Decimals Unit
Adding and Subtracting Decimal Numbers
Vocabulary Terms:
Whole Number: A number that is equal to or greater than “one” and that does not include
fractions. Examples: 1, 2, 3, 4…100, 101, 102, 103…
Decimal: A number that is less than one but greater than zero. A number placed to the
right side of a decimal point.
Decimal Point: The placeholder that divides or separates whole numbers from fractions
of whole numbers. Example: 14.21
Mixed Decimal: A number that is made up of a whole number and a fraction of a
whole number. Note: The whole number is placed to the left of a decimal point
and the fraction of a whole number is placed to the right of a decimal point.
Example: 24.17
(1) Adding Decimals: When adding numbers with decimal points in them, you must first
make sure that the decimal points in all of the numbers being added are aligned one above the
other before adding the numbers together. Once the numbers are properly lined-up, simply
add the numbers together just as you would do with whole number addition. The only
difference is that a decimal point must be brought straight down and placed in the answer
once the problem has been solved.
Example #1: Add the following decimal numbers: .6, 23.5, 1.1
Step #1: Write the numbers down in a column so that the decimal points are aligned one
above the other.
.6
23.5
1.1
Step # 2: Add the numbers together just as you would do with whole number addition.
.6
23.5
+ 1.1
25 2
Step # 3: Place the decimal point in the answer straight down in line with the position of the
decimal points in the numbers being added together.
.6
23.5
+ 1.1
Final Answer: 25.2
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Decimals Unit
Note: When adding decimals in which the numbers being added cover different place value
positions, it may be useful to add zeroes behind (to the right of) those numbers that do not
cover the same number of place value positions as the other numbers being added. When
following this procedure, you must add zeroes to each decimal number being added that does
not match the place value of the decimal number that extends farthest to the right side of the
decimal point.
Example # 2: Add the following decimals: 22.1, .0314, 8.55
Step # 1: Write the numbers being added in a column so that the decimal points are aligned
one above another.
22.1
.0314
8.55
Step # 2: Place zeroes behind any decimal numbers as needed in order to match the decimal
place in the number being added that extends furthest to the right side of the decimal point.
In the case of this problem, the number being added that extends furthest to the right of a
decimal point is .0314; therefore, extra zeroes must be added to both of the other numbers
being added (22.1 and 8.55)
22.1000
.0314
8.5500
Step # 3: Add the numbers together just as you would with whole number addition.
22.1000
.0314
+ 8.5500
30 6814
Step # 4: Place the decimal point in the answer straight down in line with the decimal points
in the numbers being added together.
22.1000
.0314
+ 8.5500
Final Answer: 30.6814
Note: When adding whole numbers that do not contain decimals, there is normally no
decimal point shown. In such cases, you might consider that the decimal point is where it
belongs behind (to the right of) the whole number but that it is “invisible.” In order to make
it easier to work decimal addition problems in which whole numbers are involved, a decimal
point can be placed behind the whole number(s) and zeroes can be placed to the right of the
decimal point to match the number of place value position of the number that extends
farthest to the right side of the decimal point just as was done in example two above.
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Decimals Unit
Example # 3: Add the following: 3.56, 44, 25.034 (notice that the number 44 is a whole
number and thus has no decimal point shown).
Step # 1: Write the numbers in a column so that the decimal point are aligned one above
another.
3.56
44. (notice that the decimal point is placed directly behind the whole number 44)
25.034
Step # 2: Place zeroes to the right side of any numbers that do not extend as far as the place
value of the number that extends furthest to the right side of the decimal point. In the case of
the numbers being added in this problem, the number that extends furthest to the right side
of a decimal point is the number 25.034. Therefore, zeroes must be added behind the other
two numbers being added together.
3.560
44.000
25.034
Step # 3: Add the numbers together just as you would with whole number addition and
bring the decimal point straight down in line with the numbers being added together.
3.560
44.000
+ 25.034
Final Answer:
72.594
2. Subtracting Decimal Numbers: When subtracting decimal numbers, you must
line up the decimal points just as you did when “adding” decimal numbers. After you have
properly aligned the numbers, subtract them in the same way you would with whole
numbers. Finally, carry the decimal point straight down into the answer as you would when
adding decimal numbers.
Example # 1: Subtract the following mixed decimals: 42.753 – 5.327
Step # 1: Write the numbers being subtracted so that the decimal points are aligned one above
the other.
42.753
5.327
Step # 2: Subtract the numbers just as you would with whole number subtraction.
42.753
– 5.327
37 426
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Decimals Unit
Step # 3: Place the decimal point in the answer straight down in line with the numbers being
subtracted.
42.753
– 5.327
Final Answer:
37.426
Note: Just as was the case with adding decimals, when subtracting decimals in which the
numbers being subtracted cover different place value positions, it may be useful to add zeroes
behind (to the right of) those numbers that do not cover the same number of place value
positions as the other numbers being subtracted. When following this procedure, you must
add zeroes to each decimal number being subtracted that does not match the place value of the
decimal number that extends farthest to the right side of the decimal point.
Example # 2: Subtract the following decimals: 97.016 – 5.3
Step # 1: Write the numbers being subtracted so that the decimal points are aligned one above
the other.
97.016
5.3
Step # 2: Place zeroes behind the number being subtracted that covers the fewest place value
positions behind the decimal point in order to match the place values of the number that
covers the greatest number of place values. In the case of the problem in this example, the
number 5.3 covers the fewest place value positions. Therefore, two zeroes must be added to
the right side of the number 5.3 in order to match the number of place values in the number it
is being subtracted from (97.016).
97.016
5.300
Step # 3: Subtract the numbers just as you would do with whole number subtraction.
97.016
– 5.300
Final Answer: 91.716
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