Decimals Tutorial Kit
Decimals are a method of writing fractional numbers without actually
writing a fraction with a numerator and a denominator. Decimals are
characterized by a number with a decimal point and numbers after the
decimal point.
The fraction 6/10 can be written a 0.6.
Example :
6/10 = 0.6  decimal


fraction decimal point
The decimal 0.6 can be pronounced as zero point six or as six tenths.
If a decimal is less than one the zero must come before the decimal point.
Example :
5/10 = 0.5  zero point five
Decimals are named by how many decimal points there are. If there is only
one decimal place, the decimal is to the tenth.
Example:
4/10 = 0.4  there is one place after the decimal point, so this
number is pronounced four tenths.
A decimal that is greater than one like 4.8 would be pronounced as four and
eight tenths.
Example:
4 8/10 = 4.8  four and eight tenths
A decimal that has two digits after the decimal point is a decimal to the
hundredths.
Example :
52 / 100 = 0.52  fifty- two hundredths.
This would be pronounced as fifty- two hundredths or as zero point fifty-two
hundredths.
A decimal that has three digits after the decimal point is a decimal to the
thousandths.
Example :
366/ 1000 = 0.366  three hundred sixty-six thousandths
This would be pronounced as three hundred sixty-six thousandths, or as
zero point three six six.
There may be zeros after the decimal point.
Example:
79/ 1000 = 0.079  seventy- nine thousandths
This would be pronounced as seventy- nine thousandths or as zero point zero
seven nine.
Addition of Decimals
Addition of decimals is just like the addition of any other numbers.
Always remember to line up the decimal points, and to put the decimal point
in the right place in your answer. Adding decimals is just like the addition of
money.
Example:
22.22
2.2
+ 0.2
24.62




two decimal places
one decimal place
one decimal place
two decimal places
The decimal points are lined up. Then reading from right to left, the
numbers are added. You can find the decimal place of your answer by
looking at all the decimal places of the numbers being added. The number
with the most decimal places will be how many places your answer will
have. The example has two decimal places at the most so the answer will
have two decimal places.
Example:
529.346  three decimal places
+ 0.92  two decimal places
530.266  three decimal places
First all the decimal places are lined up. Then reading from right to
left the numbers are added. The first number has the most decimal places,
three, so the answer will have three places.
Subtraction of Decimals
Subtracting decimals is just like the subtraction of any other numbers.
Always remember to line up the decimal points and to put the decimal point
in the correct place in you answer.
Example:
22.22
2.2
- 0.2
19.82
 two decimal places
 one decimal place
 one decimal place
 two decimal places
The decimal places are all lined up. Then reading from right to left
subtract the numbers, borrowing as is necessary with subtraction. To find
how many places the answer will have look at the number in the question
with the most decimal places, that will be how many decimal places your
answer will have.
Example:
529.346  three decimal places
- 0.92  two decimal places
528.426  three decimal places
First all the decimal places are lined up. Then reading from left to
right the numbers are subtracted, borrowing as is necessary with subtraction.
The first number in the question has the most decimal places, three, so the
answer will also have three decimal places.
Multiplying Decimals
Multiplying decimals by decimals is basically the same as multiplying
whole numbers.
Example:
0.2  two decimal places added together
x 0.2
04
+ 00
0 .04
To solve line the decimal places up, then disregard the decimal points
till the end of the question. Multiply the bottom 2 by the 2 above it and put
the answer under the line in the 2 column. Then multiply the bottom 2 by the
above zero and put the answer in the zero column. Repeat with the bottom
zero by multiplying the zero by the top 2 and zero and placing the answers
below the line under each column. Add the two columns together reading
from right to left. To find the decimal places in the answer add all the places
from the question together. This question has two decimal places.
Example:
0.233  four decimal places added together
x 0.2
0466
+0000
0.0466
First line up all the decimal places, then disregard them until the end
of the question. Multiply the bottom 2 by all four numbers above in and put
the answers under the line in their corresponding columns. The bottom zero
is then multiplied by the four numbers above it with the answers put in the
corresponding columns below the line. These columns are then added to get
the answer. To get the decimal place for the answer the decimal places in
the question are all added. This question has four decimal places all together.
Division of Decimals by Decimals
Division of decimals by decimals is the same as the division of whole
numbers by whole numbers. Make the divisor into a whole number by
multiplying both it and the dividend by the same number, like 10, 100 etc.
Example:
0.4138/ 0.17 = (0.4138/0.17) x 100 = 41.38/ 17


