Unit: Real NumbersMatch Each Number On The Left With The Correct Description On The Right. Answer Options May Be Used More Than Once.Numbers:1. $-10$2. $\sqrt{5}$3. $-5.\overline{6}$4. $3 \frac{1}{4}$5.

Match each number on the left with the correct description on the right. Answer options may be used more than once.

Numbers

1. $-10$
2. $\sqrt{5}$
3. $-5.\overline{6}$
4. $3 \frac{1}{4}$
5. $5$

Descriptions

1. A rational number with a negative sign
2. An irrational number
3. A repeating decimal
4. A mixed number
5. An integer

Solutions

1. $-10$ - A rational number with a negative sign
2. $\sqrt{5}$ - An irrational number
3. $-5.\overline{6}$ - A repeating decimal
4. $3 \frac{1}{4}$ - A mixed number
5. $5$ - An integer

Explanation

• Rational numbers are numbers that can be expressed as the ratio of two integers, i.e., in the form $\frac{p}{q}$, where $p$ and $q$ are integers and $q$ is non-zero. Rational numbers can be expressed as either terminating or repeating decimals. Examples of rational numbers include $-10$, $3 \frac{1}{4}$, and $5$.
• Irrational numbers are numbers that cannot be expressed as the ratio of two integers. They have decimal expansions that go on indefinitely without repeating. Examples of irrational numbers include $\sqrt{5}$.
• Repeating decimals are a type of rational number that can be expressed as a decimal with a repeating pattern. Examples of repeating decimals include $-5.\overline{6}$.
• Mixed numbers are a type of rational number that can be expressed as the sum of an integer and a proper fraction. Examples of mixed numbers include $3 \frac{1}{4}$.

Key Takeaways

• Rational numbers can be expressed as the ratio of two integers and can be expressed as either terminating or repeating decimals.
• Irrational numbers cannot be expressed as the ratio of two integers and have decimal expansions that go on indefinitely without repeating.
• Repeating decimals are a type of rational number that can be expressed as a decimal with a repeating pattern.
• Mixed numbers are a type of rational number that can be expressed as the sum of an integer and a proper fraction.

Practice Problems

• Match each number on the left with the correct description on the right. Answer options may be used more than once.
  • Numbers: $-7$, $\sqrt{2}$, $-2.\overline{3}$, $4 \frac{1}{2}$, $6$
  • Descriptions: A rational number with a negative sign, An irrational number, A repeating decimal, A mixed number, An integer
• Classify each of the following numbers as rational or irrational.
  • $-3$
  • $\sqrt{9}$
  • $-2.\overline{5}$
  • $4 \frac{1}{3}$
    Unit: Real Numbers ======================

Q&A: Real Numbers

Q1: What is the difference between rational and irrational numbers?

A1: Rational numbers are numbers that can be expressed as the ratio of two integers, i.e., in the form $\frac{p}{q}$, where $p$ and $q$ are integers and $q$ is non-zero. Irrational numbers, on the other hand, are numbers that cannot be expressed as the ratio of two integers. They have decimal expansions that go on indefinitely without repeating.

Q2: What is an example of a rational number with a negative sign?

A2: An example of a rational number with a negative sign is $-10$. This number can be expressed as the ratio of two integers, i.e., $-10 = \frac{-10}{1}$.

Q3: What is an example of an irrational number?

A3: An example of an irrational number is $\sqrt{5}$. This number cannot be expressed as the ratio of two integers and has a decimal expansion that goes on indefinitely without repeating.

Q4: What is a repeating decimal?

A4: A repeating decimal is a type of rational number that can be expressed as a decimal with a repeating pattern. For example, $-5.\overline{6}$ is a repeating decimal.

Q5: What is a mixed number?

A5: A mixed number is a type of rational number that can be expressed as the sum of an integer and a proper fraction. For example, $3 \frac{1}{4}$ is a mixed number.

Q6: Can a rational number have a negative sign?

A6: Yes, a rational number can have a negative sign. For example, $-10$ is a rational number with a negative sign.

Q7: Can an irrational number be expressed as a decimal with a repeating pattern?

A7: No, an irrational number cannot be expressed as a decimal with a repeating pattern. Irrational numbers have decimal expansions that go on indefinitely without repeating.

Q8: Can a mixed number be expressed as the ratio of two integers?

A8: Yes, a mixed number can be expressed as the ratio of two integers. For example, $3 \frac{1}{4}$ can be expressed as the ratio of two integers, i.e., $3 \frac{1}{4} = \frac{13}{4}$.

Q9: What is the difference between a terminating decimal and a repeating decimal?

A9: A terminating decimal is a type of rational number that can be expressed as a decimal with a finite number of digits. A repeating decimal, on the other hand, is a type of rational number that can be expressed as a decimal with a repeating pattern.

Q10: Can an irrational number be expressed as the ratio of two integers?

A10: No, an irrational number cannot be expressed as the ratio of two integers. Irrational numbers have decimal expansions that go on indefinitely without repeating.

Key Takeaways

• Rational numbers can be expressed as the ratio of two integers and can be expressed as either terminating or repeating decimals.
• Irrational numbers cannot be expressed as the ratio of two integers and have decimal expansions that go on indefinitely without repeating.
• Repeating decimals are a type of rational number that can be expressed as a decimal with a repeating pattern.
• Mixed numbers are a type of rational number that can be expressed as the sum of an integer and a proper fraction.

Practice Problems

• Match each number on the left with the correct description on the right. Answer options may be used more than once.
  • Numbers: $-7$, $\sqrt{2}$, $-2.\overline{3}$, $4 \frac{1}{2}$, $6$
  • Descriptions: A rational number with a negative sign, An irrational number, A repeating decimal, A mixed number, An integer
• Classify each of the following numbers as rational or irrational.
  • $-3$
  • $\sqrt{9}$
  • $-2.\overline{5}$
  • $4 \frac{1}{3}$