Understanding this relationship helps in solving exercises where you need to compare different forms of numbers.

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Most popular questions from this chapter

Find the decimal and fraction equivalents of the percent given in the sentence. During a slow travel season, one airline cut its seating capacity by \(15.8 \%\)

Solve the problem using a percent equation. 10 is what percent of \(2000 ?\)

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Fifty-two percent of American parents have started to put money away for their children's college educations. In a survey of 800 parents, how many would be expected to have started saving for their children's education? (Source: USA TODAY)

Find the total amount in an account for an investment subject to the following conditions. Principal \$ 4,000 Annual Interest Rate $$3 \%$$ Time, Years $$3$$ Compounded Semiannually Total Amount __________
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