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

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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.