/*! 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 23 Replace the question mark by \(&... [FREE SOLUTION] | 91影视

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Chapter 0: Problem 23

Replace the question mark by \(<,>,\) or \(=\), whichever is correct. \(\frac{2}{3} ? 0.67\)

Short Answer

Expert verified
\(\frac{2}{3} < 0.67\)

Step by step solution

01

Convert fraction to decimal

First, convert the fraction \(\frac{2}{3}\) to its decimal form. Divide 2 by 3: \(2 \div 3 = 0.6667\) (approximately)
02

Compare the numbers

Compare the decimal form of the fraction \(0.6667\) with the given decimal \(0.67\).
03

Determine the relationship

Since \(0.6667 < 0.67\), the fraction \(\frac{2}{3}\) is less than the decimal \(0.67\). Therefore, we use the symbol \(<\).

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Key Concepts

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

Fraction to Decimal Conversion
Converting fractions to decimals is a crucial skill in mathematics.
To convert a fraction like \(\frac{2}{3}\) into a decimal, you simply divide the numerator (2) by the denominator (3).
Performing the division gives us: \[\frac{2}{3} = 0.6667\text{ (approximately)}\]
Understanding this conversion is essential for comparing fractions with decimals.
Comparing Numbers
Once you have the numbers in the same format, comparing becomes straightforward.
In our example, we compare the decimal form of \(\frac{2}{3}\) which is 0.6667, with 0.67.
It's important to focus on the digits of both numbers starting from the left.
In this case:
  • 0.6667 has digits 6, 6, 6, 7
  • 0.67 has digits 6, 7
By comparing them digit by digit, starting from the left, we see that 0.6667 is less than 0.67.
Mathematical Symbols
Mathematical symbols help us express relationships between numbers.
The most common symbols used for comparison are:
  • \(<\) - Less than
  • \(>\) - Greater than
  • \(=\) - Equals
In our exercise, after converting, we found 0.6667 is less than 0.67.
Therefore, we use the \(<\) symbol: \(\frac{2}{3} < 0.67\).
Understanding and correctly using these symbols is fundamental in math.

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Most popular questions from this chapter

Simplify each expression. Assume that all variables are positive when they appear. $$\sqrt{15 x^{2}} \sqrt{5 x}$$

Rationalize the numerator of each expression. Assume that all variables are positive when they appear. $$\frac{5-\sqrt{43}}{3}$$

Simplify each expression. $$4^{3 / 2}$$

Rationalize the denominator of each expression. Assume that all variables are positive when they appear. $$\frac{2-\sqrt{5}}{2+3 \sqrt{5}}$$

Rationalize the denominator of each expression. Assume that all variables are positive when they appear. $$\frac{-2}{\sqrt[3]{9}}$$
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