Introduction to Numbers

Welcome to the complete Ultimate GED Math Course from UltimateGED.com.  The purpose of this course is to start you from scratch and give you everything you need to pass the GED Test with EASE. We’ve helped a lot of people pass and we are 100% sure we can help you Pass. All you need to do is watch all the videos in this course and be engaged in the comment section. Ask questions and answer questions. We are going to cover everything. For every topic we cover here, we will put a link in the description to ultimateged.com, where you can get more examples. Ok Let’s dive in. We are starting with Introduction to numbers.

Question 1. The Number 2 is …

Here we are supposed to select all that applies. To get this right. We need to know the kind of numbers. Counting or natural numbers are the numbers we count, so we have 1, 2, 3, 4 and so on. When you add zero to these numbers, we have whole numbers. So whole numbers are 0, 1, 2, 3, 4 and so on. When we add negatives, we have integers. We have  0, 1, 2,3 and so on and we can add, -1, -2, -3 and so on to get our integers. When you add fractions to integers, then you have rational numbers. So we have  -2, -3/2, -1, 0, 1/2, 1, 5/4, 2 and so on are rational numbers. We’ll take a deeper dive into rational numbers with the next question. Let’s just use this information for now. Ok, so looking at this, you’ll notice that once a number is in a lower level, it means it’s in all the levels above it. If a number is here. Then it will automatically be here and here. For our question, we can say that 2 is a counting or natural number, check. 2 is a whole number, check.2 is an integer, check and 2 is a rational number, check. So we have our answer

Let’s try -5. See if you can do it yourself.

-5 is not a natural number because natural numbers are 1, 2, 3 and so on. -5 is not a whole number, because whole numbers are 0, 1, 2, 3 and so on. -5 is and integer. We know that negative counting numbers are integers. And -5 is a rational number. Let’s try a more trick question. If x is a positive integer, then x is also… Please try this and leave your answer in the comment section. You can visit UltimateGED.com for the solution and more examples if you are interested.

Let’s look at question 2.

How many elements of the set {0,-1, π, -4/7, √2,} are rational numbers. A Rational number is the ratio of two integers. We know our integers are positive counting numbers (1, 2, 3, and so on) and negative counting numbers  (-1, -2, -3 and so on) and zero. So if we take any of the numbers over another number we have a rational number. So -2 over 3 is rational. 5 over 7 is also rational So 4 over 1 is also rational. Note that any number over 1 is the same number. So 4 over 1 can simple be written as 4. Please note that for a rational number the denominator or number at the bottom CANNOT be zero. Although we said you can pick any two integers. So, example, 8 over 0 is not a rational number. It is undefined. Please NOTE this as the exception. But the top or numerator can be zero. So zero over 8 is a rational number. I’ll post a video on UltimateGed.com for those who want to learn more on the concept of 1 and zero in math. It’s definitely something that will help you in math. Moving on, Irrational basically means NOT rational. You cannot write it as a ratio of two integers. The most common irrational numbers you’ll find on the GED are π, √2 and √3. Let’s look at our question now So 0 is a rational number. We know we can write 0 as 0/8 or 0/1 or 0/1000. 0 over any number is zero. -1 is also a rational number. We can write it as -1/1. π is an irrational number as we just learnt here. We will explain that more in later lessons but please take note of it. -4/7 is a rational number. It is an integer -4 over another integer 7. √2 is an irrational number. Please don’t assume all roots are irrational numbers. Example √9 is a rational number. Because the square root of 9 is 3. So we can say that 3 of the elements are rational. When dealing with fractions or integers, it’s easy to tell that a number is rational, but when dealing with decimals it becomes quite confusing if you don’t know what you’re looking for. 

In this question we are supposed to find the number that is irrational.

For decimals, we look at an irrational number as a number that has non-repeating and non-terminating decimal. Therefore for a Rational number the decimals must either repeat. Like 0.22222 repeating. We use this dots to show that the number continues. Here the 2 repeats or the decimals must terminate. Example 7.35. there are no more numbers after the 3,5. No dots to show that it continues. So for multiple choice A, we can see that the 3 is repeating so it is a rational number. This decimal is actually the same 1/3. You can check it out on your calculator. 1 divided by 3. For choice B also we can see that we have two-seven, two-seven, two-seven. The two-seven is repeating so it is a rational number. Same here. This has one-two-three, one-two-three, and one-two-three. The one-two-three is repeating so it’s a rational number. For the last one. When we look at the decimals, we have 4142356 and so on. The numbers are not repeating in any orderly form, so we say it’s NON-Repeating. Also the number continues, so we say it’s NON-TERMINATING. We can therefore say that the 1.41421356 and so on is a irrational number.

This is actually the same as √2 which we already know from the previous question to be irrational. Try it on your calculator. Square root of 2. So this is our answer.

Please note that the calculator will give you to a certain number of decimal places. So some calculators will show 0.333, others will show 0.333333 and others will show something different based on the number of decimal places. The dots are not shown. Please Note also that usually unless you are being tested on your ability to know rational and irrational numbers, most GED questions write all irrational numbers in an approximated form, making it look like a rational number. Example, although π is an irrational number, 3.141592653 and so on, on the GED you are told to use 3.14. Making it look like a rational number, although it actually irrational. Let’s end this video here. Please share this video to help a friend and most important subscribe to our Channel and watch all the videos in this course. We will cover everything. You’ll become a master at this and Easily Pass your GED and say a permanent goodbye to your math problems.

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