Convert each of the following into a fraction in its simplest form:

(1) 0.9

We have:

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

(2) 0.6

We have:

= 0.6 = \( \frac {6} {10} = \frac {3} {5} \)

(3) 0.08

We have:

= 0.08 = \( \frac {8} {100} = \frac {4} {50} = \frac {2} {25} \)

(4) 0.15

We have:

= 0.15 = \( \frac {15} {100} = \frac {3} {20} \)

(5) 0.48

We have:

= 0.48 = \( \frac {48} {100} = \frac {12} {25} \)

(6) 0.053

We have:

= 0.053 = \( \frac {53} {1000} \)

(7) 0.125

We have:

= 0.125 = \( \frac {125} {1000} = \frac {25} {200} = \frac {5} {40} = \frac {1} {8} \)

(8) 0.224

We have:

= 0.224 = \( \frac {224} {1000} = \frac {56} {250} = \frac {28} {125} \)

Convert each of the following as a mixed fraction:

(9) 6.4

We have:

= 6.4 = \( \frac {64} {10} = \frac {32} {5} = 6 \frac {2} {5} \)

(10) 16.5

We have:

= 16.5 = \( \frac {165} {10} = \frac {33} {2} = 16 \frac {1} {2} \)

(11) 8.36

We have:

= 8.36 = \( \frac {836} {100} = \frac {209} {25} = 8 \frac {9} {25} \)

(12) 4.275

We have:

= 4.275 = \( \frac {4275} {1000} = \frac {171} {40} = 4 \frac {11} {40} \)

(13) 25.06

We have:

= 25.06 = \( \frac {2506} {100} = \frac {1253} {50} = 25 \frac {3} {50} \)

(14) 7.004

We have:

= 7.004 = \( \frac {7004} {1000} = \frac {1751} {250} = 7 \frac {1} {250} \)

(15) 2.052

We have:

= 2.052 = \(\frac{2052}{1000} = \frac{513}{250} = 2\frac{13}{250}\)

(16) 3.108

We have:

= 3.108 = \( \frac {3108} {1000} = \frac {777} {250} = 3 \frac {27} {250} \)

Convert each of the following into decimal:

(17) \( \frac {23} {10} \)

We have:

\( \frac {23} {10} \) = \( 2 \frac {3} {10} \)

= 2 + 0.3 = 2.3

(18) \( \frac {167} {100} \)

We have:

\( \frac {167} {100} \) = \( 1 \frac {67} {100} \) = 1 + 0.67 = 1.67

(19) \( \frac {1589} {100} \)

We have:

\( \frac {1589} {100} \) = \( 15 \frac {89} {100} \) = 15 + 0.89 = 15.89

(20) \( \frac {5413} {1000} \)

We have:

\( \frac {5413} {1000} \) = \( 5 \frac {413} {1000} \) = 5 + 0.413 = 5.413

(21) \( \frac {21415} {1000} \)

We have:

\( \frac {21415} {1000} \) = \( 21 \frac {415} {1000} \) = 21 + 0.415 = 21.415

(22) \( \frac {25} {4} \)

We have:

\( \frac {25} {4} \) = \( 6 \frac {1} {4} \) = 6 + 0.25 = 6.25

(23) \( 3 \frac {3} {5} \)

= \( \frac {18} {5} \)

We have:

\( 3 \frac {3} {5} \) = 3 + 0.6 = 3.6

(24) \( 1 \frac {4} {25} \)

= \( 1 \frac {4} {25} \) = \( \frac {29} {25} \)

We have:

\( 1 \frac {4} {25} \) = 1 + 0.16 = 1.16

(25) \( 5 \frac {17} {50} \)

= \( 5 \frac {17} {50} \) = \( \frac {267} {50} \)

We have:

\( 5 \frac {17} {50} \) = 5 + 0.34 = 5.34

(26) \( 12 \frac {3} {8} \)

\( 12 \frac {3} {8} \) = \( \frac {99} {8} \)

We have:

\( 12 \frac {3} {8} \) = 12 + 0.375 = 12.375

(27) \( 2 \frac {19} {40} \)

\( 2 \frac {19} {40} \) = \( \frac {99} {40} \)

We have:

\( 2 \frac {19} {40} \) = 2 + 0.475 = 2.475

(28) \( \frac {19} {20} \)

\( \frac {19} {20}\)

We have:

\( \frac {19} {20}\) = 0.95

(29) \( \frac {37} {50} \)

