Let’s begin with an easy question.
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Is -3 greater than -7?
Solution: -3 is greater than -7. Let’s discuss how! |
Writing numbers down on a Number Line makes it easy to tell which numbers are greater or lesser.
A number on the left is less than a number on the right.
| Same as saying: A number on the right is greater than a number on the left. |
For example:
- 5 is less than 8 “or” 8 is greater than 5
- -1 is less than 1 “or” 1 is greater than -1
Similarly,
- -7 is less than -3 “or” -3 is greater than -7
as can be seen on this number line.
However, drawing a number line might not be very time efficient on the question. So, let’s do an alternative way….
Observe that in the case of +ve numbers, the bigger the magnitude – the bigger the number.
For example,
- 100 is bigger than 1
- 5678 is bigger than 1234
However, with -ve numbers, we have to remember that as their magnitude gets bigger, the number gets smaller (they move further to the left of the number line).
For example,
- -400 is smaller than -12 ? -400 has a bigger magnitude than -12.
- -1 is bigger than -100 ? -1 has a smaller magnitude than -100.
- -1234 is bigger than -5678 ? -1234 has a smaller magnitude than -5678.
Which of these numbers is the smallest?
Solution: All of these numbers are negative, so look for the number with the biggest magnitude. In this case, that number is ?124. |
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Let’s try another one. Which of the following are arranged in the ascending order (least to greatest)?
Solution: Start looking at the negative numbers as these are always less than positive numbers. Start with the negative number that has the biggest magnitude. That number will be the smallest. Find the next negative number and continue until the negative numbers are in order. Zero and positive numbers can then be put into order. Based on this methodology, only options C & E are correctly arranged in the ascending order. Note that options B & D have been arranged in the descending order (greatest to least). Option A is arranged fine except that 0 should come before 1 and not after it. |
What is the smallest positive integer?
The set of integers is {…,?3, ?2, ?1, 0, 1, 2, 3, …}.
The set of positive integers is the set of integers that are strictly greater than zero. So, we omit all the negative integers and zero from the set of integers, and we are left with the set {1, 2, 3, …}.
The smallest of the numbers in the set {1, 2, 3, …} is 1.
What is the smallest positive number?
Numbers (or real numbers) include fractions (or decimals) as well. Therefore, we cannot quantify the smallest positive number. It would be something infinitely small – something like 0.0000 …. 0001.
What is the largest positive integer?
Consider the never-ending sequence of positive integers
1, 2, 3, 4, ….
The smallest positive integer is 1. From there the values progress toward positive infinity. There is an infinite number of positive integers as they approach positive infinity. So the largest positive integer would be some +ve value, which is infinitely large.
What is the largest negative integer?
The set of integers is {…,?3, ?2, ?1, 0, 1, 2, 3, …}.
The set of negative integers is the set of integers that are strictly less than zero. So, we omit all the positive integers and zero from the set of integers, and we are left with the set {…., ?3, ?2, ?1}
The largest of the integers in this set is ?1.
What is the smallest negative integer?
Consider the never-ending sequence of negative integers
…., ?3, ?2, ?1
The largest negative integer is ?1. From there the values keep decreasing toward negative infinity. There is an infinite number of negative integers as they approach negative infinity. So the smallest ?ve integer would be some ?ve value, which is infinitely small. Hence, ??.
What is the largest negative number?
Numbers (or real numbers) include fractions (or decimals) as well. Therefore, we cannot quantify the largest negative number. It would be some negative value, extremely close to 0. Something like ?0.0000 …. 0001.