Samacheer Class 7 Maths - Number System Intext Questions

(i) 5 ones and 3 tenths

(ii) 6 tenths

(iii) 7 ones and 9 tenths

(iv) 6 ones and 4 tenths

(v) Seven tenths

(Try These Text book Page No. 5 & 6)

(i) 56.78
(a) Expanded form
56.78 = 5 × 10 1 + 6 × 10 0 + 7 × 10 -1 + 8 × 10 -2
(b) Place value grid

(ii) 123.32
(a) Expanded form
123.32 = 1 × 10 2 + 2 × 10 1 + 3 × 10 0 + 3 × 10 -1 +2 × 10 -2
(b) Place value grid

(iii) 354.56
(a) Expande form
354.56 = 3 × 10 2 + 5 × 10 1 + 4 × 10 0 + 5 × 10 -1 + 6 × 10 -2
(b) Place value grid

(i) Place value of 3 in 36.37 is Tenths.
(ii) Place value of 6 in 267.06 is Hundredths.
(iii) Place value of 2 in 0.23 is Tenths.
(iv) Place value of 9 in 27.69 is Hundredths.
(v) Place value of 2 in 53.27 is Tenths.
Exercise 1.2
(Try These Text book Page No. 10)

(i) \(\frac { 16 }{ 1000 } \) = 0.016
(ii) \(\frac { 638 }{ 10 } \) = 63.8
(iii) \(\frac { 1 }{ 20 } \) = \(\frac{1 \times 5}{20 \times 5}\) = \(\frac { 5 }{ 100 } \) = 0.05
(iv) \(\frac { 3 }{ 50 } \) = \(\frac{3 \times 2}{50 \times 2}\) = \(\frac { 6 }{ 100 } \) = 0.06

(i) 6 hundreds + 3 tens + 3 ones + 6 hundreds + 3 thousandths.
= 6 × 100 + 3 × 10 + 3 × 1 + 0 × \(\frac { 1 }{ 10 } \) + 6 × \(\frac { 1 }{ 100 } \) + 3 × \(\frac { 1 }{ 1000 } \)
= 600 + 30 + 3 + 0 + \(\frac { 6 }{ 100 } \) + \(\frac { 3 }{ 1000 } \)
= 633 + 0.06 + 0.003
= 633.063
(ii) 3 thousands + 3 hundreds + 4 tens + 9 ones + 6 tenths.
= 3 × 1000 + 3 × 100 + 4 × 10 + 9 × 1 + 6 × \(\frac { 1 }{ 10 } \)
= 3000 + 300 + 40 + 9 + \(\frac { 6 }{ 10 } \)
= 3349 + 0.6
= 3349.6

(i) 0.0005 = \(\frac { 5 }{ 10000 } \) = \(\frac{5 \div 5}{10000 \div 5}\) = \(\frac { 1 }{ 2000 } \)
(ii) 6.24 = \(\frac { 624 }{ 100 } \) = \(\frac{624 \div 4}{100 \div 4}\) = \(\frac { 156 }{ 25 } \)
Exercise 1.4
(Try These Text book Page No. 22)

(i) 0.3
We know that 0.3 is more than 0, but less than 1.
There are 3 tenths in it. Divide the unit lenght between O and 1 on the number line
into 10 equal parts and take 3 parts, which represent 0.3.

(ii) 1.7
We know that 1.7 is more than 1, but less than 2.
There are one ones and 7 tenths in it. Divide the unit length between 1 and 2 on the number line into 10 equal parts and take 7 parts which represents 1.7 = 1 + 0.7

(iii) We know that 2.3 is more than 2 and less than 3.
There are 2 ones and 3 tenths in it. Divide the unit length between 2 and 3 into 10 equal parts and take 3 parts, which represents 2.3 = 2 + 0.3

(i) 5 mm
1 mm = \(\frac { 1 }{ 10 } \) cm = 0.1 cm
5 mm = \(\frac { 5 }{ 10 } \) = 0.5 cm
(ii) 9 mm
1 mm = \(\frac { 1 }{ 10 } \) cm = 0.1 cm
9 mm = \(\frac { 9 }{ 10 } \) cm = 0.9 cm
(iii) 42 mm
1 mm = \(\frac { 1 }{ 10 } \) cm = 0.1 cm
42 mm = \(\frac { 42 }{ 10 } \) cm = 4.2 cm
(iv) 8 cm 9 mm
1 mm = \(\frac { 1 }{ 10 } \) cm = 0.1 cm
8 cm 9 mm = 8 cm + \(\frac { 9 }{ 10 } \) cm = 8.9 cm
(v) 375 mm
1 mm = \(\frac { 1 }{ 10 } \) cm = 0.1 cm
375 mm = \(\frac { 375 }{ 10 } \) cm = 37.5 cm