\( \frac {37} {50} \)

We have:

\( \frac {37} {50} \) = 0.74

(30) \( \frac {107} {250} \)

\( \frac {107} {250} \)

We have:

\( \frac {107} {250} \) = 0.428

(31) \(\frac {3} {40}\)

\( \frac {3} {40} \)

We have:

\( \frac {3} {40} \) = 0.075

(32) \( \frac {7} {8} \)

\( \frac {7} {8} \)

We have:

\( \frac {7} {8} \) = 0.875

(33) Using decimals, express

(i) 8 kg 640 g in kilograms

8 kg + 640 gm = 8 kg + \( \frac {640} {1000} kg \)

8 kg + 0.640 kg = 8.640 kg

(ii) 9 kg 37 g in kilograms

9 kg + 37 gm = 9 kg + \( \frac {37} {1000} kg \)

9 kg + 0.037 kg = 9.037 kg

(iii) 6 kg 8 g in kilograms

6 kg + 8 gm = 6kg + \( \frac {8} {1000} kg \)

6 kg + 0.008 kg = 6.008 kg

(34) Using decimals, express

(i) 4 km 365 m in in kilometers

4 km 365 m = 4 km + \( \frac {365} {1000} \; km \; \left [ Since\; 1\; km\; =\; 1000\; m \right ] \)

4 km + 0.365 km = 4.365 km

(ii) 5 km 87 m in kilometers

5 km 87 m = 5 km + \( \frac {87} {1000} \; km \; \left [ Since\; 1\; km\; =\; 1000\; m \right ] \)

5 km + 0.087 km = 5.087 km

(iii) 3 km 6 m in kilometers

3 km 6 m = 3 km + \( \frac {6} {1000} \; km \; \left [ Since\; 1\; km\; =\; 1000\; m \right ] \)

3 km + 0.006 km = 3.006 km

(iv) 270 m in kilometers

\( \frac {270} {1000} \; km \; \; = 0.270\; km \; \left [ Since\; 1\; km\; =\; 1000\; m \right ] \)

(v) 35 m in kilometers

\( \frac {35} {1000} \; km \; = 0.035\; km \; \left [ Since\; 1\; km\; =\; 1000\; m \right ] \)

(vi) 6 m in kilometers

\( \frac {6} {1000} \; km \; = 0.006\; km \; \left [ Since\; 1\; km\; =\; 1000\; m \right ] \)

(35) Using decimals, express

(i) 15 kg 850 g in kilograms

15 kg + 850 gm = 15 kg + \( \frac {850} {1000} \; kg \; \left [ Since\; 1\; kg\; =\; 1000\; gm \right ] \)

15 kg + 0.850 kg = 15.850 kg

(ii) 8 kg 96 g in kilograms

8 kg + 96 gm = 8 kg + \( \frac {96} {1000} \; kg \; \left [ Since\; 1\; kg\; =\; 1000\; gm \right ] \)

8 kg + 0.096 kg = 8.096 kg

(iii) 540 g in kilograms

540 gm = \( \frac {540} {1000} = 0.540 \; kg \; \left [ Since\; 1\; kg\; =\; 1000\; gm \right ] \)

(iv) 8 g in kilograms

8 gm = \( \frac {8} {1000} = 0.008 \; kg \; \left [ Since\; 1\; kg\; =\; 1000\; gm \right ] \)

(36) Using decimals, express:

(i) Rs 18 and 25 paise in rupees

Rs 18 + 25 paise = Rs 18 + \( Rs\; \frac {25} {100} \; \left [ Since\;Re\; 1\;\; =\; 100\; paise \right ] \)

Rs 18 + Rs 0.25 = Rs 18.25

(ii) Rs 9 and 8 paise in rupees

Rs 9 and 8 paise = Rs 9 + \( Rs\; \frac {8} {100} \; \left [ Since\;Re\; 1\;\; =\; 100\; paise \right ] \)

Rs 9 + Rs 0.08 = Rs 9.08

(iii) 32 paise in rupees

32 paise = Rs \( Rs\; \frac {32} {100} = Rs\; 0.32 \; \left [ Since\;Re\; 1\;\; =\; 100\; paise \right ] \)

(iv) 5 paise in rupees

5 paise = \( Rs\; \frac {5} {100} = Rs\; 0.05 \; \left [ Since\;Re\; 1\;\; =\; 100\; paise \right ] \)

Exercise 7C

*Add the following decimals:*

(1) 9.6, 14.8, 37 and 5.9

Answer:

