Ordering of decimal numbers

Numbers: Ratios

Ordering of decimal numbers

Like integers, we can order decimal numbers by size.

Ordering of decimals

To determine if a decimal number is greater or smaller than another decimal number, we write the numbers below each other. In addition, we make sure the decimal points are directly below each other. When one number has more digits than the other, we fill the blank spaces with zeros.

We then compare the digits from left to right. When a digit is different, the number with the highest digit at that position is the biggest of the two.

Example

#23.1\blue{4}8#

#23.1\green{5}0#

because #\green5 \gt \blue4#

we see that

#23.150 \gt 23.148#

Negative numbers

This works the same way for two negative numbers. Only now, when we compare the digits from left to right, the number with the highest digit in the first position that differs is the smallest.

Actually, we can say that when one positive number is bigger than another positive number, and we add minus signs to both of them, the biggest number is now the smallest number. This is because this number becomes "more negative" with the added minus sign and, therefore, smaller.

Example

#-23.1\blue{4}8#

#-23.1\green{5}0#

because #\green5 \gt \blue4#

we see that

#-23.150 \lt -23.148#

Which of the two numbers below is the largest?

#10.9037#

#10.9107#

Which of the following two numbers is the smallest?

#-34.3038#

#-34.2947#