(i) 16 cm
1 cm = \(\frac { 1 }{ 100 } \) cm = 0.01 m
16 cm = \(\frac { 16 }{ 100 } \) m = 0.16 m
(ii) 7 cm
1 cm = \(\frac { 1 }{ 100 } \) cm = 0.01 m
1 cm = \(\frac { 7 }{ 100 } \) m = 0.07 m
(iii) 43 cm
1 cm = \(\frac { 1 }{ 100 } \) cm = 0.01 m
43 cm = \(\frac { 43 }{ 100 } \) m = 0.43 m
(iv) 6 m 6 cm
1 cm = \(\frac { 1 }{ 10 } \) m = 0.01 m
6 m 6 cm = 6 m + \(\frac { 6 }{ 100 } \) m = 6 m + 0.06 m = 6.06 m
(v) 2 mm 54 cm
1 cm = \(\frac { 1 }{ 100 } \) cm = 0.01 m
2 m 54 cm = 2 m + \(\frac { 54 }{ 100 } \) m = 2 m + 0.54 m = 2.54 m

(i) 37.3 = 30 + 7 + \(\frac { 3 }{ 10 } \) = 3 × 10 1 + 7 × 10 0 + 3 × 10 -1
(ii) 658.37 = 600 + 50 + 8 + \(\frac { 3 }{ 10 } \) + \(\frac { 7 }{ 100 } \)
= 6 × 10 2 + 5 × 10 1 + 8 × 100 + 3 × 10 -1 + 7 × 10 -2
(iii) 237.6 = 200 + 30 + 7 + \(\frac { 6 }{ 10 } \)
= 2 × 10 2 + 3 × 10 1 + 7 × 10 0 + 6 × 10 -1
(iv) 5678.358 = 5000 + 600 + 70 + 8 + \(\frac { 3 }{ 10 } \) + \(\frac { 5 }{ 100 } \) + \(\frac { 8 }{ 1000 } \)
= 5 × 10 3 + 6 × 10 2 + 7 × 10 1 + 8 × 10 0 + 3 × 10 -1 + 5 × 10 -2 + 8 × 10 -3

(ii) 1000
Hint: 85.073 = 8 × 10 + 5 × 1 + 0 × \(\frac { 1 }{ 10 } \) + 7 × \(\frac { 1 }{ 100 } \) + 3 × \(\frac { 1 }{ 1000 } \)

(ii) 2.64
Hint: 264 cm = \(\frac { 264 }{ 100 } \) m = 2.64 m
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(i) 20 + 1 + \(\frac { 2 }{ 10 } \) + \(\frac { 3 }{ 100 } \) + \(\frac { 7 }{ 1000 } \) = 21 + 2 × \(\frac { 1 }{ 10 } \) + 3 × \(\frac { 1 }{ 100 } \) + 7 × \(\frac { 1 }{ 1000 } \) = 21.237
(ii) 3 + \(\frac { 8 }{ 10 } \) + \(\frac { 4 }{ 100 } \) + \(\frac { 5 }{ 1000 } \) = 3 + 8 × \(\frac { 1 }{ 10 } \) + 4 × \(\frac { 1 }{ 100 } \) + 5 × \(\frac { 1 }{ 1000 } \) = 3.845
(iii) 6 + \(\frac { 0 }{ 10 } \) + \(\frac { 0 }{ 100 } \) + \(\frac { 9 }{ 1000 } \) = 6 + 0 × \(\frac { 1 }{ 10 } \) + 0 × \(\frac { 1 }{ 100 } \) + 9 × \(\frac { 1 }{ 1000 } \) = 6.009
(iv) 900 + 50 + 6 + \(\frac { 3 }{ 100 } \) = 956 + 0 × \(\frac { 1 }{ 10 } \) + 3 × \(\frac { 1 }{ 100 } \) = 956.03
(v) \(\frac { 6 }{ 10 } \) + \(\frac { 3 }{ 100 } \) + \(\frac { 1 }{ 1000 } \) = 6 × \(\frac { 1 }{ 10 } \) + 3 × \(\frac { 1 }{ 100 } \) = 0.631

