/*! This file is auto-generated */ .wp-block-button__link{color:#fff;background-color:#32373c;border-radius:9999px;box-shadow:none;text-decoration:none;padding:calc(.667em + 2px) calc(1.333em + 2px);font-size:1.125em}.wp-block-file__button{background:#32373c;color:#fff;text-decoration:none} Problem 21 Replace the question mark by \(&... [FREE SOLUTION] | 91影视

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Chapter 0: Problem 21

Replace the question mark by \(<,>,\) or \(=\), whichever is correct. \(\frac{1}{2} ? 0.5\)

Short Answer

Expert verified
The correct symbol is \(=\).

Step by step solution

01

- Convert Fraction to Decimal

To compare the fraction \(\frac{1}{2}\) with the decimal 0.5, first convert \(\frac{1}{2}\) into a decimal form. \(\frac{1}{2} = 0.5\).
02

- Compare the Values

Now compare the values of 0.5 and 0.5. Since they are equal, the correct symbol to use between them is \(=\).

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Key Concepts

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

fraction to decimal conversion
In mathematics, comparing fractions with decimals often requires converting one form into the other. Here, we'll start by converting the fraction \(\frac{1}{2}\) into a decimal.
To do this, you can divide the numerator by the denominator.
This means you'll perform the operation:
\(\frac{1}{2} = 1 \div 2 = 0.5\)
This means that \(\frac{1}{2}\) is equal to 0.5 in decimal form.
This conversion is often a crucial step before you can make accurate comparisons.
basic comparisons
Once you have converted the fraction \(\frac{1}{2}\) to its decimal form (0.5), the next step is to compare the two decimal numbers.
Comparing decimal numbers is often simpler than comparing fractions directly.
To compare the decimals:
- Look at the digits from left to right.
- Start with the tenths place.
- Move to the next decimal place if needed.
In our case, we compare 0.5 with 0.5. Since the numbers are identical, we can determine their relationship easily.
equal values
After converting and comparing, we find that 0.5 and 0.5 are equal.
This means the correct symbol to use between them is \(=\).
Understanding when values are equal is essential in mathematics and helps in ensuring that your calculations are accurate.
By knowing how to convert and compare, you can verify relationships between numbers accurately and confidently.
In this exercise, recognizing that \(\frac{1}{2} \) and 0.5 are equal clarifies the understanding of both fractions and their equivalent decimal forms.

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Most popular questions from this chapter

Simplify each expression. Assume that all variables are positive when they appear. $$9 \sqrt[3]{24}-\sqrt[3]{81}$$

Simplify each expression. Assume that all variables are positive when they appear. $$(\sqrt[3]{3} \sqrt{10})^{4}$$

Expressions that occur in calculus are given. Factor each expression. Express your answer so that only positive exponents occur. $$4(3 x+5)^{1 / 3}(2 x+3)^{3 / 2}+3(3 x+5)^{4 / 3}(2 x+3)^{1 / 2} \quad x \geq-\frac{3}{2}$$

Expressions that occur in calculus are given. Factor each expression. Express your answer so that only positive exponents occur. $$6(6 x+1)^{1 / 3}(4 x-3)^{3 / 2}+6(6 x+1)^{4 / 3}(4 x-3)^{1 / 2} \quad x \geq \frac{3}{4}$$

Use a calculator to approximate each radical. Round your answer to two decimal places. $$\frac{2+\sqrt{3}}{3-\sqrt{5}}$$
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