Samacheer Kalvi 7th Maths Solutions Term 2 Chapter 1 Number System Ex 1.2

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Tamilnadu Samacheer Kalvi 7th Maths Solutions Term 2 Chapter 1 Number System Ex 1.2

Question 1.
Fill in the following place value table.

1/2 as a decimal is 0.5.

Question 2.
Write the decimal numbers from the following place value table.

Question 3.
Write the following decimal numbers in the place value table.
(i) 25.178
(ii) 0.025
(iii) 428.001
(iv) 173.178
(v) 19.54
Solution:
(i) 25.178

(ii) 0.025

(iii) 428.001

(iv) 173.178

(v) 19.54

Question 4.
Write each of the following as decimal numbers.
(i) 20 + 1 + $$\frac { 2 }{ 10 }$$ + $$\frac { 3 }{ 100 }$$ + $$\frac { 7 }{ 1000 }$$
(ii) 3 + $$\frac { 8 }{ 10 }$$ + $$\frac { 4 }{ 100 }$$ + $$\frac { 5 }{ 1000 }$$
(iii) 6 + $$\frac { 0 }{ 10 }$$ + $$\frac { 0 }{ 100 }$$ + $$\frac { 9 }{ 1000 }$$
(iv) 900 + 50 + 6 + $$\frac { 3 }{ 100 }$$
(v) $$\frac { 6 }{ 10 }$$ + $$\frac { 3 }{ 100 }$$ + $$\frac { 1 }{ 1000 }$$
Solution:
(i) 20 + 1 + $$\frac { 2 }{ 10 }$$ + $$\frac { 3 }{ 100 }$$ + $$\frac { 7 }{ 1000 }$$ = 21 + 2 × $$\frac { 1 }{ 10 }$$ + 3 × $$\frac { 1 }{ 100 }$$ + 7 × $$\frac { 1 }{ 1000 }$$ = 21.237

(ii) 3 + $$\frac { 8 }{ 10 }$$ + $$\frac { 4 }{ 100 }$$ + $$\frac { 5 }{ 1000 }$$ = 3 + 8 × $$\frac { 1 }{ 10 }$$ + 4 × $$\frac { 1 }{ 100 }$$ + 5 × $$\frac { 1 }{ 1000 }$$ = 3.845

(iii) 6 + $$\frac { 0 }{ 10 }$$ + $$\frac { 0 }{ 100 }$$ + $$\frac { 9 }{ 1000 }$$ = 6 + 0 × $$\frac { 1 }{ 10 }$$ + 0 × $$\frac { 1 }{ 100 }$$ + 9 × $$\frac { 1 }{ 1000 }$$ = 6.009

(iv) 900 + 50 + 6 + $$\frac { 3 }{ 100 }$$ = 956 + 0 × $$\frac { 1 }{ 10 }$$ + 3 × $$\frac { 1 }{ 100 }$$ = 956.03

(v) $$\frac { 6 }{ 10 }$$ + $$\frac { 3 }{ 100 }$$ + $$\frac { 1 }{ 1000 }$$ = 6 × $$\frac { 1 }{ 10 }$$ + 3 × $$\frac { 1 }{ 100 }$$ = 0.631

