We use decimals every day while dealing with money, weight, length etc. Decimal numbers are used in situations where more precision is required than the whole numbers can provide. For example, when we calculate our weight on the weighing machine, we do not always find the weight equal to a whole number on the scale. In order to know our exact weight, we must understand what the decimal value on the scale means. This section deals with the concept of decimals in three important fields of our daily life.
- Use of decimal to represent money
Dealing with decimal numbers is inevitable when dealing with money. In many situations when we have to convert paisa into rupee. Suppose we go to a local shop to buy 500 gm of turmeric, where, one kg of turmeric costs Rs 51. So, how much money should we hand over to the shopkeeper? We divide Rs 51 by 2 which are equal to 25.5. In order to hand over the exact amount, we must understand what 25.5 means in terms of rupees. Let us learn this with the help of a simple example.
Re 1 = 100 paisa
Example 1: Converting 165 paisa to Re.
As we know, 1 paisa = 1/100 Re
So, 165 paisa = Re 165*1/100 = Re 165/100 = Rs 1.65, which is Re 1 and 65 paisa
Example 2: Converting 450 paisa to Re.
As we know, 1 paisa = Re 1/100
So, 450 paisa = 450*1/100 = Rs 450/100 = Rs 4.50 = Rs 4 and 50 paisa
Example 3: Converting Rs 35 and 70 paisa to decimal.
As we know, 1 paisa = Re 1/100
So, 70 paisa = 70*1/100
Rs (35 + 70/100) = Rs 35.70
- Use of decimal to represent the length
While measuring the length of an item, it is not necessary that the length of an object is a multiple of the given graduation. For example, while measuring the length of a table with a metre scale, the length may not be a whole number, it may lie between two graduations on the metre scale. In such situations, the decimal numbers are used.
From Conversion of units, we know
1 km = 100 m
1 m = 100 cm
1 cm = 10 mm
Now, let the length of the table top be 2 m and 75 cm, and then it can be represented as (2+ 75/100) m.
Example 4: Converting 276 cm into meters.
As we know, 100 cm = 1 m
So, 1 cm = 1/100 m
276 cm = 276 * 1/100 m = 276/100 m = 2.76 m
Example 5: Converting 5km and 75 m into decimal.
As we know, 1 km = 1000 m
So, 1 m = 1/1000 km
5 km + 75m = 5+ (75*1/1000) km = 5.075 km
Example 6: Converting 80 mm to km
As we know 1 km = 1000 m and 1 m = 100 cm
So 1 km = 1000 * 100 cm
1 cm = 1/10000km
80 cm = 80*1/100000 km
80 cm = 0.00080 km
- Use of decimal to represent weight
We use decimal numbers while dealing with weight. For example, when we are buying a watermelon, it cannot always weigh in whole numbers, it can be less than 2 kg but more than 1kg. In such situations, the shopkeeper has to calculate how much to charge for a watermelon, based on its weight. As we know,
1 kg = 1000 gm
1 gm = 1000 mg
Now suppose it is 1kg and 750 gm. Then, he will charge as per the price of 1kg + (750/1000) kg of the watermelon. We will learn more about the conversion of weight into decimal in the following examples:
Example 7: Converting 250 gm to kg
As we know, 1000 gm = 1 kg
So, 1 gm = 1/1000 kg
250 gm = 250 * 1/1000 kg = 250/1000 kg = 0.250 kg
Example 8: Representing 3kgs and 767 gm in decimal.
As we know, 1gm = 1/1000 kg
767gm = 767/1000 kg
So, 3kg + 767/1000 kg = 3.767 kg
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