He absolute and relative value they are two definitions that apply to natural numbers. Although they may look similar, they are not. The absolute value of a number, as its name implies, is the figure itself that represents that number. For example, the absolute value of 10 is 10.
On the other hand, the relative value of a number is applied to a particular figure that makes up the natural number. That is, in this definition we can observe the position occupied by the figure, which can be the units, tens, hundreds and so on. For example, the relative value of 1 in the number 123 will be 100, since 1 occupies the position of the hundreds.
Absolute value and relative value
Index
- 1 What is the relative value of a number?
- 1.1 How to calculate it in a simple way?
- 2 Exercises
- 2.1 First example
- 2.2 Second example
- 2.3 Third example
- 3 References
What is the relative value of a number?
As previously stated, the absolute value of a number is the same number itself. That is, if you have the number 321 then the absolute value of 321 is equal to 321.
While, when asking about the relative value of a number, one should ask for one of the figures that make up the number in question. For example, if you have 321, then you can ask for the relative value of 1, 2 or 3, because these are the only numbers that are part of 321.
-If you ask about the relative value of 1 in the number 321, the answer is that its relative value is 1.
-If the question is what is the relative value of 2 in the number 321, the answer is 20, since the 2 is located over the tens.
-If you ask about the relative value of 3 in the number 321, the answer is 300, since 3 occupies the position of the hundreds.
How to calculate it in a simple way?
Given a whole number, it can always be decomposed as a sum of certain factors, where each factor represents the relative value of the figures involved in the number.
For example, the number 321 can be written as 3 * 100 + 2 * 10 + 1, or equivalently 300 + 20 + 1.
In the previous example, you can quickly see that the relative value of 3 is 300, of 2 is 20 and of 1 is 1.
Exercises
In the following exercises, we ask about the absolute and relative value of a given number.
First example
Calculate the absolute and relative value (of each figure) of the number 579.
Solution
If the number 579 is rewritten as mentioned above, we have 579 equals 5 * 100 + 7 * 10 + 9, or equivalently, equal to 500 + 70 + 9. Therefore the relative value of 5 is 500, the relative value of 7 is 70 and that of 9 is 9.
On the other hand, the absolute value of 579 is equal to 579.
Second example
Given the number 9,648,736, what is the relative value of 9 and of the first 6 (from left to right)? What is the absolute value of the given number?
Solution
When you rewrite the number 9,648,736 you get that this is equivalent to
9 * 1,000,000 + 6 * 100,000 + 4 * 10,000 + 8 * 1,000 + 7 * 100 + 3 * 10 + 6
or you can write as
9,000,000 + 600,000 + 40,000 + 8,000 + 700 + 30 + 6.
So the relative value of 9 is 9,000,000 and the relative value of the first 6 is 600,000.
On the other hand, the absolute value of the given number is 9,648,736.
Third example
Calculate the subtraction between the absolute value of 473 and the relative value of 4 in the number 9,410.
Solution
The absolute value of 473 is equal to 473. On the other hand, the number 9,410 can be rewritten as 9 * 1,000 + 4 * 100 +1.10 + 0. This implies that the relative value of 4 in 9,410 is equal to 400.
Finally, the value of the requested subtraction is 473 - 400 = 73.
References
- Barker, L. (2011). Leveled Texts for Mathematics: Number and Operations. Teacher Created Materials.
- Burton, M., French, C., & Jones, T. (2011). We Use Numbers. Benchmark Education Company.
- Doudna, K. (2010). No One Slumbers When We Use Numbers! ABDO Publishing Company.
- Fernández, J. M. (1996). Chemical Bond Approach project. Reverte
- Hernández, J. D. (s.f.). Math notebook. Threshold.
- Lahora, M. C. (1992). Mathematical activities with children from 0 to 6 years old. Narcea Editions.
- Marín, E. (1991). Spanish grammar Progress Editorial.
- Tocci, R. J., & Widmer, N. S. (2003). Digital systems: principles and applications. Pearson Education.