GED Math : Types of Numbers and Number Theory

Study concepts, example questions & explanations for GED Math

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Example Questions

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Example Question #31 : Numbers

Give the Arabic number equivalent for the Roman numeral:

Possible Answers:

Correct answer:

Explanation:

The Roman numeral can be broken down as follows:

:

:

; since the smaller-valued symbol precedes the greater-valued symbol, this is a subtraction, so .

:

Add these: , the correct response.

 

Example Question #31 : Types Of Numbers And Number Theory

Which of the following numbers is an integer?

Possible Answers:

Correct answer:

Explanation:

Which of the following numbers is an integer?

An integer is any positive or negative whole number, including 0. 

 is the ratio of circumference to diameter, and is a never ending decimal

  and is known as an imaginary number.

-46.4 is a decimal, and thus not an integer.

Therefore our only integer here is 0

Example Question #31 : Numbers And Operations

What sort of solutions are found when  is solved?

Possible Answers:

 real, rational solutions

No real solutions

 real, irrational solutions

 real, irrational solution

Correct answer:

 real, irrational solutions

Explanation:

Look at the discriminant to figure out the number of solutions.

For this equation, 

Since the discriminant is positive, this means that there will be  real solutions. Since the discriminant is not a square of another number, this means that those two solutions will be irrational.

Example Question #32 : Types Of Numbers And Number Theory

Sarah says 3 is a rational number. Tom disagrees and says 3 is an integer. Who is right? 

Possible Answers:

Both

Sarah

Tom

Neither

42

Correct answer:

Both

Explanation:

They are both correct.

3 is most certainly an integer as integers are our positive and negative whole numbers.

Sarah is right too. Rational numbers are any number that can be written as a fraction of integers. 3 can be written as a fraction , so it is a rational number too.

In fact, all integers are rational (but not all rational numbers are integers)

Example Question #31 : Types Of Numbers And Number Theory

The set of real numbers is divided into several subsets including positive numbers and negative numbers, prime numbers and composite number, rational numbers and irrational numbers, etc. For the following questions, select the answer that is a member of the stated subset.

Which number is irrational?

Possible Answers:

Correct answer:

Explanation:

A rational number is any number that can be expressed in the form  where  and  are integers. 

One of the answers is already in that form:  is the ratio of two integers.  And the repeating decimal  is the decimal equivalent of that same ratio of 1:3.

 

 is equal to 27 itself a rational number.

 

But  cannot be written as the ratio of two integers, so it is an irrational number.

 

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