Decimals

A decimal point separates whole numbers from numbers with value less than 1.

Example: 3.232

Thousands Hundreds Tens Units Tenths Hundredths Thousandths
3 2 3 2


The number 3, which is to the right, is a whole number and the numbers to the left are as follows:



More Examples!


Example 1

6.22

Six is a whole number (6 units) and .22 is less than one
2/10 + 2/100 = 22/100.



Th H T U 1/10 1/100 1/1000
6 2 2



Example 2

56.134

56 is a whole number (5 tens and 6 units) and .134 is less than one
1/10 + 3/100 + 4/1000 = 134/1000.

Th H T U 1/10 1/100 1/1000
5 6 1 3 4



Example 3

734.356

734 is a whole number (7 hundreds,3 tens and 4 units) and .356 is less than one
3/10 + 5/100 + 6/1000 = 356/1000.

Th H T U 1/10 1/100 1/1000
7 3 4 3 5 6



Addition


We have to align the decimal points, before we add up.

U 1/10
2. 4 +
5. 1
7. 5
U 1/10 1/100
4. 2 9
2. 3 8 +
6. 6 7
1
T U 1/10 1/100
1 6. 5 2
3 5. 2 4 +
5 1. 7 6
1







Subtraction


Just like addition, we have to align the decimal points.









Multiplication


Example 1: 2.5 x 3 = ?

1. Remove the decimal point
and multiply as normal.

Note! 2.5 has only one number after the decimal
point.

2 5 x
3
7 5
1


2. Add a decimal point after the 7.
Hence, the answer has one number after the
decimal point.

Answer=7.5






Example 2: 4.2 x 2.1=?

1. Remove the decimal points and multiply
as normal.

Note! 4.2 has one number after the decimal
point and 2.1 has one number after the decimal
point 1+1=2.


4 2 x
2 1
4 2
8 4 0
8 8 2


2. The answer should have two numbers
after the decimal point. Hence, add the
decimal point after the 8.

Answer=8.82






Multiply by 10

If we multiply by 10 we move the decimal point one place to the right.


Example 1

3.5 × 10= ?

Answer=35

Example 2

4.678 × 10= ?

Answer=46.78

Example 3

45.43 × 10= ?

Answer=454.3





Multiply by 100

If we multiply by 100 we move the decimal point two places to the right.

Example 1

4.56 x 100= ?

Answer=456

Example 2

13.23 x 100= ?

Answer=1323

Example 3

3.384 x 100= ?

Answer=338.4





Multiply by 1000

If we multiply by 1000 we move the decimal point three places to the right.


Example 1

0.64 x 1000= ?

Answer=640

Example 2

1.230 x 1000= ?

Answer=1230

Example 3

7.254 x 1000= ?

Answer=7254






Division


Divide as normal but the decimal point for the answer should be aligned to the decimal point inside the division bracket.

Example 1

Divide 5.5 by 5


Example 2

Divide 12.3 by 3






In the above division we divided decimal numbers by whole numbers. Now we are going to divide decimal numbers by decimal numbers.


Example 1

7.5 ÷ 2.5 = ?

  1. Multiply both the numbers by 10 to make it easier for us to divide.

    7.5 x 10 = 75
    2.5 x 10 = 25

  2. Divide 75 by 25


Dividing 75 by 25 is the same as dividing 7.5 by 2.5. Therefore the answer is 3

.


Example 2

1.4412 ÷ 0.12=?

  1. Multiply both the numbers by 100 to make it easier for us to divide.

    1.4412 x 100 = 144.12
    0.12 x 100 = 12

  2. Divide 144.12 by 12.
    It helps if you know
    your 12 times table!



Dividing 144.12 by 12 is the same as dividing 1.4412 by 0.12 Therefore the answer is 12.1.



Divide by 10

If we divide by 10 we move the decimal point one place to the left.


Example 1

44 ÷ 10= ?

Answer=4.4

Example 2

67.42 ÷ 10= ?

Answer=6.742

Example 3

4.54 x 10= ?

Answer=0.454





Divide by 100

If we divide by 100 we move the decimal point two places to the left.

Example 1

236.2 ÷ 100= ?

Answer=2.362

Example 2

12.34 ÷ 100= ?

Answer=0.1234

Example 3

3.45 ÷ 100= ?

Answer=0.0345






Divide by 1000

If we divide by 1000 we move the decimal point three places to the left.


Example 1

435.2 ÷ 1000= ?

Answer=0.4352

Example 2

12382.5 ÷= ?

Answer=12.3825

Example 3

5325.34 ÷= ?

Answer=5.32534




Recurring Decimal Number

A recurring decimal number is a number that is continously repeated. For example dividing 2 by 3 will give us a continous repeated decimal number 6.
2/3 = 0.6666666666666

0.66666666666 can be shortened to





Decimals to Percentages

Multiply the decimal number by 100 for example 0.5 x 100= 50%

0.546 x 100 = 54.6%

0.035 x 100 = 3.5%

To convert the percentages back to decimals divide by 100.



Fractions to Decimals

2/5 means 2 divide by 5


2/5 = 0.4


Decimals to Fractions

0.4 means 4/10

.
Th H T U 1/10 1/100 1/1000
4

We can say 4/10 equals 2/5 by dividing the top and bottom numbers by 2.



0.75 means 7/10 + 5/100 = 75/100

Th H T U 1/10 1/100 1/1000
7 5

We can say 75/100 = 3/4 by dividing the top and bottom number by 25.



Whole Numbers

Whole numbers can be converted into fractions. For example we know 0.4 means 4/10 so 1.4 would mean 10/10 + 4/10 = 14/10.


More Examples!

2.4 in fractions means 20/10 + 4/10 = 24/10

3.6 in fractions means 30/10 + 6/10 = 36/10

1.75 in fractions means 100/100 + 75/100 = 175/100

2.75 in fraction means 200/100 + 75/100 = 275/100



Now try the Exercises!