How do you order 6.037, 6.37, 6.5, 6.3772 from least to greatest?

2 Answers
smendyka
Jan 8, 2018

See a solution process below:

Explanation:

Because the 1's digit is the same for all the numbers we next look at the digit in the 10ths position. The number with the smallest value in the 10ths position is 6.037 so it is first in order.

The number with the largest digit in the 10ths position is 6.5 so it is last in order:

#6.037, ?, ?, 6.5#

We are left with 6.37 and 6.3772. We can rewrite 6.37 as: 6.3700

So we have 6.3700 and 6.3772

These to numbers have the same 1's digit, 10ths digit and 100ths digit. Therefore we look at the 1000ths digit. The first number has a 0 in this position which is smaller than the 7 in this position in the other number. Therefore the order is:

#6.037, 6.37, 6.3772, 6.5#

EZ as pi
Jan 9, 2018

#6.037," "6.37," "6.3772," "6.5#

Explanation:

Write the number with the same number of decimal places first.
The most number of decimal places is #4#, so use that for all of them.

This makes comparing them much easier. Look at the units digits first: They are all #6#, so at this point they are all the same.

#color(blue)(6).0370#
#color(blue)(6).3700#
#color(blue)(6).5000#
#color(blue)(6).3772#

Look at the first decimal place next (tenths)

#color(blue)(6)color(red)(.0)370" "larr# this one is the smallest #(0)#
#color(blue)(6).3700#
#color(blue)(6)color(red)(.5)000" "larr# this one is the biggest #(5)#
#color(blue)(6).3772#

For the two remaining numbers - look at the second decimal place:
They are both #color(magenta)(7)#, so the two numbers are equal at this point

#color(blue)(6).3color(magenta)(7)00#
#color(blue)(6).3color(magenta)(7)72#

Now look at the third decimal place:

#color(blue)(6).3color(magenta)(7)color(limegreen)(0)0" "larr# this is smaller #(0)#
#color(blue)(6).3color(magenta)(7)color(limegreen)(7)2" "larr# this is bigger #(7)#

Now we can order the numbers from smallest to biggest:

#color(blue)(6)color(red)(.0)370," "color(blue)(6).3color(magenta)(7)color(limegreen)(0)0," "color(blue)(6).3color(magenta)(7)color(limegreen)(7)2," "color(blue)(6)color(red)(.5)000#

Now you can write them as the original values.

#6.037," "6.37," "6.3772," "6.5#

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