Exercise 1.2 - Chapter 1 Number Systems Term 2 7th Maths Guide Samacheer Kalvi Solutions - SaraNextGen [2024-2025]

Updated By SaraNextGen

On April 24, 2024, 11:35 AM

Ex $1.2$
Question 1 .
Fill in the following place value table.

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:

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) $6+\frac{0}{10}+\frac{10}{100}+\frac{9}{1000}$
(iv) $900+50+6+\frac{3}{100}$
(v) $\frac{6}{10}+\frac{3}{100}+\frac{1}{1000}$
Solution:
(i) $20+1+\frac{2}{10}+\frac{3}{100}+\frac{7}{1000}=21+2 \times \frac{1}{10}+3 \times \frac{1}{100}+7 \times \frac{1}{1000}=21.237$
(ii) $3+\frac{8}{10}+\frac{4}{100}+\frac{5}{1000}=3+8 \times \frac{1}{10}+4 \times \frac{1}{100}+5 \times \frac{1}{1000}=3.845$
(iii) $6+\frac{0}{10}+\frac{0}{100}+\frac{9}{1000}=6+0 \times \frac{1}{10}+0 \times \frac{1}{100}+9 \times \frac{1}{1000}=6.009$
(iv) $900+50+6+\frac{3}{100}=956+0 \times \frac{1}{10}+3 \times \frac{1}{100}=956.03$
(v) $\frac{6}{10}+\frac{3}{100}+\frac{1}{1000}=6 \times \frac{1}{10}+3 \times \frac{1}{100}=0.631$
 

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) $3 \frac{12}{25}$
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) $\frac{4}{5}=\frac{4 \times 2}{5 \times 2}=\frac{5}{10}=0.8$
(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) 30499
(iii) $3.0049$
(iv) $3.049$
Answer:
(iv) $3.049$
Hint: $=3 \times 1+\frac{0}{10}+\frac{4}{100}+\frac{9}{1000}=3.049$

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: $0.35=\frac{35}{100}=\frac{35 \div 5}{100 \div 5}=\frac{7}{20}$