Question 5.
Convert the following fractions into decimal numbers.
(i) $$\frac { 3 }{ 10 }$$
(ii) 3 $$\frac { 1 }{ 2 }$$
(iii) 3 $$\frac { 3 }{ 5 }$$
(iv) $$\frac { 3 }{ 2 }$$
(v) $$\frac { 4 }{ 5 }$$
(vi) $$\frac { 99 }{ 100 }$$
(vii) 3 $$\frac { 19 }{ 25 }$$
Solution:
(i) $$\frac { 3 }{ 10 }$$ = 0.3
(ii) 3 $$\frac { 1 }{ 2 }$$ = $$\frac { 7 }{ 2 }$$ = $$\frac{7 \times 5}{2 \times 5}$$ = $$\frac { 35 }{ 10 }$$ = 3.5
(iii) 3 $$\frac { 3 }{ 5 }$$ = $$\frac { 18 }{ 5 }$$ = $$\frac{18 \times 2}{5 \times 2}$$ = $$\frac { 36 }{ 10 }$$ = 3.6
(iv) $$\frac { 3 }{ 2 }$$ = $$\frac{3 \times 5}{2 \times 5}$$ = $$\frac { 15 }{ 10 }$$ = 1.5
(v) $$\frac { 4 }{ 5 }$$ = $$\frac{4 \times 2}{5 \times 2}$$ = $$\frac { 8 }{ 10 }$$ = 0.8
(vi) $$\frac { 99 }{ 100 }$$ = 0.99
(vii) 3 $$\frac { 19 }{ 25 }$$ = $$\frac { 94 }{ 25 }$$ = $$\frac{94 \times 4}{25 \times 4}$$ = $$\frac { 376 }{ 100 }$$ = 3.76

Question 6.
Write the following decimals as fractions.
(i) 2.5
(ii) 6.4
(iii) 0.75
Solution:
(i) 2.5 = 2 + $$\frac { 5 }{ 10 }$$ = $$\frac { 25 }{ 10 }$$
(ii) 6.4 = 6 + $$\frac { 4 }{ 10 }$$ = $$\frac { 64 }{ 10 }$$
(iii) 0.75 = 0 + $$\frac { 7 }{ 10 }$$ + $$\frac { 5 }{ 100 }$$ = $$\frac { 70+5 }{ 100 }$$ = $$\frac { 75 }{ 100 }$$

Question 7.
Express the following decimals as fractions in lowest form.
(i) 2.34
(ii) 0.18
(iii) 3.56
Solution:
(i) 2.34 = 2 + $$\frac { 34 }{ 100 }$$ = 2 + $$\frac{34 \div 2}{100 \div 2}$$ = 2 + $$\frac { 17 }{ 50 }$$ = 2$$\frac { 17 }{ 50 }$$ = $$\frac { 117 }{ 50 }$$
(ii) 0.18 = 0 + $$\frac { 18 }{ 100 }$$ = $$\frac{18 \div 2}{100 \div 2}$$ = $$\frac { 9 }{ 50 }$$
(iii) 3.56 = 3 + $$\frac { 56 }{ 100 }$$ = 3 + $$\frac{56 \div 4}{100 \div 4}$$ = 3 + $$\frac { 14 }{ 25 }$$ = 3 $$\frac { 14 }{ 25 }$$ = $$\frac { 89 }{ 25 }$$

Objective Questions

Question 8.
3 + $$\frac { 4 }{ 100 }$$ + $$\frac { 9 }{ 1000 }$$ = ?
(i) 30.49
(ii) 3049 9
(iii) 3.0049
(iv) 3.049
(iv) 3.049
Hint: = 3 × 1 + $$\frac { 0 }{ 10 }$$ + $$\frac { 4 }{ 100 }$$ + $$\frac { 9 }{ 1000 }$$ = 3.049

Question 9.
$$\frac { 3 }{ 5 }$$ = _______
(i) 0.06
(ii) 0.006
(iii) 6
(iv) 0.6
Hint: $$\frac { 3 }{ 5 }$$ = $$\frac{3 \times 2}{5 \times 2}$$ = $$\frac { 6 }{ 10 }$$ = 0.06
(i) $$\frac { 35 }{ 1000 }$$
(ii) $$\frac { 35 }{ 10 }$$
(iii) $$\frac { 7 }{ 20 }$$
(iv) $$\frac { 7 }{ 100 }$$
(iii) $$\frac { 7 }{ 20 }$$
Hint: 0.35 = $$\frac { 35 }{ 100 }$$ = $$\frac{35 \div 5}{100 \div 5}$$ = $$\frac { 7 }{ 20 }$$