Last Updated on September 10, 2026 by Maged kamel
Definition of absolute value, rational numbers, and fractions.
What is the absolute value of a number?
This reviews absolute value, usually written with two small vertical lines around a number; for example, the absolute value of -4 is 4. If we draw a number line with equal distances, writing from 0 to 5 to infinity, and from the left side, we write (-1) to (-5) to infinity—absolute value means how far from zero.
For any number, regardless of whether it is positive or negative. When someone needs to know the distance from zero for any given number, the answer will be 4, 5, or 6, depending on that number.
The absolute value of a number is the distance of that number from zero. We will not say(+4) or(+5); you will write a number without a sign. Then, the distance for the ABS of (-4) is four spaces from zero, which is the same distance as the positive value of 4.
The fraction of a number.
Then the rational number is(1/5). But if the denominator is zero, we get infinity when dividing any number by zero.
Fractions like 1/2, 3/4, and 7/10 are a family of fractions; the upper part is called the numerator, and the lower part is the denominator. The fraction can be divided into parts; the first part is the proper fraction. If the denominator is greater than the numerator, the value is <1.
If the numerator is greater than the denominator, for instance, this gives a value greater than 1. Like (4/3) and 6/3 = 2, and 8/5 will give 1.60. The second type is called an improper fraction. Atsame time.
The following slide images explain the definition of fractions and the various types of fractions, quoted from Basic College Mathematics by Prof. Aufmann.
What is factoring?
The Product and factoring. When we have x^2 + 4x + 2 and are required to factor it, we can say that (x^2 + 4x + 2) is a factor of itself, i.e., (x + 2 (x + 2), which means it is returned to its significant elements. When multiplied, we get the original element. For instance, the number 12 has the following factors: (1 × 2), (3 × 4), and (2 × 6). These elements, when multiplied, give 12. Or, elements a and b multiply to yield c.
Then c is the Product of factors a and b. The Product can be broken down into its elements by factoring. Is that an Irrational number? e have said that every number i a ratio.
The integer 5 can be written as 5/1. Also, 7 can be written as 7/1, which is an Improper fraction.
Irrational numbers.
What are the irrational numbers? These are real numbers t that can’t be written as simple fractions. For example, if we use the calculator to get the square root of 3, we get 1.732050808.
The square root of 2 is 1.41412135. π is an irrational number; its value is 3.14159 and continues to infinity.
Non-terminating, non-recurring decimal. Non-terminating: to give an example of a terminating number, 1/2 = 0.50; there is a continuation of numbers.
The square roots of 3 and 2 are never terminating.
Additionally, Pi is written as 3.14159, followed by dots, indicating a non-terminating decimal. For example, 1/3 equals 0.33333. At the same Time, the square root of 2’s decimal is neither terminating nor repeating.
The definition of irrational numbers encompasses these two conditions and results in a non-rational number. These are the expansions for irrational numbers.
A general shape for all types of numbers.
Here is a shape::: he started with the Natural numbers, then added set oset ofole numbers after adding zero.
Then add the negative numbers and call that box Integers. It moves up to a higher degree. Then it’s followed by rational numbers, then irrational numbers, including, for instance, the negative value (-) of the square root of 8, sqrt(15), and PI. The big box is called the Real number set, and the symbol R represents it.
The expanded form of a whole number.
The next slide image shows the expanded form of a whole number and how we can express any number as a combination of ones, tens, hundreds, thousands, and more, depending on its value.
What is rounding a number?
Rounding is an essential topic. Rounding numbers: for instance, if the number is 5 or greater, round it up to the next higher value. In contrast, if the number is less than 5, round it down. Numbers from 1, 2, 3, and 4 can be rounded down.
For numbers 5, 6, 7, 8, and 9, round to the nearest 10. For example, round 27 to the nearest 10.
We put a line after the 2; since the number on the right side of the 2 is more than 5, we round to 30. For the number 33, put a line to the 3. The digit to the right of the line is < 5, so 33 rounds to 30, and it is a round-down.
For rounding to the nearest hundred, the nearest thousand, and beyond. The next slide provides examples of God’s will.
Round 4827 to the nearest ten. Since 7> 5, the number to the left of 7 will be upgraded to 3, and 7 will be 0. The final number will be 4830.For the same number, round to the nearest hundred. For 4827, put a line to the left of 2; since 2 is <5, then 4827 will be rounded down, and then 4827 will be rounded to 4800.
To round 4827 to the nearest thousand, draw a line between 4 and 8 and check the right side; since 8 > 5, 4827 rounds up to 5000. We cannot say 4900, since we upgraded 4 to 5.
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For the next post, how to round decimal numbers?