Decimal Fractions — Exercise 5(E)

Rajan purchased a geometry box for ₹ 136.75, a colour box for ₹ 48.80 and a register for ₹ 64.50. What amount did he pay to the shopkeeper?

Answer

Cost of the geometry box = ₹ 136.75

Cost of the colour box = ₹ 48.80

Cost of the register = ₹ 64.50

Total amount = 136.75 + 48.80 + 64.50

Writing in column form and adding:

$\begin{array}{r} \phantom{+}136.75 \\ 48.80 \\ +\space 64.50 \\ \hline 250.05 \end{array}$

Hence, the total amount paid is ₹ 250.05.

Sakshi bought 3 m 28 cm cloth for her shirt and 2 m 7 cm for her trousers. What is the total length of cloth bought by her?

Answer

Length of cloth for shirt = 3 m 28 cm

= 3 m + $\dfrac{28}{100}$ m = 3 m + 0.28 m = 3.28 m

Length of cloth for trousers = 2 m 7 cm

= 2 m + $\dfrac{7}{100}$ m = 2 m + 0.07 m = 2.07 m

Total length of the cloth = 3.28 + 2.07

Writing in column form and adding:

$\begin{array}{r} \phantom{+}3.28 \\ +\space 2.07 \\ \hline 5.35 \end{array}$

Hence, the total length of the cloth bought by Sakshi is 5.35 m or 5 m 35 cm.

A bag contains 95 kg 80 g of rice and the mass of the empty bag is 860 g. What is the weight of the bag filled with rice?

Answer

Mass of rice = 95 kg 80 g

= 95 kg + $\dfrac{80}{1000}$ kg = 95 kg + 0.080 kg = 95.080 kg

Mass of empty bag = 860 g = $\dfrac{860}{1000}$ = 0.860 kg

Total weight of the bag filled with rice = 95.080 + 0.860

Writing in column form and adding:

$\begin{array}{r} \phantom{+}95.080 \\ +\space 0.860 \\ \hline 95.940 \end{array}$

Hence, the total weight of the bag filled with rice is 95.940 kg or 95 kg 940 g.

Distance between Delhi and Meerut is 85 km 850 m and the distance between Meerut and Muzaffarnagar is 56 km 85 m. What is the distance between Delhi and Muzaffarnagar?

Answer

Distance between Delhi and Meerut = 85 km 850 m

= 85 km + $\dfrac{850}{1000}$ = 85 km + 0.850 = 85.850 km

Distance between Meerut and Muzaffarnagar = 56 km 85 m

= 56 km + $\dfrac{85}{1000}$ = 56 km + 0.085= 56.085 km

The total distance between Delhi and Muzaffarnagar = 85.850 + 56.085

$\begin{array}{r} \phantom{+}85.850 \\ +\space 56.085 \\ \hline 141.935 \end{array}$

Hence, the total distance between Delhi and Muzaffarnagar is 141.935 km or 141 km 935 m.

Divya purchased a book worth ₹ 256.85 and a set of note-books worth ₹ 546.70. She gave a ₹ 2000 note to the shopkeeper. How much money did she get back?

Answer

Cost of the book = ₹ 256.85

Cost of note-books = ₹ 546.70

Total cost = 256.85 + 546.70

Writing in column form and adding:

$\begin{array}{r} \phantom{+}256.85 \\ +\space 546.70 \\ \hline 803.55 \end{array}$

Money given to the shopkeeper = ₹ 2000

Amount returned to Divya = 2000.00 - 803.55

Writing in column form and subtracting:

$\begin{array}{r} \phantom{+}2000.00 \\ -\space 803.55 \\ \hline 1196.45 \end{array}$

Hence, the total amount returned by the shopkeeper is ₹ 1196.45.

The weight of a gas cylinder filled with gas is 32 kg 200 g. If the weight of the gas contained in it is 17 kg 80 g, find the weight of the empty cylinder.

