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## Tamilnadu Samacheer Kalvi 7th Maths Solutions Term 2 Chapter 1 Number System 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.

∴ 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

∴ 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.

∴ 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

∴ 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.

∴ 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.

∴ Comparing the digit in tenths place we get

2.53 > 2.35 ……(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

∴ 123.45 < 123.54 …(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

∴ 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 …(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

∴ 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.

∴ 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.

∴ 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.

∴ 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.

∴ 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.

∴ 4.578 > 4.571

∴ 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, 745.63 457.71

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, 745.63 457.71

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) ≠

Answer:

(i) =

Question 7.

78.56 [ ] 78.57

(i) <

(ii) >

(iii) =

(iv) ≠

Answer:

(i) <