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Chapter 5: Problem 224

Order each pair of numbers, using \(<\) or \(>\) \(\frac{1}{4}\) ____ \(0.4\)

Short Answer

Expert verified
\(\frac{1}{4} < 0.4\).

Step by step solution

01

- Convert the Fraction to Decimal

Convert \(\frac{1}{4}\) to a decimal by dividing the numerator by the denominator. \(\frac{1}{4} = 0.25\).
02

- Compare the Decimals

Compare the two decimals: \0.25\ and \0.4\. Since \0.25 < 0.4\, \(\frac{1}{4} < 0.4\).

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Key Concepts

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

comparing numbers
When comparing numbers, it's important to make sure the numbers you are comparing are in the same format. This makes it easier to identify which number is larger or smaller. For instance, comparing fractions to decimals might be tricky if they aren't in a similar form. In our exercise, we compared \(\frac{1}{4}\) and 0.4. This might seem difficult at first, but with a straightforward approach, it becomes clear.

First, you need to ensure the numbers are either both in fraction form or both in decimal form. This brings us to our next crucial step: converting fractions to decimals.
fraction to decimal conversion
Fractions and decimals represent the same concept but in different forms. To compare them accurately, it's often helpful to convert fractions to decimals.

For example, to convert the fraction \(\frac{1}{4}\) to a decimal, you divide the numerator (1) by the denominator (4). Doing this gives you 0.25. So, \(\frac{1}{4} = 0.25\).

Now that we have two decimals, 0.25 and 0.4, the comparison becomes straightforward. This method works for most simple fractions. For more complex fractions, the concept remains the same - divide the numerator by the denominator to get the decimal equivalent.
inequalities
Inequalities are useful in comparing numbers. They help us understand the relationship between two values. In mathematics, we use symbols like \( < \) (less than) and \( > \) (greater than) to denote these relationships.

In our exercise, we converted \(\frac{1}{4}\) to 0.25. So, we had 0.25 and 0.4 as our decimals. When we compare 0.25 and 0.4, we see that 0.25 is smaller than 0.4. Therefore, we write 0.25 \( < \) 0.4. So, \(\frac{1}{4} < 0.4\).

Remember, it's crucial to ensure both numbers are in the same format (either both as decimals or both as fractions) before using inequality symbols to compare them. This makes the comparison clear and accurate.

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Most popular questions from this chapter

In the following exercises, find the unit rate. Round to two decimal places, if necessary. The bindery at a printing plant assembles 96,000 magazines in 12 hours. How many magazines are assembled in one hour?

Kathryn ate a 4 -ounce cup of frozen yogurt and then went for a swim. The frozen yogurt had 115 calories. Swimming burns 422 calories per hour. For how many minutes should Kathryn swim to burn off the calories in the frozen yogurt? Explain your reasoning.

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