Exercise 1.5 - 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 $1.5$
Question $1 .$
Write the following decimal numbers in the place value table.
(i) $247.36$
(ii) $132.105$
Solution:

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, $8>2$.
$0.888>0.28 \therefore 0.888$ 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.
$\therefore$ Comparing the thousandths place, we get $5>4$.
$23.915>23.914 \therefore 23.915$ is greater.
 

Question $4 .$
In a $25 \mathrm{~m}$ swimming competition, the time taken by 5 swimmers $\mathrm{A}, \mathrm{B}, \mathrm{C}, \mathrm{D}$ and $\mathrm{E}$ 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 $25 \mathrm{~m}$.
Comparing the time taken by $\mathrm{A}, \mathrm{B}, \mathrm{C}, \mathrm{D}, \mathrm{E}$ the whole number part is equal for all participants. Comparing digit in tenths place we get $6<7$.
$\therefore$ 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. $\therefore \mathrm{C}$ 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) $256 \mathrm{~m}$
(ii) $4567 \mathrm{~m}$
Solution:

$1 \mathrm{~m}=\frac{1}{1000} \mathrm{~km}=0.001 \mathrm{Km}$
(i) $256 \mathrm{~m}=\frac{256}{1000} \mathrm{~km}=0.256 \mathrm{~km}$
(ii) $4567 \mathrm{~m}=\frac{4567}{1000} \mathrm{~km}=4.567 \mathrm{~km}$
 

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 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 $=₹ 809.99$

Question 9 .
Express the following in metres using decimals.
(i) $1328 \mathrm{~cm}$
(ii) $419 \mathrm{~cm}$
Solution:
$100 \mathrm{~cm}=1 \mathrm{~m} ; 1 \mathrm{~cm}=\frac{1}{100} \mathrm{~m}$
(i) $1328 \mathrm{~cm}=\frac{1328}{100} \mathrm{~m}=13.28 \mathrm{~m}$
(ii) $419 \mathrm{~cm}=\frac{419}{100} \mathrm{~m}=4.19 \mathrm{~m}$

Question $10 .$
Express the following using decimal notation.
(i) $8 \mathrm{~m} 30 \mathrm{~cm}$ in metres
(ii) $24 \mathrm{~km} 200 \mathrm{~m}$ in kilometres
Solution:
(i) $8 \mathrm{~m} 30 \mathrm{~cm}$ in metres
$8 \mathrm{~m}+\frac{30}{100} \mathrm{~m}=8 \mathrm{~m}+0.30 \mathrm{~m}=8.30 \mathrm{~m}$
(ii) $24 \mathrm{~km} 200 \mathrm{~m}$ in kilometres
$24 \mathrm{~km}+\frac{200}{1000} \mathrm{~km}=24 \mathrm{~km}+0.200 \mathrm{~km}=24.200 \mathrm{~km}$
 

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 7 th 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 7 th 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 $\frac{9}{10} \mathrm{~km}$ less than $1 \mathrm{~km}$. Express the same in decimal form.
Solution:
Given measures are $1 \mathrm{~km}$ and $\frac{9}{10} \mathrm{~km}$. i.e., $1 \mathrm{~km}$ and $0.9 \mathrm{~km}$.
Difference $=1.0-0.9=0.1 \mathrm{~km}$.