Decimal Fractions — Exercise 7(E)

The cost of a fountain pen is ₹ 13.25. Find the cost of 8 such pens.

Answer

Cost of 1 fountain pen = ₹ 13.25

∴ Cost of 8 fountain pens = ₹ 13.25 × 8 = ₹ 106

Hence, the cost of 8 pens = ₹ 106.

The cost of 25 identical articles is ₹ 218.25. Find the cost of one article.

Answer

Cost of 25 articles = ₹ 218.25

∴ Cost of 1 article = ₹ $\dfrac{218.25}{25}$ = ₹ 8.73

Hence, the cost of one article = ₹ 8.73

The length of an iron rod is 10.32 m. The rod is divided into 4 pieces of equal length. Find the length of each piece.

Answer

Length of the rod = 10.32 m

Since the rod is divided into 4 equal pieces,

∴ Length of each piece = $\dfrac{10.32}{4}$ = 2.58 m

Hence, the length of each piece = 2.58 m

What will be the total length of cloth required to make 5 shirts if 2.15 m of cloth is needed for each shirt?

Answer

Cloth needed for 1 shirt = 2.15 m

∴ Cloth needed for 5 shirts = 2.15 × 5 = 10.75 m

Hence, the total length of cloth required = 10.75 m

Find the distance walked by a boy in $1\dfrac{1}{2}$ hours if he walks 2.150 km every hour.

Answer

Distance walked in 1 hour = 2.150 km

Time = $1\dfrac{1}{2}$ hours = 1.5 hours

∴ Distance walked in 1.5 hours = 2.150 × 1.5 = 3.225 km

Hence, the distance walked = 3.225 km

83 notebooks are sold at ₹ 15.25 each. Find the total money (in rupees) obtained by selling these notebooks.

Answer

Cost of 1 notebook = ₹ 15.25

∴ Total money for 83 notebooks = ₹ 15.25 × 83 = ₹ 1265.75

Hence, the total money obtained = ₹ 1,265.75

If the length of one bedcover is 2.1 m, find the total length of 17 bedcovers.

Answer

Length of 1 bedcover = 2.1 m

∴ Total length of 17 bedcovers = 2.1 × 17 = 35.7 m

Hence, the total length of 17 bedcovers = 35.7 m

A piece of rope is 10 m 67 cm long. Another rope is 16 m 32 cm long. By how much is the second rope longer than the first one?

Answer

Length of first rope = 10 m 67 cm = 10.67 m

Length of second rope = 16 m 32 cm = 16.32 m

Required difference = 16.32 m - 10.67 m = 5.65 m

Hence, the second rope is longer by 5.65 m = 5 m 65 cm

12 cakes of soap together weigh 5 kg and 604 g. Find the weight of:

(i) one cake in both kg and grams

(ii) 5 cakes in kg.

Answer

Weight of 12 cakes = 5 kg 604 g = 5.604 kg

(i) Weight of 1 cake = $\dfrac{5.604}{12}$ = 0.467 kg = 467 g

Hence, the weight of one cake = 0.467 kg = 467 g

(ii) Weight of 5 cakes = 0.467 × 5 = 2.335 kg

Hence, the weight of 5 cakes = 2.335 kg

Three strings of lengths 50 m 75 cm, 68 m 58 cm and 121 m 3 cm respectively, are joined together to get a single string of the greatest length. Find the length of the single string obtained. If this single string is then divided into 12 equal pieces, find the length of each piece.

Answer

The lengths of the three strings are:

50 m 75 cm = 50.75 m

68 m 58 cm = 68.58 m

121 m 3 cm = 121.03 m

Length of single string = 50.75 + 68.58 + 121.03 = 240.36 m

Now, this string is divided into 12 equal pieces.

∴ Length of each piece = $\dfrac{240.36}{12}$ = 20.03 m

Hence, the length of the single string = 240.36 m and the length of each piece = 20.03 m