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Uses of Decimals

We will learn uses decimals in every day. In daily life we use decimals while dealing with length, weight, volume, money etc.

 

Use of Decimals while Dealing with Money:

Let us learn about some uses of decimal notation in money transactions.

We know that 100 paise = 1 rupee;

                   [We know that one paise in one hundredth of a rupee.]

1 paise = 1100 rupee = 0.01 rupee

5 paise = 5100 rupee = 0.05 rupee

9 paise = 9100 rupee = 0.09 rupee

21 paise = 21100 rupee = 0.21 rupee

75 paise = 75100 rupee = 0.75 rupee

Thus, 8 rupees 15 paise = 815100 = 8.15 rupees


Similarly,

10 rupees 5 paise = 105100 = 10.05 rupees

10 rupees 45 paise = 10 rupees + 45 paise = ₹ 10 + ₹ 0.45 = 10.05 rupees = ₹ 10.45

75 rupees 50 paise = 75 rupees + 50 paise = ₹ 75 + ₹ 0.50 = 75.50 rupees = ₹ 75.50


We read 6.45 rupees as six rupees 45 paise

16.25 rupees as sixteen rupees 25 paise

Use of Decimals while Dealing with Lengths:

Let us learn about some uses of decimal notation in measuring lengths.

We know that 10 mm = 1 cm

So, one millimeter is one tenth of a centimeter.

Therefore, 1 mm = 110 cm = 0.1 cm;

                                   [One millimetre is one tenth of a centimetre.]

So, 1 mm = 0.1 cm;

Therefore, 4 mm = 4910 cm = 0.4 cm

                9 mm = 910 cm = 0.9 cm

Thus, 4 cm 8 mm = 4810 cm = 4.8 cm

       13 cm 6 mm = 13610 cm = 13.6 cm

         9 cm 5 mm = 9 cm + 5 mm = 9 cm + 0.5 cm = 9.5 cm

We know that 100 cm = 1 m;

                                [One centimetre is one hundredth of a metre.]

1 cm = 1100 m = 0.01 m

Hence, 1 cm = 0.01 m

2 cm = 2100 m = 0.02 m

10 cm = 10100 m = 0.10 m or 0.1 m

40 cm = 40100 m = 0.40 m or 0.4 m

89 cm = 89100 m = 0.89 m

Thus, 4 m 56 cm = 456100 m = 4.56 m

18 m 8 cm = 188100 m = 18.08 m

Similarly, 42 m 35 cm = 42.35 m

              68 m 75 cm = 68.75 m


We know that, 1000 m = 1 km

Therefore, 1 m = 11000 km = 0.001 m;

                                 [One metre is one thousandth of a kilometre.]

So, 1 m = 0.001 m;

Therefore, 8 m = 81000 km = 0.008 km

18 m = 181000 km = 0.018 km

75 m = 751000 km = 0.075 km

356 m = 3561000 km = 0.356 km

528 m = 5281000 km = 0.528 km

Thus, 9 km 426 m = 94261000 km = 9.426 km

25 km 693 m = 256931000 km = 25.693 km

Similarly, 29 km 54 m = 29.054 km

              12 km 75 m = 12.075 km


Use of Decimals while Dealing with Weights:

Let us learn about some uses of decimal notation in measuring weight.

We know that, 1000 g = 1 kg

1 g = 11000 kg = 0.001 kg;

                                 [One gram is one thousandth of a kilogram.]

So, 5 g = 51000 kg = 0.005 kg

    12 g = 121000 kg = 0.012 kg

    49 g = 491000 kg = 0.049 kg

    85 g = 851000 kg = 0.085 kg

  365 g = 3651000 kg = 0.365 kg

Thus, 7 kg 118 g = 71181000 kg

                          = 7.118 kg

20 kg 48 g = 20481000 kg

                = 20.048 kg

Similarly, 12 kg 450 g = 12.450 kg

              62 kg 75 gm = 62.075 kg


Use of Decimals while Dealing with Volumes/Capacity:

We know that, 1000 ml = 1 l

1 ml = 11000 l = 0.001 l;

                                 [One millilitre is one thousandth of a litre.]

So, 1 ml = 0.001 l

6 ml = 61000 l = 0.006 l

8 ml = 81000 l = 0.008 l

28 ml = 281000 l = 0.028 l

75 ml = 751000 l = 0.075 l

146 ml = 1461000 l = 0.146 l

Thus, 5 l 450 ml = 54501000 l

                         = 5.450 l

19 l 32 ml = 19321000 l

                = 19.032 l

Similarly, 14 litres 355 ml = 14.355 litres

              53 litres 56 ml = 53.056 litres, etc.


Questions and Answers on Uses of Decimals:

1. Write in decimals. (One has been done for you):

(i) 21 rupees 55 paise  21.55 rupees

(ii) 250 rupees 5 paise → ....................

(iii) 3 cm 9 mm → ....................

(iv) 4 km 314 m → ....................

(v) 17 kg 50 g → ....................

(vi) 3 rupees 10 paise → ....................

(vii) 12 m 32 cm → ....................

(viii) 20 m 8 cm → ....................

(ix) 26 km 19 m → ....................

(x) 10 l 70 ml ....................


Answer:

1. (ii) 250.05 rupees

(iii) 3.9 cm

(iv) 4.314 km

(v) 17.05 kg

(vi) 3.10 rupees

(vii) 12.32 m 

(viii) 20.08 m

(ix) 26.019 km

(x) 10.07 l


2. Express each of the following using decimal point:

(i) 9 m 80 cm

(ii) 5 kg 580 g

(iii) 25 kg 92 g

(iv) 12 km 40 m

(v) 9 kg 27 g

(vi) 16 cm 5 mm

(vii) 17 km 2 m

(viii) 5155 ml

(ix) 51308 ml

(x) 2718 ml

(xi) 5 paise

(xii) ₹ 20 and 75 paise


Answer:

2. (i) 9.80 m

(ii) 5.580 kg

(iii) 25.092 kg

(iv) 12.040 km

(v) 9.027 kg

(vi) 16.5 cm

(vii) 17.002 km

(viii) 5.155 litres

(ix) 51.308 litres

(x) 2.718 litres

(xi) 0.05 paise

(xii) ₹ 20.75


3. Express each of the following without decimal point:

(i) 8.5 cm

(ii) 4.55 km

(iii) 28.06 m

(iv) 62.009 kg

(v) 27.406 kg

(vi) 75.97 kg

(vii) 18.611 l

(viii) ₹ 0.5

(ix) 15.006 l

(x) ₹ 65.35

(xi) ₹ 9.76

(xii) 2.805 l


3. (i) 8 cm 5 mm

(ii) 4 km 55 m

(iii) 28 m 06 m

(iv) 62 kg 009 g

(v) 27 kg 406 g

(vi) 75 kg 97 kg

(vii) 18 l 61 ml

(viii) 5 paise

(ix) 15 l 006 ml

(x) 65 rupees 35 paise

(xi) 9 rupees 76 paise

(xii) 2 l 805 ml

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