Answer

Weight of the filled cylinder = 32 kg 200 g

= 32 kg + $\dfrac{200}{1000}$ kg = 32 kg + 0.200 kg = 32.200 kg

Weight of gas contained in the cylinder = 17 kg 80 g

= 17 kg + $\dfrac{80}{1000}$ kg = 17 kg + 0.080 kg = 17.080 kg

Weight of empty cylinder = 32.200 − 17.080

Writing in column form and subtracting:

$\begin{array}{r} \phantom{+}32.200 \\ -\space 17.080 \\ \hline 15.120 \end{array}$

Hence, weight of empty cylinder is 15.120 kg or 15 kg 120 g.

Stuti went to the market with ₹ 3000 in cash. Out of this money, she purchased one frock, one toy and one bag costing ₹ 675.85, ₹ 318 and ₹ 1972.75 respectively. How much money is left with her?

Answer

Initial amount with Stuti = ₹ 3000

Total amount spent:

Cost of the frock = ₹ 675.85

Cost of the toy = ₹ 318.00

Cost of the bag = ₹ 1972.75

Total amount spent = 675.85 + 318.00 + 1972.75

Writing in column form and adding:

$\begin{array}{r} \phantom{+}675.85 \\ 318.00 \\ +\space 1972.75 \\ \hline 2966.60 \end{array}$

Money left = 3000.00 - 2966.60

Writing in column form and subtracting:

$\begin{array}{r} \phantom{+}3000.00 \\ -\space 2966.60 \\ \hline 33.40 \end{array}$

Hence, Stuti has ₹ 33.40 left with her.

The total weight of a bag containing 25 kg 750 g of potatoes and 18 kg 80 g of melon is 44 kg 200 g. How much is the weight of the empty bag?

Answer

Weight of potatoes = 25 kg 750 g

= 25 kg + $\dfrac{750}{1000}$ kg = 25 kg + 0.750 kg= 25.750 kg

Weight of melon = 18 kg 80 g

= 18 kg + $\dfrac{80}{1000}$ kg = 18 kg + 0.080 kg = 18.080 kg

Total weight of the bag = 44 kg 200 g

= 44 kg + $\dfrac{200}{1000}$ kg = 44 kg + 0.200 kg = 44.200 kg

Weight of empty bag = 44.200 − (25.750 + 18.080)

$\begin{array}{r} \phantom{+}25.750 \\ +\space 18.080 \\ \hline 43.830 \end{array} \qquad \text{and} \qquad \begin{array}{r} \phantom{+}44.200 \\ -\space 43.830 \\ \hline 0.370 \end{array}$

Hence, the weight of the empty bag is 0.370 kg or 370 g.

If the school bags of Divya and Rahul weigh 8 kg 60 g and 6 kg 275 g respectively, whose bag is heavier and by how much?

Answer

Weight of Divya’s bag = 8 kg 60 g

= 8 kg + $\dfrac{60}{1000}$ kg = 8 kg + 0.060 kg = 8.060 kg

Weight of Rahul’s bag = 6 kg 275 g

= 6 kg + $\dfrac{275}{1000}$ kg = 6 kg + 0.275 kg = 6.275 kg

Since 8.060 > 6.275, Divya's bag is heavier than Rahul's bag.

The difference in weight = 8.060 - 6.275

Writing in column form and subtracting:

$\begin{array}{r} \phantom{+}8.060 \\ -\space 6.275 \\ \hline 1.785 \end{array}$

Divya's bag is heavier by 1.785 kg or 1 kg 785 g.

The distance between Naman's office and his house is 19 km. He covers 14 km 65 m by scooter, 3 km 75 m by bus and the rest on foot. How much distance does he cover by walking?

Answer

Total distance = 19 km

Distance covered by scooter = 14 km 65 m

= 14 km + $\dfrac{65}{1000}$ km = 14 km + 0.065 km = 14.065 km

Distance covered by bus = 3 km 75 m

= 3 km + $\dfrac{75}{1000}$ km = 3 km + 0.075 km= 3.075 km

Total distance covered = 14.065 + 3.075

Writing in column form and adding:

$\begin{array}{r} \phantom{+}14.065 \\ +\space 3.075 \\ \hline 17.140 \end{array}$

So, the total distance covered = 17.140 km

Distance covered on foot = 19.000 - 17.140

Writing in column form and subtracting:

$\begin{array}{r} \phantom{+}19.000 \\ -\space 17.140 \\ \hline 1.860 \end{array}$

The distance covered by walking is 1.860 km or 1 km 860 m.

