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Chapter 2: Problem 89

Convert each decimal to a percent. $$ 2.2 $$

Short Answer

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Step by step solution

01

Understand the Relationship Between Decimals and Percents

Recognize that a percent is a way of expressing a number as a fraction of 100. To convert a decimal to a percent, multiply the decimal by 100.
02

Multiply the Decimal by 100

Take the decimal value 2.2 and multiply it by 100. \[2.2 \times 100 = 220\]
03

Add the Percent Symbol

After multiplying by 100, add the percent (%) symbol to your answer. So, 2.2 becomes 220%.

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Key Concepts

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

Multiplying by 100
When converting a decimal to a percent, one of the crucial steps is multiplying the decimal by 100.
This action helps in changing the decimal representation to a more recognizable percent format.
Let's break down why this is necessary.

In mathematics, a percent means 'per hundred.' Therefore, if you have a decimal and want to convert it to a percent, you need to know how many parts out of 100 it represents.
  • For instance, if you start with the decimal 2.2, you multiply it by 100 to scale it up to a percentage.
  • The calculation looks like this: \[ 2.2 \times 100 = 220 \]
  • This result, 220, tells you the equivalent value per 100 units.
This simple multiplication helps bring clarity and make comparisons easier when dealing with percentages.
Remember, multiplying by 100 is a mechanical step, but understanding this conversion infuses meaning into your calculations.
Decimal Representation
Decimals are another way to represent fractions or parts of a whole.
For example, 2.2 is a decimal that can also be written as the fraction \[ \frac{22}{10} \] or simply 2 and 2/10.
Decimals are essential because they offer a clear and straightforward way to understand values that are not whole numbers.
  • Decimals work based on the power of 10.
  • Each place to the right of the decimal point holds a value that is a fraction of 10 (i.e., tenths, hundredths, etc.).
Understanding decimals helps in their conversion to other formats like percentages.
This relationship with fractions and whole numbers makes decimals versatile in different mathematical contexts.

While the decimal 2.2 represents a value greater than 2, when converted into a percentage, it helps to visualize this value more clearly.
Percent Symbol
The percent (%) symbol is a pivotal part of expressing percentages.
When converting a decimal to a percent, it is not enough to just multiply by 100; you must also add the % symbol at the end of your number.
This symbol conveys that the number is a part of 100.
  • After multiplying the decimal by 100, you get your numerical answer.
  • Adding the % symbol tells everyone that this number is a percentage.
For example, converting 2.2 to a percent:
\[ 2.2 \times 100 = 220 \]
When we add the % symbol:
220 becomes 220%.
This complete form is essential for clarity and correct representation in various applications of math, finance, and science.

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Most popular questions from this chapter

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