Exercise 1.3 - 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 $1.3$
Question $1 .$
Compare the following decimal numbers and find out the smaller number.
(i) $2.08,2.086$
(ii) $0.99,1.9$
(iii) $3.53,3.35$
(iv) $5.05,5.50$
(v) $123.5,12.35$
Solution:
(i) $2.08,2.086$
Let us take $2.080,2.086$.
Comparing $2.08$ and $2.086$ the whole number part, tenths place digit and the digit in the hundredths place are equal.
Comparing the digits at thousandths place we get $0<6$.
Therefore $2.08<2.086$.
Smallest number is $2.08$
(ii) $0.99,1.9$
Comparing $0.99$ and $1.9 .$
First when we compare the digit in the whole number parts we get $0<1$.
$\therefore 0.99<1.9$ Smallest number is $0.99$
(iii) $3.53,3.35$
Comparing $3.53$ and $3.35$
Here the whole number parts of the given two numbers are equal.
Comparing the digits at tenths place, we get $3<5$
$\therefore 3.35<3.53$
Smallest number is $3.35$

(iv) $5.05,5.50$
Comparing $5.05$ and $5.50$
Here the whole number parts of the given two numbers are equal.
Comparing the digits at tenths place, we get $0<5$.
$\therefore 5.5<5.50$
Smallest number is $5.05$
(v) $123.5,12.35$
Comparing $123.5$ and $12.35$.
Comparing the whole number parts, we get $12<123$
$\therefore 12.35<123.5$
Smallest number is $12.35$

Question 2 .
Arrange the following in ascending order.
(i) $2.35,2.53,5.32,3.52,3.25$
(ii) $123.45,123.54,125.43,125.34,125.3$
Solution:
(i) $2.35,2.53,5.32,3.52,3.25$
Comparing the whole number parts of all the numbers 5 is the greatest and $5>3>2$.
$\therefore$ Greatest number is $5.32$
Next $3.52$ and $3.25$ are equal in their whole number.
So comparing their digits in tenths place, we get $5>2$
So $3.52>3.25$
Now comparing $2.35$ and $2.53$ their whole number parts also equal.
$\therefore$ Comparing the digit in tenths place we get
$2.53>2.35 \ldots \ldots$ (2)
Ascending order:
$2.35<2.53<3.25<3.52<5.32$

(ii) $123.45,123.54,125.43,125.34,125.3$
Comparing the whole number parts we have 123 is the smallest number and two numbers $123.45$ and $123.54$ have same whole number part.
So in $123.45$ and $123.54$ comparing their digits in the tenths place we get $4<5$
$\therefore 123.45<123.54 \ldots$ (1)
Now comparing the remaining numbers
$125.43,125.34,125.3$ they all have the same whole number part.
Comparing the numbers in the tenths place we have $3<4$
$\therefore 125.43$ is the greatest ...(2)
Also tenths place value $3=3$ in $125.34$ and $125.3$
Again comparing the hundredths place value in $125.34$ and $125.3$, we get
$125.3<125.34 \ldots(3)$
From (1), (2) and (3) we have,
$123.45<123.54<125.3<125.34<125.43$

Question $3 .$
Compare the following decimal numbers and find the greater number.
(i) $24.5,20.32$
(ii) $6.95,6.59$
(iii) $17.3,17.8$
(iv) $235.42,235.48$
(v) $0.007,0.07$
(vi) $4.571,4.578$
Solution:
(i) $24.5,20.32$
Comparing the whole number part we get $24>20$
$\therefore 24.5>20.32$
greater number is $24.5$
(ii) $6.95,6.59$
Here the whole number part of given two numbers are equal.
Comparing the digits at tenths place we get $9>5$.
$\therefore 6.95>6.59$
Greater number is $6.95$
(iii) $17.3,17.8$
Here the whole number part of given two numbers are equal.
Comparing the digits at tenths place we get $8>3$.
$\therefore 17.8>17.3$
Greater number is $17.8$
(iv) $235.42,235.48$
Here the whole number part of given two numbers are equal.
Also the digits at tenths place also equal.
Comparing the digits at the hundredths place we get $8>4$.
$\therefore 235.48>235.42$
Greater number is $235.48$
(v) $0.007,0.07$
Here the whole number part of given two numbers are equal.
Also the digits at the tenths place also equal.
$\therefore$ Comparing the the digits at the hundredths place we get $7>0$.

$0.07>0.007$
greater number is $0.07$.
(vi) $4.571,4.578$
Here the whole number part of given two numbers are equal.
Also the digits at the tenths place and the hundredths place also equal.
Again comparing the digits in the thousandths place we get $8>1$.
$\therefore 4.578>4.571$
$\therefore$ Greater number is $4.578$
 

Question $4 .$
Arrange the given decimal numbers in descending order.
(i) $17.35,71.53,51.73,73.51,37.51$
(ii) $456.73,546.37,563.47,745.63457 .71$
Solution:
(i) $17.35,71.53,51.73,73.51,37.51$
Comparing the whole number parts of the given numbers we get $73>71>51>37>17$.
Descending order:
$73.51,71.53,51.73,37.51,17.35$
(ii) $456.73,546.37,563.47,745.63457 .71$
Comparing the whole number parts of the given numbers from left to right we get $745>563>546>457>456$
Descending Order: $745.63,563.47,546.37,457.71,456.73$

Objective Question
Question $5 .$
$0.009$ is equal to
(i) $0.90$
(ii) $0.090$
(iii) $0.00900$
(iv) $0.900$
Answer:
(iii) $0.00900$

Question $6 .$
$37.70[] 37.7$
(i) $=$
(ii) $<$
(iii) $>$
(iv) $\neq$
Answer:
(i) $=$

Question $7 .$
$78.56$ [ ] $78.57$
(i) $<$
(ii) $>$
(iii) $=$
(iv) $\neq$
Answer:
(i) $<$