MULTIPLICATION OF DECIMALS

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 x 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 x 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.

Solution :

All the sides of a square are equal.

Length of each side = 3.2 cm.

Perimeter of a square = 4 x side

Thus, perimeter = 4 x 3.2 = 12.8 cm.

Problem 2 :

The length of a rectangle is 6.3 cm and its width is 3.2 cm. What is the area of the rectangle?

Solution :

Length of the rectangle = 6.3 cm

Width of the rectangle = 3.2 cm.

Area of the rectangle :

= length x breath

= 6.3 x 3.2

= 20.16 cm²

Multiplying Decimals by 10 100 and 1000

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.

For example,

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.

Problem 3 :

If the cost of a pencil is $0.25, then find the total cost of 100 pencils.

Solution :

Total cost of 100 pencils :

= 100 x 0.25

Since we multiply 100, decimal point has to be shifted two digits to the right.

= $25

Problem 2 :

Weight of one paper sheet is 0.45678 grams. If David has 1000 paper sheets, find the total weight.

Solution :

Total weight of 1000 paper sheets :

= 1000 x 0.45678

Since we multiply by 1000, decimal point has to be shifted three digits to the right.

= 1000 x 0.45678

= 456.78 grams

Problem 3 :

Find the cost of 72 books at $5.75 each

Solution :

Cost of each book = $5.75

Cost of 72 books = 72 x 5.75

= $414

Cost of 72 books is $414.

Problem 4 :

Find the cost of 8.6 m of plastic sheeting at $4.62 per meter.

Solution :

Cost of plastic sheeting = $4.62 per meter

Quantity of material = 8.6 m

Required cost = 8.6 x 4.62

= $39.732

Problem 5 :

In order to bake cakes for the school fair, I buy 180 kg of flour at $0.84 per kg and 25 kg of sugar at $1.17 per kg. How much money have i spent ?

Solution :

Quantity of flour = 180 kg

Cost of flour = $0.84 per kg

Quantity of sugar = 25 kg

Cost of sugar =$1.17 per kg

Total amount = 180 x 0.84 + 25 x 1.17

= 151.2 + 29.25

= $180.45

So, total amount i spent is $180.45

Problem 6 :

Evaluate :

a) 0.3 x 6

b) 0.5 x 0.4

c) 0.03 x 7

d) 0.03 x 700

e) 2.5 x 8

Solution :

a) 0.3 x 6

= (3/10) x 6

= (3 x 6)/10

= 18/10

= 1.8

b) 0.5 x 0.4

= (5/10) x (4/10)

= (5 x 4) / (10 x 10)

= 20/100

= 0.20

c) 0.03 x 7

= (3/100) x 7

= (3 x 7)/100

= 21/100

= 0.21

d) 0.03 x 700

= 3/100 x 700

= (3 x 700) / 100

= 21

e) 2.5 x 8

= 20

Problem 7 :

I load 450 bags of salt onto my lorry, each having 0.15 kg. Find the total mass of all bags.

Solution :

Number of bags = 450

Load carried by each bag = 0.15 kg

Total mass of all bags = 450 x 0.15

= 67.5 kg

Problem 8 :

House bricks have a mass of 4.3 kg each and i buy 2500 of them to build a wall around courtyard.

a) Find the total mass of the bricks.

b) If my truck can carry only 2 tonnes at a time, how many truck loads are necessary to transport the bricks ?

Solution :

Weight of each bag = 4.3 kg

Number of bags i purchase = 2500

a) Total mass = 4.3 x 2500

= 10750 kg

b) 1 tonne = 1000 kg

10750 kg = 10750 / 1000

= 10.750 tonne

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MULTIPLICATION OF DECIMALS

Multiplying Decimals by 10 100 and 1000

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