Comparing, Ordering and Rounding Decimals
 Comparing Decimals
At the beginning of this course, we we encountered the number
line, a graphical device that helps us visualize the relationships
between two numbers. Just as we can place whole numbers on the number
line, we can also place decimals on the number line. If two numbers
are on a number line, then the number to the right is the larger
one.
We see that that
0.5 <
2
and 0.3 < 0.5
To compare two decimals without placing them on a number line, follow the
following method:
 Start from left to right and compare
corresponding digits. If the digits are the same, move to the
right.
 If the digits are different then the larger
number is the one with the larger digit.
Example
Fill in the blank with a "<", ">", or an
"=" sign
 3.1714
3.169
Solution
We see that the ones digits, 3 and
3, are the same, the tenths
digit, 1 and 1 are the same, but the hundredths digits,
7 and 6, are
different with 7 > 6. Hence the inequality is ">"
3.1714 > 3.169
 0.0005
0.0023
Solution
We see that the ones digits, the tenths digits, and the hundredths
digits are all 0. The left hand side has 0
for the thousandths
digit while the right hand side has 2 for its thousandths digit.
Hence the inequality is "<"
0.0005 < 0.0023
Exercises
Fill in the blank with a "<", ">", or an
"=" sign
 34.916
34.924
 18.126
18.1260
 123.437
123.337
Example
Place the following decimals from in order from smallest to largest
2.753 2.75 2.357
3 2.7
Solution
We first add zeros to the ends of the shorter decimals to make comparison
easier
2.753 2.750 2.357
3.000 2.700
Now we see that the smallest is 2.357, since its tenths digit,
5, is
smaller than 5. Next is
2.700, since its hundredths digit,
0, is
smaller than 5. Next comes
2.750 since its thousandths digit,
0, is
smaller than 3.
Example
Place the following decimals from in order from smallest to largest
49.1
49.16
49.31 27 49.01
Rounding Decimals to a Specified Decimal Place
It is often necessary to round a decimal to the nearest tenth, hundredth,
thousandth, etc. When dealing with money we usually round to the
nearest hundredth so that we can read the number in dollars and cents.
The rules of rounding decimals are the same as the rules
for rounding whole numbers. We look at the digit to the right and
determine if it is 5 or greater. If it is greater than
4, round
up. Otherwise round down.
Example
Round 32.537 to the nearest hundredth.
Solution
The digit to the right of the hundredth place is "7".
Since 7 is greater than 4, we round up. Change the
3 to a 4. We
write
32.54
Example
Round 27.8149 to the nearest tenth.
Solution
The digit to the right of the tenth place is "1".
Since 1 is not greater than 4, we round down. Keep the
8 the
same. We write
27.8
Exercise
Round the following numbers as indicated.
651.955 to the nearest
tenth
49.942 to the nearest
hundredth
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