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Chapter 2: Problem 34

Classify each of the inequalities as true or false. $$\frac{3}{10} \geq 0.3$$

Short Answer

Expert verified
The inequality is true.

Step by step solution

01

Convert Fraction to Decimal

First, we need to convert the fraction \( \frac{3}{10} \) into its decimal form. To do this, divide 3 by 10. This yields 0.3.
02

Compare the Decimals

Now, compare the two decimals obtained from the previous step. We have 0.3 (from \( \frac{3}{10} \)) and 0.3 from the inequality. Seeing these are equal, we can analyze the inequality \(0.3 \geq 0.3\).
03

Evaluate the Inequality Expression

Evaluate the inequality \(0.3 \geq 0.3\). Since 0.3 is equal to 0.3, the inequality holds true because the symbol \(\geq\) means "greater than or equal to."

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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 a fraction to a decimal is a simple yet essential skill in mathematics. It involves dividing the numerator (the top number) of the fraction by the denominator (the bottom number).

In our example, we have the fraction \( \frac{3}{10} \). To convert this to a decimal, you divide 3 by 10. When you perform this division, you get 0.3.

Here are some key points to remember about converting fractions to decimals:
  • Always divide the numerator by the denominator.
  • If the division doesn't result in a terminating decimal, you may need to round or express it as a repeating decimal.
  • Knowing how to move between fractions and decimals helps in solving equations, inequalities, and in real-world applications.
The ability to switch between these two forms can make it easier to compare quantities or perform calculations.
Decimal Comparison
Once you have both numbers in decimal form, comparing them becomes straightforward. For example, in our scenario, we need to compare 0.3 (obtained from the fraction) with 0.3.

When comparing decimals:
  • Check digit by digit from left to right.
  • If the digits of the two numbers at each place value are all the same, they are equal.
  • If one number has more digits, but they are all zeros after the matching part, they are still equal (e.g., 0.30 = 0.3).
The goal is to determine which is larger, or if they are indeed equal. In our exercise, since both decimals are 0.3, they are equal.
Inequality Symbols
Inequality symbols are used to indicate the relationship between two values. The inequality symbol used in the exercise is \( \geq \), which stands for "greater than or equal to".

Understanding inequality symbols is crucial:
  • \( > \) means "greater than".
  • \( < \) means "less than".
  • \( \geq \) means "greater than or equal to".
  • \( \leq \) means "less than or equal to".
To evaluate an inequality correctly, you must understand these symbols and determine whether the statement is true or false based on the comparison of the numbers involved.

In our problem, the inequality \( 0.3 \geq 0.3 \) is true because 0.3 is equal to 0.3, satisfying the "equal to" part of our symbol.

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Most popular questions from this chapter

Solve the equations by using the multiplication property. $$\frac{x}{3}=9$$

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