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## Tamilnadu Samacheer Kalvi 7th Maths Solutions Term 2 Chapter 1 Number System Ex 1.5

Question 1.

Write the following decimal numbers in the place value table.

(i) 247.36

(ii) 132.105

Solution:

(i) 247.36

(ii) 132.105

Question 2.

Write each of the following as decimal number.

(i) 300 + 5 + \(\frac { 7 }{ 10 } \) + \(\frac { 9 }{ 100 } \) + \(\frac { 2 }{ 100 } \)

(ii) 1000 + 400 + 30 + 2 + \(\frac { 6 }{ 10 } \) + \(\frac { 7 }{ 100 } \)

Solution:

(i) 300 + 5 + \(\frac { 7 }{ 10 } \) + \(\frac { 9 }{ 100 } \) + \(\frac { 2 }{ 100 } \) = 305.792

(ii) 1000 + 400 + 30 + 2 + \(\frac { 6 }{ 10 } \) + \(\frac { 7 }{ 100 } \) = 1432.67

Question 3.

Which is greater?

(i) 0.888 (or) 0.28

(ii) 23.914 (or) 23.915

Solution:

(i) 0.888 (or) 0.28

The whole number parts is equal for both the numbers.

Comparing the digits in the tenths place we get, 8 > 2.

0.888 > 0.28 ∴ 0.888 is greater.

(ii) 23.914 or 23.915

The whole number part is equal in both the numbers.

Also the tenth place and hundredths place are also equal.

∴ Comparing the thousandths place, we get 5 > 4.

23.915 > 23.914 ∴ 23.915 is greater.

Question 4.

In a 25 m swimming competition, the time taken by 5 swimmers A, B, C, D and E are 15.7 seconds, 15.68 seconds, 15.6 seconds, 15.74 seconds and 15.67 seconds respectively. Identify the winner.

Solution:

The winner is one who took less time for swimming 25 m.

Comparing the time taken by A, B, C, D, E the whole number part is equal for all participants.

Comparing digit in tenths place we get 6 < 7.

∴ Comparing 15.68, 15.6, 15.67, that is comparing the digits in hundredths place we get 15.60 < 15.67 < 15.68

One who took 15.6 seconds is the winner. ∴ C is the winner.

Question 5.

Convert the following decimal numbers into fractions

(i) 23.4

(ii) 46.301

Solution:

(i) 23.4 = \(\frac { 234 }{ 10 } \) = \(\frac{234 \div 2}{10 \div 2}\) = \(\frac { 117 }{ 5 } \)

(ii) 46.301 = \(\frac { 46301 }{ 1000 } \)

Question 6.

Express the following in kilometres using decimals,

(i) 256 m

(ii) 4567 m

Solution:

1 m = \(\frac { 1 }{ 1000 } \) km = 0.001 Km

(i) 256 m = \(\frac { 256 }{ 1000 } \) km = 0.256 km

(ii) 4567 m = \(\frac { 4567 }{ 1000 } \) km = 4.567 km

Question 7.

There are 26 boys and 24 girls in a class. Express the fractions of boys and girls as decimal numbers.

Solution:

Boys = 26; Girls = 24; Total = 50

Fraction of boys = \(\frac { 26 }{ 50 } \) = \(\frac{26 \times 2}{50 \times 2}\) = \(\frac { 52 }{ 100 } \) = 0.52

Fraction of girls = \(\frac { 24 }{ 50 } \) = \(\frac{24 \times 2}{50 \times 2}\) = \(\frac { 48 }{ 100 } \) = 0.48

Challenge Problems

Question 8.

Write the following amount using decimals.

(i) 809 rupees 99 paise

(ii) 147 rupees 70 paise

Solution:

100 paise = 1 rupee; 1 paise = \(\frac { 1 }{ 100 } \) rupee

(i) 809 rupees 99 paise = 809 rupees + \(\frac { 99 }{ 100 } \) rupees

= 809 + 0.99 rupees = ₹ 809.99

(ii) 147 rupees 70 paise = 147 rupees + \(\frac { 70 }{ 100 } \) rupees

= 147 rupees + 0.70 rupees = ₹ 147.70

Question 9.

Express the following in metres using decimals.

(i) 1328 cm

(ii) 419 cm

Solution:

100 cm = 1 m; 1 cm = \(\frac { 1 }{ 100 } \) m

(i) 1328 cm = \(\frac { 1328 }{ 100 } \) m = 13.28 m

(ii) 419 cm = \(\frac { 419 }{ 100 } \) m = 4.19 m

Question 10.

Express the following using decimal notation.

(i) 8 m 30 cm in metres

(ii) 24 km 200 m in kilometres

Solution:

(i) 8 m 30 cm in metres

8 m + \(\frac { 30 }{ 100 } \) m = 8 m + 0.30 m = 8.30 m

(ii) 24 km 200 m in kilometres

24 km + \(\frac { 200 }{ 1000 } \) km = 24 km + 0.200 km = 24.200 km

Question 11.

Write the following fractions as decimal numbers.

(i) \(\frac { 23 }{ 10000 } \)

(ii) \(\frac { 421 }{ 100 } \)

(iii) \(\frac { 37 }{ 10 } \)

Solution:

(i) \(\frac { 23 }{ 10000 } \) = 0.0023

(ii) \(\frac { 421 }{ 100 } \) = 4.21

(iii) \(\frac { 37 }{ 10 } \) = 3.7

Question 12.

Convert the following decimals into fractions and reduce them to the lowest form,

(i) 2.125

(ii) 0.0005

Solution:

(i) 2.125 = \(\frac { 2125 }{ 1000 } \) = \(\frac{2125 \div 25}{1000 \div 25}\) = \(\frac { 85 }{ 40 } \) = \(\frac{85 \div 5}{40 \div 5}\) = \(\frac { 17 }{ 8 } \)

(ii) 0.0005 = \(\frac { 5 }{ 1000 } \) = \(\frac{5 \div 5}{10000 \div 5}\) = \(\frac { 1 }{ 2000 } \)

Question 13.

Represent the decimal numbers 0.07 and 0.7 on a number line.

Solution:

0.07 lies between 0.0 and 0.1

The unit space between 0 and 0.1 is divided into 10 equal parts and 7th part is taken. Also 0.7 lies between 0 and 1.

The unit space between 0 and 1 is divided into 10 equal parts, and the 7th part is taken.

Question 14.

Write the following decimal numbers in words.

(i) 4.9

(ii) 220.0

(iii) 0.7

(iv) 86.3

Solution:

(i) 4.9 = Four and nine tenths

(ii) 220.0 = Two hundred and twenty

(iii) 0.7 = Seven tenths

(iv) 86.3 = Eighty six and three tenths.

Question 15.

Between which two whole numbers the given numbers lie?

(i) 0.2

(ii) 3.4

(iii) 3.9

(iv) 2.7

(v) 1.7

(vi) 1.3

Solution:

(i) 0.2 lies between 0 and 1.

(ii) 3.4 lies between 3 and 4.

(iii) 3.9 lies between 3 and 4.

(iv) 2.7 lies between 2 and 3.

(v) 1.7 lies between 1 and 2.

(vi) 1.3 lies between 1 and 2.

Question 16.

By how much is \(\frac { 9 }{ 10 } \) km less than 1 km. Express the same in decimal form.

Solution:

Given measures are 1 km and \(\frac { 9 }{ 10 } \) km. i.e., 1 km and 0.9 km.

Difference = 1.0 – 0.9 = 0.1 km.