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.

Answer:

1/2 as a decimal is 0.5.

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

Answer:

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
Answer:
(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
Answer:
(iv) 0.6
Hint: $$\frac { 3 }{ 5 }$$ = $$\frac{3 \times 2}{5 \times 2}$$ = $$\frac { 6 }{ 10 }$$ = 0.06

Question 10.
The simplest form of 0.35 is
(i) $$\frac { 35 }{ 1000 }$$
(ii) $$\frac { 35 }{ 10 }$$
(iii) $$\frac { 7 }{ 20 }$$
(iv) $$\frac { 7 }{ 100 }$$
Answer:
(iii) $$\frac { 7 }{ 20 }$$
Hint: 0.35 = $$\frac { 35 }{ 100 }$$ = $$\frac{35 \div 5}{100 \div 5}$$ = $$\frac { 7 }{ 20 }$$