9.6, 14.8, 37 and 5.9

Converting the decimals into like decimals:

9.6, 14.8, 37.0 and 5.9

Let us write the given numbers in the column form:

Now, adding

Hence, the sum of the given numbers is 67.3

(2) 23.7, 106.94, 68.9 and 29.5

Answer:

23.7, 106.94, 68.9 and 29.5

Converting the decimals into like decimals:

23.70, 106.94, 68.90 and 29.50

Let us write the given numbers in the column form:

Now, adding

Hence, the sum of the given numbers is 229.04

(3) 72.8, 7.68, 16.23 and 0.7

Answer:

72.8, 7.68, 16.23 and 0.7

Converting the decimals into like decimals:

72.80, 7.68, 16.23 and 0.70

Let us write the given numbers in the column form:

Now, adding

Hence, the sum of the given numbers is 97.41.

(4) 18.6, 84.75, 8.345 and 9.7

Answer\;

18.6, 84.75, 8.345 and 9.7

Converting the decimals into like decimals:

18.600, 84.750, 8.345 and 9.700

Let us write the given numbers in the column form:

Now, adding

Hence, the sum of the given numbers is 121.395

(5) 8.236, 16.064, 63.8 and 27.53

Answer:

8.236, 16.064, 63.8 and 27.53

Converting the decimals into like decimals:

8.236, 16.064, 63.800 and 27.530

Let us write the given numbers in the column form:

Now, adding

Hence, the sum of the given numbers is 115.630.

(6) 28.9, 19.64, 123.697 and 0.354

Answer:

28.9, 19.64, 123.697 and 0.354

Converting the decimals into like decimals:

28.900, 19.640, 123.697 and 0.354

Let us write the given numbers in the column form:

Now, adding

Hence, the sum of the given numbers is 172.591

(7) 4.37, 9.638, 17.007 and 6.8

Answer:

4.37, 9.638, 17.007 and 6.8

Converting the decimals into like decimals:

4.370, 9.638, 17.007 and 6.800

Let us write the given numbers in the column form:

Now, adding

Hence, the sum of the given numbers is 37.815.

(8) 14.5, 0.038, 118.573 and 6.84

Answer:

14.5, 0.038, 118.573 and 6.84

Converting the decimals into like decimals:

14.500, 0.038, 118.573 and 6.840

Let us write the given numbers in the column form:

Now, adding

Hence, the sum of the given numbers is 139.951

9. During three days of week, a rickshaw puller earns Rs 32.60, Rs 56.80 and Rs 72 respectively. What is his total earning during these days?

Answer:

Earning on the 1^{st} day of the week = Rs 32.60

Earning on the 2^{nd} day of the week = Rs 56.80

Earning on the 3^{rd} day of the week = Rs 72.00

Total earning = Rs 161.40

10. A man purchases an almirah for Rs 11025, gives Rs 172.50 as its cartage and spends Rs 64.80 on its repair. How much does the almirah cost him?

Answer:

Cost of the almirah = Rs 11025.00

Money spend on cartage = Rs 172.50

Money spent on repair = Rs 64.800

Total cost of the almirah = Rs 11262.3

11. Ramesh covers 36 km 235 m by taxi, 4 km 85 m by rickshaw and 1 km 80 m on foot. What is the total distance covered by him?

Answer:

Distance covered by the taxi = 36 km 235 m

Distance covered by the rickshaw = 4 km 085 m

Distance covered on foot = 1 km 080 m

Total distance covered = 41km 400m

12. A bag contains 45 kg 80 g of sugar and the mass of the empty bag is 950 g. What is the mass of the bag containing this much of sugar?

Answer:

Weight of sugar in the bag = 45 kg 080 g

Weight of the empty bag = 0 kg 950 g

Total weight of the bag = 46kg 30g

13. Ramu bought 2 m 70 cm cloth for his shirt and 2 m 60 cm cloth of his pyjamas. Find the total length of cloth bought by him.

Answer:

Length of the cloth for his shirt = 2 m 70 cm

Length of the cloth for his pyjamas = 2 m 60 cm

The total length of the cloth bought = 5m 30 cm

14. Radhika bought 2 m 5 cm cloth for her salwar and 3 m 35 cm cloth for her shirt. Find the total length of cloth bought by her.

Answer:

Length of the cloth for her salwar = 2 m 05 cm

Length of the cloth for her shirt = 3 m 35 cm

Total length of cloth bought = 5m 40m