First of all, we need to understand the concept of absolute value: the distance between the number representing a and the origin on the general number line is called the absolute value of the number a, which is denoted as |a|, which is read as "the absolute value of a".
From a geometric point of view, the absolute value of a number is the distance from the point of the number to the origin on the number line, and the farther away from the origin, the greater the absolute value; The closer you are to the origin, the smaller the absolute value.
So, how do you compare the magnitude of the absolute value?
First, we need to understand the fundamental nature of absolute values. An important property of absolute values is that for any real number a, its absolute value is always non-negative, i.e., |a| ≥0。Also, if a itself is non-negative, then |a|is equal to a; If a is negative, then |a|is equal to a; This property allows us to easily handle absolute values in a variety of cases.
Next, let's look at how to compare the magnitude of the absolute values. For two positive numbers a and b, if a>b, then |a|>|b|；If a
However, when it comes to negative numbers, the situation is a little different. For two negative numbers a and b, if a > b (i.e., the absolute value of a is less than the absolute value of b), then |a|
Finally, when it comes to 0, we know that the absolute value of 0 is 0, so |0|Less than the absolute value of any positive number and greater than the absolute value of any negative number.
To sum up, to compare the magnitude of the absolute value, we need to first judge the positive and negative nature of the number, and then compare it according to the definition and nature of the absolute value. This way, we can accurately compare the absolute magnitude of any two numbers.