Ordering of integers

Numbers: Integers

Ordering of integers

If we move to the left on the number line, the numbers become smaller. For example, #-3# is smaller than #2#. In symbols we write this as #-3<2#.

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The arrow on the number line indicates the numbers smaller than or equal to #2#. Here, #2# itself is also smaller than or equal to #2#. In symbols, we write this as #2\leq 2#.

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If we now move to the right on the number line, the numbers become bigger. For example, #3# is bigger than #1#. In symbols we write #3\gt1#.

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The arrow on the number line indicates the numbers bigger than or equal to #1#. Here, #1# itself is also bigger than or equal to #1#. In symbols, we write this as #1\geq 1#.

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Larger positive numbers

If we want to compare larger positive numbers, we can place the numbers below each other, with the last digits exactly below one another. Next, we write down zeros in any empty space at the beginning of the number. Next, we compare the numbers from left to right. At the first position where the numbers differ, the number with the highest digit is the biggest.

Example

#231\blue{4}8#

#231\green{5}0#

Since #\green5 \gt \blue4#

we have

#231\green{5}0 \gt 231\blue{4}8#

Larger negative numbers

If we want to compare larger negative numbers, we can place the numbers below each other, with the last digits exactly below one another. Next, we write down zeros in any empty space at the beginning of the number. Next, we compare the numbers from left to right. At the first position where the numbers differ, the number with the highest digit is the smallest.

Example

#-231\blue{4}8#

#-231\green{5}0#

Since #\green5 \gt \blue4#

we have

#-231\green{5}0 \lt -231\blue{4}8#

Which statements are true?