How do you order the rational numbers from least to greatest: 0.11, -1/9, -0.5, 1/10?

2 Answers
Oct 25, 2016

Numbers from least to greatest are #{-0.5,-1/9,1/10,0.11}#

Explanation:

The easiest way to order rational numbers is to write them so that they are up to same places of decimal.

Here #-1/9=-0.11111111111111......#, where number #1# repeats endlessly, but other numbers do not last beyond hundredth place (i.e. second place after decimal point), hence we write numbers say upto five places only. Then

#0.11=0.11000#
#-1/9=-0.11111#
#-0.5=-0.50000#
#1/10=0.10000#

It is apparent that least number is one with negative sign but highest absolute (or numerical) value and among these it is #-0.50000# or #-0.5#, then comes #-0.11111=-1/9# and then we positive numbers of which #0.10000=1/10# is least and greatest is #0.11000=0.11#.

Hence, numbers from least to greatest are #{-0.5,-1/9,1/10,0.11}#

Oct 29, 2016

Same thing as Shwetank but different approach using fractions

#-0.5"; "-1/9"; "1/10"; "0.11#

Explanation:

Note that the word 'least' is like saying 'less than'
There is a big difference between less than and smaller.

#-0.5 -=-1/2#

#-1/9 -> -1/9#

#0.11-=11/100#

#1/10-=10/100#

Now think of the position on the number line

#-1/9# is closer to 0 than is #-1/2." "# So #-1/2# is less than #-1/9#

#(1/10-=color(red)(10/100))# is less than #(0.11-=color(red)(11/100))#

So we have in order from left to right on the number line:

#-1/2"; "-1/9"; "10/100"; "11/100#

#-0.5"; "-1/9"; "1/10"; "0.11#