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Chapter 5: Problem 227

Order each pair of numbers, using \(<\) or \(>\) \(0.725\) ____ \(\frac{3}{4}\)

Short Answer

Expert verified
0.725 < \(\frac{3}{4}\)

Step by step solution

01

Convert the fraction to a decimal

Change \(\frac{3}{4}\) into its decimal form by dividing the numerator by the denominator. \(\frac{3}{4} = 0.75\).
02

Compare the two decimals

Now compare the two decimals: 0.725 and 0.75. Since 0.751 is greater than 0.725, we can write 0.725 < 0.75.
03

Write the final relation

Using the comparison from Step 2, write the final relation: 0.725 < \(\frac{3}{4}\)

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Key Concepts

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

decimal conversion
To compare fractions and decimals, it's important to be able to convert fractions into decimal form. This process involves dividing the numerator (top number) by the denominator (bottom number). For instance, to convert \(\frac{3}{4}\) into a decimal, you divide 3 by 4. The operation yields 0.75. Decimal conversion makes it simpler to compare different types of numbers directly.
numerator and denominator
Fractions consist of two parts: the numerator on top and the denominator on the bottom. The numerator indicates how many parts of the whole we are working with. The denominator shows the total number of equal parts the whole is divided into. Understanding how these two components interact helps in converting fractions to decimals. For example, in \(\frac{3}{4}\), 3 is the numerator and 4 is the denominator. Dividing them gives us 0.75, making comparison with other decimals easier.
inequality symbols
After converting fractions to decimals, using inequality symbols lets us compare them easily. Inequality symbols include \(<\) (less than) and \(>\) (greater than). In the example given, after converting \(\frac{3}{4}\) to 0.75, we compare 0.725 and 0.75. Since 0.725 is less than 0.75, we use the \( < \) symbol to show this relationship. Thus, it becomes clear that 0.725 < \(\frac{3}{4}\). Using these symbols helps us clearly state which numbers are larger or smaller.

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