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Chapter 5: Problem 228

Order each pair of numbers, using \(<\) or \(>\) 0.92 ____ \(\frac{7}{8}\)

Short Answer

Expert verified
0.92 \(>\) \(\frac{7}{8}\)

Step by step solution

01

Understand The Problem

The task is to compare two numbers: 0.92 and \(\frac{7}{8}\). To do this, both numbers need to be in the same form, either as decimals or fractions.
02

Convert The Fraction To A Decimal

Convert the fraction \(\frac{7}{8}\) to a decimal by performing the division: 7 divided by 8. Perform the division: \(\frac{7}{8} = 0.875\).
03

Compare The Numbers

Now you have 0.92 and 0.875. Compare these two decimals. Since 0.92 is greater than 0.875, we can write 0.92 \(>\) \(\frac{7}{8}\).

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Key Concepts

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

Decimals
Decimals are a way to represent fractions using powers of 10. Each place to the right of the decimal point represents a fraction with a denominator that is a power of 10. For example, the number 0.92 has two digits after the decimal. This means it's made up of 9 tenths and 2 hundredths. In other words, 0.92 is the same as saying \( \frac{92}{100} \). Understanding how decimals work is crucial when comparing them with other numbers, such as fractions. Every digit after the decimal point contributes to the number's overall value, making it easy to compare different decimal numbers.
Fractions
Fractions consist of two numbers: the numerator and the denominator. The numerator is the number above the line, showing the number of parts we have. The denominator is the number below the line, showing the number of parts the whole is divided into. For example, \( \frac{7}{8} \) has 7 parts out of a total of 8 parts. Understanding fractions is essential because it allows us to represent parts of a whole. To compare fractions and decimals easily, fractions often need to be converted into decimal form.
Converting Fractions to Decimals
To compare a fraction with a decimal, it's helpful to convert the fraction to a decimal. This can be done through division. For example, to convert \( \frac{7}{8} \) to a decimal, you divide 7 by 8. Carry out the division to get 0.875. Now, you can compare this decimal with another decimal, like 0.92.

The decimal 0.92 is larger than 0.875 because 92 is greater than 87 when comparing their hundredths place. Therefore, 0.92 > 0.875, and hence, 0.92 > \( \frac{7}{8} \).

This conversion method is straightforward and very useful for comparing fractions with decimals accurately.

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