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Chapter 5: Problem 584

In the following exercises, order each pair of numbers, using < or >. \(\frac{1}{2}\)___0.2

Short Answer

Expert verified
\( \frac{1}{2} > 0.2 \)

Step by step solution

01

Understand the Problem

You need to compare the fraction \( \frac{1}{2} \) with the decimal 0.2 and determine which is larger.
02

Convert Fraction to Decimal

Convert the fraction \( \frac{1}{2} \) to its decimal form. \( \frac{1}{2} = 0.5 \).
03

Compare the Numbers

Now, compare the converted decimal 0.5 with 0.2. Since 0.5 is greater than 0.2, you use the '>' symbol.

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Key Concepts

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

comparing fractions and decimals
Understanding how to compare fractions and decimals is crucial. Fractions and decimals are two different ways to represent numbers. To compare them, it's often easiest to convert one form to the other. This allows you to make a straightforward comparison. In many cases, converting fractions to decimals can simplify the process. For example, in the exercise given, we are asked to compare \( \frac{1}{2} \) with 0.2. Converting \( \frac{1}{2} \) to a decimal gives us 0.5, making it easier to compare with 0.2.
converting fractions to decimals
To compare fractions and decimals, converting fractions to decimals can greatly help. To convert a fraction to a decimal, you divide the numerator by the denominator.
Let's take the fraction \( \frac{1}{2} \):
  • The numerator (top number) is 1.
  • The denominator (bottom number) is 2.
When you divide 1 by 2, you get 0.5. This makes it simpler to compare \( \frac{1}{2} \) with 0.2, as both are now in decimal form.
number comparison
Once you have both numbers in the same form, comparing them is straightforward. You just look at the value of each number. For example, compare 0.5 and 0.2:
  • 0.5 is greater than 0.2.
  • Thus, \( \frac{1}{2} \) (or 0.5) is greater than 0.2.
Using the '>' symbol, we show this comparison. So, \( \frac{1}{2} > 0.2 \).
This approach can be applied to any fraction and decimal comparison!

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