Page 55 - Start Up Mathematics_7

Example 11: A car covers a distance of 14.75 km in 1 kg of CNG. How much distance will it
cover in 10 kg of CNG?
Solution: Distance covered by car in 1 kg of CNG = 14.75 km
∴ Distance covered by car in 10 kg of CNG = 14.75 × 10 = 147.5 km

Multiplication of a Decimal Number by a Whole Number
In order to multiply a decimal number by a whole number, follow these steps:

Step 1: Multiply the decimal number by the given whole number ignoring the decimal point.
Step 2: Count the number of digits starting from the extreme right digit to the left and put the
decimal point at the place equivalent to the number of decimal places that are in the given
decimal number.

Example 12: Evaluate each of the following:
(a) 0.3 × 8 (b) 2.15 × 5 (c) 15 × 81.09 (d) 3 × 0.701

Solution: (a) 0.3 × 8
In order to find the product, we first multiply 3 and 8, i.e., 3 × 8 = 24.
Now 0.3 has 1 decimal place. So, the product must have 1 decimal place.

Hence, 0.3 × 8 = 2.4
Proceeding as above, we get

(b) 2.15 × 5 = 10.75 (c) 15 × 81.09 = 1,216.35 (d) 3 × 0.701 = 2.103
Example 13: If 1 kg of full cream milk contains 0.315 kg of fat, how much fat is there in 20 kg
of milk?

Solution: Quantity of fat in 1 kg of pure milk = 0.315 kg
∴ Quantity of fat in 20 kg of pure milk = 0.315 × 20 = 6.3 kg

Multiplication of Decimal Number by Another Decimal Number
In order to multiply two decimal numbers, follow these steps:

Step 1: Multiply the decimal numbers after ignoring the decimal point, i.e., multiply them as
whole numbers.
Step 2: For the position of decimal in the product, count the number of digits starting from the
extreme right digit to the left and put the decimal point at the place equivalent to the sum
of the decimal places that are in the given decimal numbers.
Example 14: Find: (a) 3.2 × 0.7 (b) 2.001 × 1.1 (c) 0.1 × 0.03

Solution: (a) 3.2 × 0.7
In order to find the product, we first multiply 32 and 7, i.e., 32 × 7 = 224.

Now 3.2 has 1 decimal place and 0.7 also has 1 decimal place. So the product
must have 1 + 1 = 2 decimal places. Now put the decimal 2 digits to the left
from rightmost digit in 224 (i.e., 4). Hence, 3.2 × 0.7 = 2.24.
Proceeding as above, we get
(b) 2.001 × 1.1 = 2.2011 (c) 0.1 × 0.03 = 0.003

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