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Chapter 4: Problem 53

Convert to decimal notation. \(12.2 \%\)

Short Answer

Expert verified
0.122

Step by step solution

01

Understanding percent notation

Percent means 'per hundred,' so any percentage can be expressed as a fraction with a denominator of 100. For example, 12.2% means 12.2 out of 100.
02

Convert the percentage to a fraction

Write 12.2% as a fraction: \[ \frac{12.2}{100} \]
03

Convert the fraction to decimal notation

To convert \[ \frac{12.2}{100} \] to decimal notation, divide the numerator (12.2) by the denominator (100): \[ 12.2 \div 100 = 0.122 \]

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Key Concepts

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

percent notation
Percent notation is a way to express numbers as parts of 100. The term 'percent' comes from the Latin phrase 'per centum,' which means 'by the hundred.' This implies that when we talk about percentages, we are discussing how many parts out of 100.
For example, when we say 50%, we mean 50 out of 100 or half of something.
Similarly, 12.2% represents 12.2 out of 100. Using percent notation helps to easily compare different quantities as it standardizes the value to a common base of 100.
This notation is widely used in various fields like finance, statistics, and health to report data in a comprehensible manner.
fraction to decimal conversion
Converting a percentage to a decimal often involves two intermediary steps: converting the percent to a fraction and then converting the fraction to a decimal. When we have a percentage like 12.2%, we can write it as a fraction first. This is done by placing the percentage number over 100, like this: \( \frac{12.2}{100} \).
Next, we convert this fraction to a decimal by performing the division of the numerator by the denominator.
For our example, this means dividing 12.2 by 100, which gives 0.122.
Understanding this process is crucial because it provides a solid foundation for other mathematical operations and conversions.
basic arithmetic
Basic arithmetic skills are essential in many everyday tasks and are fundamental for learning more advanced mathematical concepts.
The operations commonly involved in basic arithmetic include addition, subtraction, multiplication, and division.
In the context of converting percentages to decimals, division plays a key role.
For instance, to convert \( \frac{12.2}{100} \) to a decimal, we divide 12.2 by 100.
The division can be understood simply: how many times does 100 fit into 12.2? Since it fits 0.122 times, the decimal equivalent is 0.122.
Proficiency in these basic arithmetic operations ensures smoother navigation through various mathematical tasks and problems.

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Most popular questions from this chapter

Solve each system using the substitution method. If a system has an infinite number of solutions, use set-builder notation to write the solution set. If a system has no solution, state this. $$ \begin{aligned} &y-2 x=-6\\\ &2 y-x=5 \end{aligned} $$

Solve by the substitution method. $$ \begin{aligned} &\frac{x}{5}-\frac{y}{2}=3\\\ &\frac{x}{4}+\frac{3 y}{4}=1 \end{aligned} $$

A train leaves Union Station for Central Station, \(216 \mathrm{km}\) away, at \(9 \mathrm{A} . \mathrm{M}\). One hour later, a train leaves Central Station for Union Station. They meet at noon. If the second train had started at 9 A.M. and the first train at 10: 30 A.M., they would still have met at noon. Find the speed of each train.

Monica makes a \$9.25 purchase at the bookstore with a \(\$ 20\) bill. The store has no bills and gives her the change in quarters and fifty-cent pieces. There are 30 coins in all. How many of each kind are there?

Solve each system using the substitution method. If a system has an infinite number of solutions, use set-builder notation to write the solution set. If a system has no solution, state this. $$ \begin{aligned} &5 x=y-3\\\ &5 x=y+5 \end{aligned} $$
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