Expert: Josh - 1/30/2009

Question
can you give me a basic understanding on how to put decimals in order from smallest to largest ?

Answer
Well, Alexis, we will refer to a decimal figure in two parts.

Consider the number 4.5
The "4" appearing before (to the left of) the decimal point is called the integer part (or pre-decimal figure). The "5" appearing after (to the right of) the decimal point may be referred to as the fractional part (or post-decimal figure).

In any number you read, everything written to the left of the decimal is always bigger in magnitude compared to anything that appears on the right hand side of the decimal point. In the number 4.5, the "4" tells us we have four whole units, whereas the "5" in its current position represents 5 times "one tenth" which amounts to only half a unit.

It is easier to put decimals in order from largest to smallest first, then the ordering required from the smallest to the largest is read in reverse order.

Consider the numbers 2.1, 1.3 and  2.3.
Comparing the pre-decimal figure of "2.1" to that of "1.3", the "2" left of the decimal point in the first number is greater than the "1" left of the decimal point in the second number, it suffices to say that the first number is GREATER than the second number. Our comparison stops here.

At this point, we know 2.1 > 1.3 (note: the symbol > is read "greater than", it means the quantity on its left is greater than the quantity on its right).

Next, compare 2.1 with 2.3. Here, the integer part (left of the decimal point) are identical. So, we need to compare the post-decimal figure. We see that "1" is smaller than "3", so 2.1 is SMALLER than 2.3. Thus, in decreasing order from left to right, we write
2.3 > 2.1 > 1.3

To order these from smallest to largest, we read in the opposite order (from RIGHT to LEFT), we have 1.3 < 2.1 < 2.3. (note: the symbol < is read "smaller than", it means the quantity on its left is smaller than the quantity on its right).

What happens when we have something like 2.14 and 2.145?
Well, we keep comparing the post-decimal figures.
First, the 1's are identical, then the 4's are identical....we can't tell anything about their size just yet....until we reach the third decimal figure. The absence of a third post-decimal figure in 2.14" implicitly means we have 2.140. Now, comparing 2.140 with 2.145, clearly, the "5" in the second number is greater than the "0" at the corresponding spot in the first number. Now, we can say that 2.145 is greater than 2.14.