numbers and the decimal system

Question

In order to compare two decimal numbers, we first look at the place of largest value in which at least one of the numbers has a nonzero entry. Why does this make sense?

Answer 1

It works in the same way that integers work:

10 > 1 (the tens column is larger than the ones column)

100 > 10 (the hundreds column is larger than the tens column)

101 > 100 (the hundreds and tens columns are the same, but the 1 in the ones column is larger than 0)

 

In decimals, the number to the left (tenths) is the largest column:

1.1 > 1.01 (one tenth ¹/₁₀ is larger than one hundredth ¹/₁₀₀)

 

Compare that to:

2.51 > 2.5

2.5 can be translated into 2.50 (as an infinite number of zeros can follow after the final decimal column). Following that,:

51 > 50

 

Now compare and contrast that to:

4.2 > 4.09

While nine may be greater than two, remember the infinite zeros mentioned before, and the zero that needs to be put in the hundredths column to match the hundredths in the 4.09 number:

20 > 09,  or 20 > 9