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Chapter 2: Problem 24

Convert to decimal notation. $$ 150 \% $$

Short Answer

Expert verified
150% in decimal notation is 1.5.

Step by step solution

01

Understand Percentages

Percentages represent parts per hundred. Specifically, 1% is equivalent to 1/100.
02

Set Up the Equation

Convert the percentage to a fraction. For instance, 150% can be written as 150/100.
03

Simplify the Fraction

Simplify the fraction 150/100 by dividing the numerator and the denominator by their greatest common divisor, which is 50. Therefore, \(150 \div 50 = 3\) and \(100 \div 50 = 2\). So, the fraction simplifies to 3/2.
04

Convert to Decimal Notation

Now, convert the fraction to a decimal. Divide the numerator by the denominator: \(3 \div 2 = 1.5\). Thus, 150% in decimal notation is 1.5.

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Key Concepts

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

Percentages
When we talk about percentages, we are referring to a portion out of 100. The term 'percent' literally means 'per hundred'. For example, 1% simply means 1 out of 100.
So, if you have 150%, it means 150 out of 100. This notion is very useful in various fields like finance, statistics, and many more.
The keyword here is: it helps in making comparisons easier.
  • 1% = 1/100
  • 150% = 150/100
Fraction simplification
Fractions represent a part of a whole and simplifying them makes calculations easier. For any fraction, you can simplify it by dividing both the numerator (the top number) and the denominator (the bottom number) by their greatest common divisor (GCD).
In our example, the fraction is 150/100.
The GCD of 150 and 100 is 50.
So, we divide both numbers by 50, simplifying 150/100 to 3/2.
Simplifying fractions makes them more manageable and easier to work with.
  • Simplified: 150/100 = 3/2
Decimal notation
Decimals are a way to represent fractions using the base 10 system. To convert a fraction into a decimal, you divide the numerator by the denominator.
For the fraction 3/2, the division is:
\( \frac{3}{2} = 1.5 \)
Therefore, 3/2 in decimal form is 1.5. Knowing how to convert between fractions and decimals is key to handling numerical data efficiently.
  • 3/2 = 1.5
Basic arithmetic
Arithmetic forms the building block for all other math concepts. It includes operations like addition, subtraction, multiplication, and division.
Understanding these basic operations is crucial for solving more complex problems.
For instance, dividing the numerator by the denominator to convert a fraction into a decimal, like we did with 3/2, is a fundamental arithmetic operation.
Mastery of these basic operations makes it easier to understand more complex concepts.
  • Addition
  • Subtraction
  • Multiplication
  • Division

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Most popular questions from this chapter

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