There was an electric wire of length 100 m. Out of it, three pieces of length 26 m 85 cm, 3 m 18 cm, and 18 m 70 cm were cut off. What is the length of the remaining wire?

Answer

Total length of the wire = 100 m

Length of the first piece = 26 m 85 cm

= 26 m + $\dfrac{85}{100}$ m = 26 m + 0.85 m = 26.85 m

Length of the second piece = 3 m 18 cm

= 3 m + $\dfrac{18}{100}$ m = 3 m + 0.18 m = 3.18 m

Length of the third piece = 18 m 70 cm

= 18 m + $\dfrac{70}{100}$ m = 18 m + 0.70 m = 18.70 m

Total length cut off = 26.85 + 3.18 + 18.70

Writing in column form and adding:

$\begin{array}{r} \phantom{+}26.85 \\ 3.18 \\ +\space 18.70 \\ \hline 48.73 \end{array}$

Total length cut off = 48.73 m

Length of remaining wire = 100.00 - 48.73

$\begin{array}{r} \phantom{+}100.00 \\ -\space 48.73 \\ \hline 51.27 \end{array}$

The remaining wire is 51.27 m or 51 m 27 cm long.

A bag contained 98 kg 300 g of wheat. There was a consumption of 36 kg 450 g, 28 kg 360 g and 32 kg 880 g during three months. How much wheat remains in the bag?

Answer

Total amount of wheat present in the bag = 98 kg 300 g

= 98 kg + $\dfrac{300}{1000}$ kg = 98 kg + 0.300 kg = 98.300 kg

Consumption in month 1 = 36 kg 450 g

= 36 kg + $\dfrac{450}{1000}$ kg = 36 kg + 0.450 kg = 36.450 kg

Consumption in month 2 = 28 kg 360 g

= 28 kg + $\dfrac{360}{1000}$ kg = 28 kg + 0.360 kg = 28.360 kg

Consumption in month 3 = 32 kg 880 g

= 32 kg + $\dfrac{880}{1000}$ kg = 32 kg + 0.880 kg = 32.880 kg

Total consumption during the three months = (36.450 + 28.360 + 32.880 ) kg

Writing in column form and adding:

$\begin{array}{r} \phantom{+}36.450 \\ 28.360 \\ +\space 32.880 \\ \hline 97.690 \end{array}$

Total wheat consumed in three months = 97.690 kg

Amount of wheat remaining in the bag = 98.300 - 97.690

$\begin{array}{r} \phantom{+}98.300 \\ -\space 97.690 \\ \hline 0.610 \end{array}$

Therefore 0.610 kg or 610 g of wheat is remaining in the bag.

Out of 260 litres of milk, a milkman sold 36 l 500 ml, 75 l 750 ml, 68 l 400 ml and 42 l 850 ml. How much milk is left with him?

Answer

Initial amount of milk = 260 l

We know that,

36 l 500 ml = 36 l + $\dfrac{500}{1000}$ l = 36 l + 0.500 l = 36.500 l

75 l 750 ml = 75 l + $\dfrac{750}{1000}$ l = 75 l + 0.750 l = 75.750 l

68 l 400 ml = 68 l + $\dfrac{400}{1000}$ l = 68 l + 0.400 l = 68.400 l

42 l 850 ml = 42 l + $\dfrac{850}{1000}$ l = 42 l + 0.850 l = 42.850 l

Total amount of milk sold = (36.500 + 75.750 + 68.400 + 42.850) l

Writing in column form and adding:

$\begin{array}{r} \phantom{+}36.500 \\ 75.750 \\ 68.400 \\ +\space 42.850 \\ \hline 223.500 \end{array}$

Total amount of milk sold is 223.500 l.

Milk remaining = (260.000 - 223.500) l

Writing in column form and subtracting,

$\begin{array}{r} \phantom{+}260.000 \\ -\space 223.500 \\ \hline 36.500 \end{array}$

The milkman has 36.500 l or 36 l 500 ml of milk left.