Definition of decimals.
Decimals are numbers, which has a whole number and the fractional part separated by a decimal point.
The dot present between the whole number and the fractional part is called the decimal point. For example, 78.965 is a decimal number.
Here, 78 is a whole number part and 965 is the fractional part.
‘ . ‘ is the decimal point.
Types of Decimal Numbers
Types of decimal numbers includes:
1) Recurring Decimal Numbers (Repeating or Non-Terminating Decimals)
Example.
5.55 (Finite)
5.333333333….. (Infinite)
2) Non-Recurring Decimal Numbers (Non Repeating or Terminating Decimals)
Example.
5.325(Finite)
5.23456…. (Infinite)
Place values of decimal numbers.
When we write numbers, the position (or “place”) of each digit is important.
The first digit to the right of the decimal point indicates the number of tenths.
For example, the decimal 0.56 the first digit to the right of the decimal point which is 5 indicates the number of tenths.
The second digit to the right of the decimal point which is 6 indicates the number of hundredths.
You can write decimals with many places to the right of the decimal point. For example, this is a representation of the decimal number 324.156789 which is equal to
324 156 789/1 000 000, with the place values named:
3-Hundreds
2-Tens
4-Ones
1-Tenths
5-Hundredths
6-Thousandths
7-Ten thousandths
8-Hundred thousandths
9-Millionths
OPERATIONS ON DECIMALS
Addition of decimals.
Example
Evaluate
a) 7.6+1.9
Solution
7.6+1.9=9.5
b) 7.004+0.368
Solution
7.004+0.368=7.372
c) 4.2+42
Solution
4.2+42=46.2
Try these
d) 20.4+20.399
e) 0.06+0.006
Subtraction of decimals.
Example
Evaluate
a) 3.84-2.62
Solution
3.84-2.62=1.22
b) 4.61-3
Solution
4.61-3=1.61
c) 25-7.8
Solution
25-7.8=17.2
Try these
d) 11.4-9.73
e) 0.06-0.006
Multiplication of decimals.
You multiply decimals just like you would normal whole numbers. The important thing in multiplying decimals is understanding how and when to move the decimal point so you get the correct answer.
Example
78.12×0.7
Remember place value. That means 78 and 12 hundredths multiplied by 0.7, or seven-tenths.
In solving the problem, pretend (for just a moment) that the decimal point isn’t there. That would give you this equation:
7812×7
NOTE: The zero 0 is not needed since it doesn’t add anything to the equation. If we solve this equation, we get:
7812
× 7
The answer is 54684.
The next step we have to figure out where to place the decimal. Here’s how it’s done.
Go back to the original equation and count how many numbers are behind each decimal point. In this case, there are three. Two here (78.12) and one here (0.7).
Now that we know there are three numbers behind the decimals, we go back to our answer and place the decimal three places from the last number. So the first answer we got was 54,684. But remember, we have to move our decimal point three places to the left because we had 3 places behind our decimal points here. So when we do that, our decimal point ends up right after our 54.
Hence our final answer is 54.684.
EXERCISE
Evaluate
a) 2.6×0.6
Solution
2.6×0.6=1.56
b) (0.01) ^2
Solution
(0.01) ^2=0.01×0.01
=0.0001
c) 0.36×1000
Solution
0.36×1000=360
Try these
d) 0.1×0.2
e) 11.4×9.73
Division of decimals
For dividing decimal numbers, there are two (2) cases to consider- one in which we need to divide decimals by a whole number, and the other in which we divide decimals by decimals.
1st Case.
Dividing decimals by whole numbers.
Dividing decimals by whole numbers is similar to normal division. Here, the dividend is a decimal number and the divisor is a whole number, so the decimal point in the quotient will be placed according to the decimal point of the dividend.
Example:
Evaluate 4.5÷9
Solution
4.5÷9
Here the dividend is a decimal number 4.5 and the divisor is the whole number 9.
Hence dividing 4.5 by 9 we get the quotient 0.5.
So the quotient (result of division) obtained has one decimal place just like the dividend which also has one decimal place.
2nd Case.
Dividing decimals by decimals.
When we divide decimals by decimals we have to convert the divisor to a whole number by moving the decimal point to the left. Then, we carry the dividend’s decimal point up to the same number of places to the left and divide the resultant numbers in the usual way as we perform in regular long division.
Example.
0.49÷ 0.7
Here, the Divisor = 0.7
And Dividend = 0.49
Change the divisor 0.7 to a whole number by moving the decimal point 1 place to the left by multiplying 0.7 by 10. Then move the decimal point in the dividend the same, 1 place to the left by multiplying by 10 also.
0.49×10÷ 0.7×10 = 4.9÷ 7
Now, divide the decimal number 4.9 by the whole number, i.e. 7.
Thus the quotient is 0.7
EXERCISE
a) 7.004÷0.368
Solution
(7.004×1000)/(0.368×1000)
=7004/368
=19.0326
b) 3.6÷0.2
Solution
3.6÷0.2
=(3.6×10)/(0.2×10)
=36/2
=18
c) 0.007÷4
Solution
0.007/4=0.00175
Try these
d) 1100÷5.5
e) (0.3) ^2÷100
To SIGN UP and get started in crypto on BINANCE CLICK HERE
OTHER RELATED TOPICS:
Study heaven academy 