Exercise 1.1 - 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 $1.1$
Question $1 .$
Write the decimal numbers for the following pictorial representation of numbers.

Solution: (i) Tens 2 ones 2 tenths $=12.2$
(ii) Tens 1 ones 3 tenths $=21.3$

Question 2 .
Express the following in $\mathrm{cm}$ using decimals.
(i) $5 \mathrm{~mm}$
(ii) $9 \mathrm{~mm}$
(iii) $42 \mathrm{~mm}$
(iv) $8 \mathrm{~cm} 9 \mathrm{~mm}$
(v) $375 \mathrm{~mm}$
Solution:
(i) $5 \mathrm{~mm}$
$1 \mathrm{~mm}=\frac{1}{10} \mathrm{~cm}=0.1 \mathrm{~cm}$
$5 \mathrm{~mm}=\frac{5}{10}=0.5 \mathrm{~cm}$
(ii) $9 \mathrm{~mm}$
$1 \mathrm{~mm}=\frac{1}{10} \mathrm{~cm}=0.1 \mathrm{~cm}$
$9 \mathrm{~mm}=\frac{9}{10} \mathrm{~cm}=0.9 \mathrm{~cm}$
(iii) $42 \mathrm{~mm}$
$1 \mathrm{~mm}=\frac{1}{10} \mathrm{~cm}=0.1 \mathrm{~cm}$
$42 \mathrm{~mm}=\frac{42}{10} \mathrm{~cm}=4.2 \mathrm{~cm}$

(iv) $8 \mathrm{~cm} 9 \mathrm{~mm}$
$1 \mathrm{~mm}=\frac{1}{10} \mathrm{~cm}=0.1 \mathrm{~cm}$
$8 \mathrm{~cm} 9 \mathrm{~mm}=8 \mathrm{~cm}+\frac{9}{10} \mathrm{~cm}=8.9 \mathrm{~cm}$
(v) $375 \mathrm{~mm}$
$1 \mathrm{~mm}=\frac{1}{10} \mathrm{~cm}=0.1 \mathrm{~cm}$ $375 \mathrm{~mm}=\frac{375}{10} \mathrm{~cm}=37.5 \mathrm{~cm}$
$375 \mathrm{~mm}=$

Question $3 .$
Express the following in metres using decimals.
(i) $16 \mathrm{~cm}$
(ii) $7 \mathrm{~cm}$
(iii) $43 \mathrm{~cm}$
(iv) $6 \mathrm{~m} 6 \mathrm{~cm}$
(v) $2 \mathrm{~m} 54 \mathrm{~cm}$
Solution:
(i) $16 \mathrm{~cm}$
$1 \mathrm{~cm}=\frac{1}{100} \mathrm{~cm}=0.01 \mathrm{~m}$
$16 \mathrm{~cm}=\frac{16}{100} \mathrm{~m}=0.16 \mathrm{~m}$
(ii) $7 \mathrm{~cm}$
$1 \mathrm{~cm}=\frac{1}{100} \mathrm{~cm}=0.01 \mathrm{~m}$
$1 \mathrm{~cm}=\frac{7}{100} \mathrm{~m}=0.07 \mathrm{~m}$
(iii) $43 \mathrm{~cm}$
$1 \mathrm{~cm}=\frac{1}{100} \mathrm{~cm}=0.01 \mathrm{~m}$
$43 \mathrm{~cm}=\frac{43}{100} \mathrm{~m}=0.43 \mathrm{~m}$
(iv) $6 \mathrm{~m} 6 \mathrm{~cm}$
$1 \mathrm{~cm}=\frac{1}{10} \mathrm{~m}=0.01 \mathrm{~m}$
$6 \mathrm{~m} 6 \mathrm{~cm}=6 \mathrm{~m}+\frac{6}{100} \mathrm{~m}=6 \mathrm{~m}+0.06 \mathrm{~m}=6.06 \mathrm{~m}$
(v) $2 \mathrm{~mm} 54 \mathrm{~cm}$
$1 \mathrm{~cm}=\frac{1}{100} \mathrm{~cm}=0.01 \mathrm{~m}$
$2 \mathrm{~m} 54 \mathrm{~cm}=2 \mathrm{~m}+\frac{54}{100} \mathrm{~m}=2 \mathrm{~m}+0.54 \mathrm{~m}=2.54 \mathrm{~m}$

Question $4 .$
Expand the following decimal numbers.
(i) $37.3$
(ii) $658.37$
(iii) $237.6$
(iv) $5678.358$
Solution:
(i) $37.3=30+7+\frac{3}{10}=3 \times 10^{1}+7 \times 10^{0}+3 \times 10^{-1}$
$=6 \times 10^{2}+5 \times 10^{1}+8 \times 100+3 \times 10^{-1}$
(iii) $237.6=200+30+7+\frac{1}{10}$
(iii) $237.6=200+30+7+\frac{6}{10}$
$=2 \times 10^{2}+3 \times 10^{1}+7 \times 10^{0}+6 \times 10^{-1}$
(iv) $5678.358=5000+600+70+8+\frac{3}{10}+\frac{5}{100}+\frac{8}{1000}$
$=5 \times 10^{3}+6 \times 10^{2}+7 \times 10^{1}+8 \times 10^{0}+3 \times 10^{-1}+5 \times 10^{-2}+8 \times 10^{-3}$

Question $5 .$
Express the following decimal numbers in place value grid and write the place value of the underlined digit.
(i) $53.61$
(ii) $263.271$
(iii) $17.39$
(iv) $9.657$
(v) $4972.068$

Objective Type Questions
Question $6 .$
The place value of 3 in $85.073$ is
(i) tenths
(ii) hundredths
(iii) thousands
(iv) thousandths
Answer:
(iv) thousandths
Hint: $1000 \mathrm{~g}=1 \mathrm{~kg} ; 1 \mathrm{~g}=\frac{1}{1000} \mathrm{~kg}$

Question $7 .$
To convert grams into kilograms, we have to divide it by
(i) 10000
(ii) 1000
(iii) 100
(iv) 10
Answer:
(ii) 1000
Hint: $85.073=8 \times 10+5 \times 1+0 \times \frac{1}{10}+7 \times \frac{1}{100}+3 \times \frac{1}{1000}$

Question $8 .$
The decimal representation of $30 \mathrm{~kg}$ and $43 \mathrm{~g}$ is $\mathrm{kg}$.
(i) $30.43$
(ii) $30.430$
(iii) $30.043$
(iv) $30.0043$
Answer:
(iii) $30.043$
Hint: $30 \mathrm{~kg}$ and $43 \mathrm{~g}=30 \mathrm{~kg}+\frac{43}{1000} \mathrm{~kg}=30+0.043=30.043$

Question $9 .$
A cricket pitch is about $264 \mathrm{~cm}$ wide. It is equal to $\mathrm{m}$.
(i) $26.4$
(ii) $2.64$
(iii) $0.264$

(iv) $0.0264$
Answer:
(ii) $2.64$
Hint: $264 \mathrm{~cm}=\frac{264}{100} \mathrm{~m}=2.64 \mathrm{~m}$