The Number System - Common Core: 8th Grade Math

To solve this problem, we first need to know what number represents:

We are looking for a point on the number line that is between and , about right between them. Based on the number line provided, point A is the best representation of

To solve this problem, we first need to know what number represents:

We are looking for a point on the number line that is on . Based on the number line provided, point B is the best representation of

To solve this problem, we first need to know what number represents:

We are looking for a point on the number line that is on . Based on the number line provided, point D is the best representation of

To solve this problem, we can think of perfect squares around

This means that has to be between and on the number line. Based on the number line provided, point E is the best representation of

To solve this problem, we can think of perfect squares around

This means that has to be between and on the number line. Based on the number line provided, point F is the best representation of

To solve this problem, we first need to know what number represents:

We are looking for a point on the number line that is on . Based on the number line provided, point G is the best representation of

To solve this problem, we can think of perfect squares around

This means that has to be between and on the number line, but closer to because is closer to than . Based on the number line provided, point H is the best representation of

To solve this problem, we can think of perfect squares around

This means that has to be between and on the number line, but closer to because is closer to than . Based on the number line provided, point I is the best representation of

To solve this problem, we can think of perfect squares around

This means that has to be between and on the number line. Based on the number line provided, point J is the best representation of

To solve this problem, we first need to know what number represents:

We are looking for a point on the number line that is on . Based on the number line provided, point K is the best representation of

To solve this problem, we can think of perfect squares around

This means that has to be between and on the number line, but closer to because is closer to than . Based on the number line provided, point L is the best representation of

An irrational number is any number that cannot be written as a fraction of whole numbers. The number pi and square roots of non-perfect squares are examples of irrational numbers.

can be written as the fraction . The term is a whole number. The square root of is , also a rational number. , however, is not a perfect square, and its square root, therefore, is irrational.

A rational number is any number that can be expressed as a fraction where both the numerator and denominator are integers. The denominator also cannot be equal to 0. In this set, the irrational number is because the There is no fraction that can be made, it's decimal goes on and on and does not repeat in a pattern. Using the fraction test, we can prove that the following numbers are rational:

An irrational number is any number that can not be expressed as a ratio of integers, i.e. a fraction. Therefore, the only irrational number listed is .

Pi is the only irrational number listed. Irrational numbers are in the form of infinite non-repeating decimals.

A root of an integer is one of two things, an integer or an irrational number. By testing all five on a calculator, only comes up an exact integer - 5. This is the correct choice.

A rational number is any number that can be expressed as a fraction/ratio, with both the numerator and denominator being integers. The one limitation to this definition is that the denominator cannot be equal to .

Using the above definition, we see , and (which is ) cannot be expressed as fractions. These are non-terminating numbers that are not repeating, meaning the decimal has no pattern and constantly changes. When a decimal is non-terminating and constantly changes, it cannot be expressed as a fraction.

is the correct answer because , which can be expressed as , fullfilling our above defintion of a rational number.

The definition of an irrational number is a number which cannot be expressed in a simple fraction, or a number that is not rational.

Using the above definition, we see that is already expressed as a simple fraction.

any number and

. All of these options can be expressed as simple fractions, making them all rational numbers, and the incorrect answers.

cannot be expressed as a simple fraction and is equal to a non-terminating, non-repeating (ever-changing) decimal, begining with

This is an irrational number and our correct answer.

An irrational number is defined as any number that cannot be expressed as a simple fraction or does not have terminating or repeating decimals. Of the answer choices given, the only number that cannot be expressed as a simple fraction or with repeating or terminating decimals is .