Multiplication of Decimal Numbers
Reshma purchased 1.5 kg vegetable at the rate of 8.50 rupees per kg. How much money should she pay? Certainly it would be Rs.(8.50 × 1.50). Both 8.5 and 1.5 are decimal numbers.
So, we have come across a situation where we need to know how to multiply two decimals. Let us now learn the multiplication of two decimal numbers.
First we find 0.1 × 0.1.
Now, 0.1 =
Let us see it’s pictorial representation
The fraction
The shaded part in the picture represents
We know that,
To do this lets take another grid divided into 10 equal parts horizontally(shown above). Now move the second grid over the first grid to see how each
Instructions: Overlap the two grids while maintaining the given alignment.
How many small squares do you find in the above overlapped figure?
There are 100 small squares. The coloured square is one part out of 10 of the
How can we represent the square which has both the red and green colour?
The red and green coloured square represents one out of 100 or 0.01. Hence, 0.1 × 0.1 =
Note: 0.1 occurs two times in the product. In 0.1 there is one digit to the right of the decimal point. In 0.01 there are
Let us now find 0.2 × 0.3.
We have, 0.2 × 0.3 =
As we did for
Again divide each of these three equal parts into 10 equal parts and take two from each. We get
Instructions: Overlap the two grids while maintaining the given alignment.
The intersected squares represent
Since there are 6 intersected squares out of 100, so they also reprsent 0.06. Thus, 0.2 × 0.3 =
Observe that 2 × 3 = 6 and the number of digits to the right of the decimal point in 0.06, is 2 (= 1 + 1).
Lets check whether this applies to 0.1 × 0.1 also. We have: 0.1 × 0.1 =
1 × 1 = 1 and the number of digits to the right of the decimal point in 0.01 is 2 (= 1 + 1).
Lets find 0.2 × 0.4 by applying these observations.
While finding 0.1 × 0.1 and 0.2 × 0.3, you might have noticed that first we multiplied them as whole numbers ignoring the decimal point. In 0.1 × 0.1, we found 0.1 × 0.1 or 1 × 1.
Similarly in 0.2 × 0.3 we found 0.2 × 0.3 or
Then, we count the number of digits starting from the rightmost digit and moved towards left. We then put the decimal point there. The number of digits to be counted is obtained by adding the number of digits to the right of the decimal point in the decimal numbers that are being multiplied.
Let us now find 1.2 × 2.5.
Multiply
We get 300. Both, in the individual decimal numbers 1.2 and 2.5, there is
So, count 1 + 1 = 2 digits from the rightmost digit (i.e.,
We get 3.00 or
While multiplying 2.5 and 1.25, you will first multiply 25 and 125.
For placing the decimal in the product obtained, you will count 1 + 2 =
Thus, 2.5 × 1.25 =
Find: (i) 2.7 × 4 (ii) 1.8 × 1.2 (iii) 2.3 × 4.35 .Arrange the products obtained in descending order.
Solution:
(i) 2.7 × 4 =
(ii) 1.8 × 1.2 =
(iii) 2.3 × 4.35 =
In descending order, the products are
The side of an equilateral triangle is 3.5 cm. Find its perimeter.
The length of a rectangle is 7.1 cm and its breadth is 2.5 cm. What is the area of the rectangle?
Let us see if we can find a pattern of multiplying numbers by 10 or 100 or 1000. Have a look at the table given below and fill in the blanks:
| Size (in inches) | Size (in inches) |
|---|---|
| 1.76 × 10 = | 2.35 × 10 = |
| 1.76 × 100 = | 2.35 × 100 = |
| 1.76 × 1000 = | 2.35 × 1000 = |
Observe the shift of the decimal point of the products in the table. Here, the numbers are multiplied by 10,100 and 1000.
In 1.76 × 10 =
The decimal point has shifted to the
Note that 10 has one zero over 1 while 100 has two zeros over 1.
So we say, when a decimal number is multiplied by
Answer the below questions