dividend divisor
Place the divisor (17) before the division bracket and place the dividend
beneath it.
Example:
17)
41.38
Divide as you normally would except the decimal point should be put in the
answer exactly above where it is in the dividend.
Example:
2.43
17) 41.38
- 34 
73 
-68 
58
-51
7
To solve the decimal point of the answer is put directly above the
dividend decimal point. The divisor 17 goes into 41 twice. The number two
is put above the dividend. Then 17 is multiplied by two and subtracted from
41 underneath. The remainder is 7. The three from the fraction is brought
down to make the seven seventy-three. The divisor seven goes into 73 four
times. The four is placed above the dividend. The divisor multiplied by four,
which is 68, is then subtracted from 73, and you get the remainder 5. The
eight from the dividend is then brought down to make the five into fiftyeight. The divisor 17 goes into 58, three times. So number 3 is put above the
dividend. The divisor multiplied by 3 is 51. Fifty-one subtracted from fiftyeight gives us the remainder 7. The answer is 2.43.
Rounding Decimals
Rounding decimals to the nearest hundredth:
Rounding decimals is the same as rounding other numbers. If the thousandth
place of a decimal is below the number four it is dropped and the hundredths
place is not changed.
Example:
Round 0.853 to the nearest hundredth = 0.85
The three on the end is below four so it is dropped. The hundredth place is
not changed.
If the thousandth place is above the number 5, the hundredth place is
increased by one.
Example:
Round 0.856 to the nearest hundredth = 0.86
The hundredth place is rounded up because the thousandth place is above 5.
Rounding Decimals to the Nearest Tenth
To round decimals to the nearest tenth you follow the same rules for
rounding to the nearest hundredth. If the hundredth place is below four then
the last number is dropped and the tenth place does not change. If the
hundredth place is above 5 then the tenth place is rounded up one.
Example:
Round 0.86 to the nearest tenth = 0.9
Round 0.83 to the nearest tenth = 0.8
Fractions and Equivalent Decimals
Decimals are a type of fractional number. Each fraction has an
equivalent decimal that coincides with it. Some decimals are easy to convert
from decimal to fraction and back again. Decimal fractions always have a
denominator based on a power of ten.
Example:
0.1 = 1/10
0.2 = 2/10 or 1/5
0.5 = 5/10 or 1/2
0.25 = 25/100 or 1/4
0.50 = 50/100 or 1/2
0.75 = 75/100 or 3/4
1.0 = 1/1 or 2/2 or 1
The number of decimal places a decimal has determines the power of
ten in the equivalent fraction. A number with one decimal place will be a
fraction over 10. A number with two decimal places will be a fraction over
100. A number with three decimal places will be a fraction over 1000.
Fractions can be reduced by dividing the term by two, 2/10 reduces to 1/5.
The fraction 5/10 can be reduced to ½ because 5 is ½ of the number 10.
Converting a Fraction to a Decimal
Converting a fraction to a decimal is fairly easy. All you have to do is divide
the numerator of a fraction by the denominator.
Example:
Convert 4/9 to a decimal
4/9 = o.44444444
The numerator, four, is divided by the denominator, 9. The answer can be
rounded to a desired decimal place.
Converting a Decimal to Scientific Notation
Scientific notation is used as a simple way to express very small or
very large numbers. Scientific notation is an integer or decimal multiplied by
10 to an exponent. If the is below 1 then the exponent on the ten is a
negative number. The exponent on the 10 represents the number of times the
decimal was moved.
Example:
Convert 0.00000456 to scientific notation = 4.56 x 10 –6
The decimal place has been moved back 6 places, so the exponent on
the 10 is to the –6. This very small number has been put into an easier
number to read and convey. You don’t have to deal with so many zeros.
Examples To Try
1. 0.987 + 0.23 + 5.9245
2. 899.672 + 67.45 + 78.23
3. 364.1782 – 28.67 + 89.34
4. 564.34 – 346.26
5. Round .878 to the nearest hundredth
6. Round .673 to the nearest tenth
7. Round 8.289 to the nearest whole number
8. Put 4/10 into decimal form
9. Put 75/100 into decimal form
10. .782 x .98
11. .35 x 12.32
12. 0.4539 / .12
13. .9823 / .67
14. .5648 x .65
15. .1234 / .0789
Answers
1.
5.9245
0.987
+ 0.23
6.1415
2.
899.672
67.45
+ 78.23
1045.352
3.
364.1782
- 28.67
335.5082
4.
564.34
+ 346.26
218.08
5.
.88
6.
.7
7.
8
8.
.04
9.
.75
335.5082
+ 89.34
424.8482
10. .782
x .98
0.76636
11. 12.32
x 0.32
4.312
12. .4539 / .12 = 3.7825
13. .9823/ .67 = 1.4661
14. .5648
x .65
0.36712
15. .1234/ 0.0789 = 1.5640
Test
1. Round .567 to the nearest hundredth
2. Round .42 to the nearest tenth
3. Put 0.00000002737 into scientific notation
4. 8372.472 + 92.236 + .18
5. .456 + .234
6. .435 - .12
7. 56.78 / .34
8. 89.2 / 0.01
9. .388 x .81
10. 134.2321 x 829.34
11. Convert 7/100 into a decimal
12. Convert 34/1000 into a decimal
Answers
1. .57
2. .4
3.
2.737 x 10 –8
4. 8464.888
5. .69
6. .315
7. 167
8. 8920
9. 0.31428
10. 111324.0498
11. 0.07
12. 0.034