WHAT IS ABSOLUTE AND RELATIVE VALUE? (WITH EXAMPLES) - MATHS - 2025

The absolute and relative value are two definitions that apply to natural numbers. Although they may seem 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, the position occupied by the figure is observed, which can be units, tens, hundreds and so on. For example, the relative value of 1 in the number 123 will be 100, since 1 occupies the hundreds place.

Absolute value vs relative value

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.

Whereas, when asking for the relative value of a number, one must 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, since these are the only numbers that are part of 321.

-If you ask for 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 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 hundreds place.

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 example above, you can quickly see that the relative value of 3 is 300, 2 is 20, and 1 is 1.

Exercises

In the following exercises, the absolute and relative value of a given number is asked.

First example

Find the absolute and relative value (of each digit) of the number 579.

Solution

If the number 579 is rewritten as mentioned above, it follows that 579 is equal to 5 * 100 + 7 * 10 + 9, or equivalently, it is 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 the 9 and the first 6 (from left to right)? What is the absolute value of the given number?

Solution

By rewriting the number 9,648,736 it is obtained that this is equivalent to

9 * 1,000,000 + 6 * 100,000 + 4 * 10,000 + 8 * 1,000 + 7 * 100 + 3 * 10 + 6

or can be written 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

Find 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

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