Lily purchased 2.5 lbs fruits at the rate of $3.50 per lb. How much money should she pay?
Certainly it would be $(2.5 × 3.50). Both 2.5 and 3.5 are decimal numbers.
Now, we have come across a situation where we need to know how to multiply two decimals. So we now learn the multiplication of two decimal numbers.
Now, let us find 1.5 × 4.3
Multiplying 15 and 43, we get 645.
Both, in 1.5 and 4.3, there is 1 digit to the right of the decimal point. So, count 2 digits from the right and put a decimal point.
So, we get 1.5 x 4.3 = 6.45
While multiplying 1.43 and 2.1, you will first multiply 143 and 21. For placing the decimal in the product obtained, you will count 2 + 1 = 3 digits starting from the right most digit.
Thus 1.43 × 2.1 = 3.003.
Problem 1 :
The side of a square is 3.2 cm. Find its perimeter.
All the sides of a square are equal.
Length of each side = 3.2 cm.
Perimeter of a square = 4 × side
Thus, perimeter = 4 × 3.2 = 12.8 cm.
Problem 2 :
The length of a rectangle is 6.3 cm and its breadth is 3.2 cm. What is the area of the rectangle?
Length of the rectangle = 6.3 cm
Breadth of the rectangle = 3.2 cm.
Area of the rectangle = ( length) × (breath)
= 6.3 × 3.2
= 20.16 cm²
Lily observed that
3.7 = 37/10
3.72 = 372/100
3.723 = 23723/1000
Thus, she found that depending on the position of the decimal point the decimal number can be converted to a fraction with denominator 10 , 100 or 1000.
Now let us see what would happen if a decimal number is multiplied by 10 or 100 or 1000.
3.23 x 10 = (323/100) x 10 = 323/10 = 32.3
Decimal point shifted to the right by one place since 10 has one zero.
3.23 x 100 = (323/100) x 100 = 32.3
Decimal point shifted to the right by one place since 100 has two zeros.
3.23 x 1000 = (323/100) x 1000 = 323 x 10 = 3230
Decimal point shifted to the right by one place since 1000 has three zeros.
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