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 = \(\frac{1}{100}\) rupee = 0.01 rupee

5 paise = \(\frac{5}{100}\) rupee = 0.05 rupee

9 paise = \(\frac{9}{100}\) rupee = 0.09 rupee

21 paise = \(\frac{21}{100}\) rupee = 0.21 rupee

75 paise = \(\frac{75}{100}\) rupee = 0.75 rupee

Thus, 8 rupees 15 paise = 8\(\frac{15}{100}\) = 8.15 rupees

Similarly,

10 rupees 5 paise = 10\(\frac{5}{100}\) = 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 = \(\frac{1}{10}\) cm = 0.1 cm;

                                   [One millimetre is one tenth of a centimetre.]

So, 1 mm = 0.1 cm;

Therefore, 4 mm = \(\frac{49}{10}\) cm = 0.4 cm

                9 mm = \(\frac{9}{10}\) cm = 0.9 cm

Thus, 4 cm 8 mm = 4\(\frac{8}{10}\) cm = 4.8 cm

       13 cm 6 mm = 13\(\frac{6}{10}\) 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 = \(\frac{1}{100}\) m = 0.01 m

Hence, 1 cm = 0.01 m

2 cm = \(\frac{2}{100}\) m = 0.02 m

10 cm = \(\frac{10}{100}\) m = 0.10 m or 0.1 m

40 cm = \(\frac{40}{100}\) m = 0.40 m or 0.4 m

89 cm = \(\frac{89}{100}\) m = 0.89 m

Thus, 4 m 56 cm = 4\(\frac{56}{100}\) m = 4.56 m

18 m 8 cm = 18\(\frac{8}{100}\) 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 = \(\frac{1}{1000}\) km = 0.001 m;

                                 [One metre is one thousandth of a kilometre.]

So, 1 m = 0.001 m;

Therefore, 8 m = \(\frac{8}{1000}\) km = 0.008 km

18 m = \(\frac{18}{1000}\) km = 0.018 km

75 m = \(\frac{75}{1000}\) km = 0.075 km

356 m = \(\frac{356}{1000}\) km = 0.356 km

528 m = \(\frac{528}{1000}\) km = 0.528 km

Thus, 9 km 426 m = 9\(\frac{426}{1000}\) km = 9.426 km

25 km 693 m = 25\(\frac{693}{1000}\) 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 = \(\frac{1}{1000}\) kg = 0.001 kg;

                                 [One gram is one thousandth of a kilogram.]

So, 5 g = \(\frac{5}{1000}\) kg = 0.005 kg

    12 g = \(\frac{12}{1000}\) kg = 0.012 kg

    49 g = \(\frac{49}{1000}\) kg = 0.049 kg

    85 g = \(\frac{85}{1000}\) kg = 0.085 kg

  365 g = \(\frac{365}{1000}\) kg = 0.365 kg

Thus, 7 kg 118 g = 7\(\frac{118}{1000}\) kg

                          = 7.118 kg

20 kg 48 g = 20\(\frac{48}{1000}\) 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 = \(\frac{1}{1000}\) l = 0.001 l;

                                 [One millilitre is one thousandth of a litre.]

So, 1 ml = 0.001 l

6 ml = \(\frac{6}{1000}\) l = 0.006 l

8 ml = \(\frac{8}{1000}\) l = 0.008 l

28 ml = \(\frac{28}{1000}\) l = 0.028 l

75 ml = \(\frac{75}{1000}\) l = 0.075 l

146 ml = \(\frac{146}{1000}\) l = 0.146 l

Thus, 5 l 450 ml = 5\(\frac{450}{1000}\) l

                         = 5.450 l

19 l 32 ml = 19\(\frac{32}{1000}\) 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

4th Grade Math Activities

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