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Chapter 3: Problem 88

Decide whether the statement is true or false. Justify your answer. $$\frac{1}{2} \%=50 \%$$

Short Answer

Expert verified
False. The statement \(\frac{1}{2} \% = 50 \%\), is false because when 1/2 is converted into a percentage it equals 50% not \(\frac{1}{2}\%\). Therefore, 1/2% is significantly smaller than 50%.

Step by step solution

01

Making sense of the problem

The exercise misrepresents a fraction as a percentage. 1 divided by 2 is indeed 0.5 when represented as a first decimal and 50% when transformed into a percentage. However, the left side of the equation is incorrect as it states that 1/2 is 50 hundredths of a percent, which is an error.
02

Convert Fraction into Percentage

Converting 1/2 (0.5) into a percentage gives 50% and not 0.5% because the percentage is calculated as (Fraction)*(100)
03

Comparison

Now compare 1/2% with 50%. We quickly recognize that 1/2% is equivalent to 0.005 in decimal format, and is not the same as 50% which is 0.5 in decimal, so the provided statement is false.

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Key Concepts

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

Percentages
Understanding percentages is important in math and everyday life. A percentage represents a fraction out of 100. It allows us to easily compare different values or changes over time. When we say 50%, it means 50 out of 100 or half of something. Think of percentages as a handy way to express large or complex numbers in a simple form that is easy to understand.

To convert a decimal number to a percentage, multiply it by 100 and add the percentage sign (%). For example, converting 0.5 into a percentage would involve multiplying by 100, which results in 50%. This is a straightforward yet powerful way to look at numbers and their relationships.
Fractions
Fractions are used to describe parts of a whole. They consist of a numerator (top number) and a denominator (bottom number). The fraction \(\frac{1}{2}\) defines a half, meaning one part out of two equal parts.

Fractions can be converted to decimals and percentages for easier comparisons. For example, \(\frac{1}{2}\) can be converted to 0.5 as a decimal, and 50% as a percentage, by multiplying 0.5 by 100.
  • Converting a fraction to a decimal involves dividing the numerator by the denominator.
  • For instance, for \(\frac{1}{2}\), dividing 1 by 2 equals 0.5.
  • After getting the decimal, the next step is to multiply this by 100 to obtain the percentage format.
Fractions offer a precise method for describing exactly how much of something there is.
Decimal Conversion
Decimal conversion is the process of transforming fractions and percentages into decimal form. This is useful for calculations that require more precision or when using digital tools like calculators.

Converting \(\frac{1}{2}\) into a decimal involves simple division: 1 divided by 2 results in 0.5. The decimal format is often more intuitive for performing arithmetic operations like addition and subtraction.

When converting percentages to decimals, you divide by 100. So, 50% becomes 0.5. This allows for easier mathematical operations and comparisons.
  • To go from a percentage to a decimal, perform the operation by removing the % sign and dividing by 100.
  • This rule helps in seamlessly transitioning between different number formats.
Decimal conversion turns complex numbers into simpler forms, aiding quick understanding and efficient calculations.

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Most popular questions from this chapter

Comparing Costs You can rent a minivan from Company A for \(\$ 270\) per week with unlimited mileage. A similar minivan can be rented from Company B for \(\$ 180\) per week plus an additional 25 cents for each mile driven. How many miles must you drive per week so that the rental foe for Company B is more than that for Company A?

Solve and graph the inequality. $$9(y-4) \leq 36$$

Solve and graph the inequality. $$1-\frac{5 x}{4} \geq 2 x+13$$

Match the statement with the property it represents. (a) Addition Property of Inequality (b) Subtraction Property of Inequality (c) Multiplication Property of Inequality (d) Division Property of Inequality \(2>-6\), so \(2(7)>-6(7)\).

Think About It When the height of a triangle doubles, does the area of the triangle double? Explain.
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