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Chapter 8: Problem 22

In Exercises \(21-34\), express each percent as a decimal. \(38 \%\)

Short Answer

Expert verified
The decimal equivalent to \(38 \%\)\ is 0.38.

Step by step solution

01

Step 1:percent to decimal conversion

To express a percent as a decimal, move the decimal point two places to the left. In other words, divide the percent value by 100. In this case, \(38 \%\) becomes \(38 \div 100\) or 0.38.

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Key Concepts

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

Mathematical Conversion Methods
Mathematical conversion methods are essential skills that help in transforming numbers from one format into another. This is particularly useful in translating percentages into decimals.
One key method is the movement of the decimal point. When converting a percentage to a decimal, you move the decimal point two places to the left. This can be understood as dividing by 100, simplifying the number into a decimal form.
  • For example, converting 38% involves moving the decimal two places left, transforming 38% into 0.38.
  • Practicing such conversions can help you get more comfortable with numbers in different forms.
Exploring a variety of conversion methods will strengthen your numerical fluency.
Understanding Percentages
Understanding percentages is fundamental to grasping more complex mathematical concepts.
A percentage is a way to express a number as a part of 100. It allows for easy comparisons between different quantities. The term comes from the Latin "per centum," meaning "by the hundred."
  • For instance, 38% is equivalent to 38 out of every 100.
  • This means if you had a group of 100 items, 38% of them would be 38 items.
Having a clear understanding of percentages will make it easier to work with them in various calculations.
Decimal Representation
Decimal representation is a way of expressing numbers using the base ten.
Unlike percentages, which are out of 100, decimals represent parts of a whole using fractions. Converting a percentage like 38% into a decimal, which becomes 0.38, makes it easier to see its proportion out of 1.
  • Decimals are widely used in everyday situations, such as financial calculations where precision is needed.
  • Understanding how to read and write decimals is crucial for interpreting numerical data.
Working with decimals is an important part of everyday mathematics.
Basic Arithmetic Operations
Basic arithmetic operations are foundational skills in mathematics.
When converting from percent to decimal, basic division comes into play. Dividing by 100 helps transform percentages into decimals. This simplification allows you to use the number in a variety of mathematical operations such as addition, subtraction, multiplication, and division.
  • For instance, converting 38% involved performing a simple division: 38 divided by 100 equals 0.38.
  • Mastering these operations ensures a more efficient and effective computing process in daily life.
Having a strong grasp of these operations simplifies working with numbers.

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Most popular questions from this chapter

Suppose that you decide to buy a car for \(\$ 37,925\), including taxes and license fees. You saved \(\$ 12,000\) for a down payment and can get a five-year loan at \(6.58 \%\). Find the monthly payment and the total interest for the loan.

Make Sense? In Exercises 19-25, determine whether each statement makes sense or does not make sense, and explain your reasoning. I like to keep all my money, so I pay only the minimum required payment on my credit card.

Suppose that you drive 15,000 miles per year and gas averages \(\$ 3.50\) per gallon. a. What will you save in annual fuel expenses by owning a hybrid car averaging 60 miles per gallon rather than an SUV averaging 15 miles per gallon? b. If you deposit your monthly fuel savings at the end of each month into an annuity that pays \(5.7 \%\) compounded monthly, how much will you have saved at the end of six years?

In Exercises 11-18, a. Determine the periodic deposit. Round up to the nearest dollar. b. How much of the financial goal comes from deposits and how much comes from interest? $$ \begin{array}{|l|l|l|l|} \hline \$ \text { at the end of every three months } & 3.5 \% \text { compounded quarterly } & 5 \text { years } & \$ 20,000 \\ \hline \end{array} $$

In Exercises 1-10, use $$ P M T=\frac{P\left(\frac{r}{n}\right)}{\left[1-\left(1+\frac{r}{n}\right)^{-n t}\right]} $$ Round answers to the nearest dollar. Suppose that you decide to borrow \(\$ 40,000\) for a new car. You can select one of the following loans, each requiring regular monthly payments: Installment Loan A: three-year loan at \(6.1 \%\) Installment Loan B: five-year loan at \(7.2 \%\). a. Find the monthly payments and the total interest for \(\operatorname{Loan} A\). b. Find the monthly payments and the total interest for Loan B. c. Compare the monthly payments and the total interest for the two loans.
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