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
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