(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) \(\frac { 4 }{ 5 } \) = \(\frac{4 \times 2}{5 \times 2}\) = \(\frac { 8 }{ 10 } \) = 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

(i) 2.5 = 2 + \(\frac { 5 }{ 10 } \) = \(\frac { 25 }{ 10 } \)
(ii) 6.4 = 6 + \(\frac { 4 }{ 10 } \) = \(\frac { 64 }{ 10 } \)
(iii) 0.75 = 0 + \(\frac { 7 }{ 10 } \) + \(\frac { 5 }{ 100 } \) = \(\frac { 70+5 }{ 100 } \) = \(\frac { 75 }{ 100 } \)

(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

(iv) 3.049
Hint: = 3 × 1 + \(\frac { 0 }{ 10 } \) + \(\frac { 4 }{ 100 } \) + \(\frac { 9 }{ 1000 } \) = 3.049

(iii) \(\frac { 7 }{ 20 } \)
Hint: 0.35 = \(\frac { 35 }{ 100 } \) = \(\frac{35 \div 5}{100 \div 5}\) = \(\frac { 7 }{ 20 } \)
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(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

(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

(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

(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

(i) 1.7
We know that 1.7 is more than 1, but less than 2.
There are one ones and 7 tenths in it. Divide the unit length between 1 and 2 on the number line into 10 equal parts and take 7 parts which represents 1.7 = 1 + 0.7

(ii) 0.3
We know that 0.3 is more than 0, but less than 1.
There are 3 tenths in it. Divide the unit lenght between 0 and 1 on the number line into 10 equal parts and take 3 parts, which represent 0.3.

(iii) 2.1
We knowthat 2.1 is more than 2 and less than 3.
There are 2 ones and 1 tenths in it.
Divide the unit length between 2 and 3 into 10 equal parts and take 1 part, which represemt 2.1 = 2 + 0.1

(i) 2.3, 3.2
Comparing the whole number parts of 2.3 and 3.2 we get 3 > 2.
3.2 > 2.3 – Greater number is 3.2
(ii) 5.6, 6.5
Comparing the whole number parts of 5.6 and 6.5, we get 6 > 5.
6.5 > 5.6 – Greater number is 6.5
(iii) 1.2, 2.1
Comparing the whole number parts of 1.2 and 2.1, we get 2 > 1.
2.1 > 1.2 – Greater number is 2.1

(i) 25.3, 25.03
The whole number parts of both the numbers are equal.
∴ Comparing the digits at tenths place we get 0 < 3.
∴ 25.03 < 25.3 – Smaller number 25.03
(ii) 7.01,7.3
The whole number parts of both the numbers are equal.
Comparing the digits at tenths place we get 0 < 3.
∴ 7.01 < 7.3 – Smaller number is 7.01.
(iii) 5.6, 6.05
Comparing the whole number parts, we get 5 < 6.
∴ 5.6 < 6.05 – Smaller number is 5.6

Objective Question

(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

(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 ∴ 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.
∴ Comparing the thousandths place, we get 5 > 4.
23.915 > 23.914 ∴ 23.915 is greater.

The winner is one who took less time for swimming 25 m.
Comparing the time taken by A, B, C, D, E the whole number part is equal for all participants.
Comparing digit in tenths place we get 6 < 7.
∴ 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. ∴ C is the winner.

(i) 23.4 = \(\frac { 234 }{ 10 } \) = \(\frac{234 \div 2}{10 \div 2}\) = \(\frac { 117 }{ 5 } \)
(ii) 46.301 = \(\frac { 46301 }{ 1000 } \)

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

Boys = 26; Girls = 24; Total = 50
Fraction of boys = \(\frac { 26 }{ 50 } \) = \(\frac{26 \times 2}{50 \times 2}\) = \(\frac { 52 }{ 100 } \) = 0.52
Fraction of girls = \(\frac { 24 }{ 50 } \) = \(\frac{24 \times 2}{50 \times 2}\) = \(\frac { 48 }{ 100 } \) = 0.48
Challenge Problems

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
(ii) 147 rupees 70 paise = 147 rupees + \(\frac { 70 }{ 100 } \) rupees
= 147 rupees + 0.70 rupees = ₹ 147.70

100 cm = 1 m; 1 cm = \(\frac { 1 }{ 100 } \) m
(i) 1328 cm = \(\frac { 1328 }{ 100 } \) m = 13.28 m
(ii) 419 cm = \(\frac { 419 }{ 100 } \) m = 4.19 m

(i) 8 m 30 cm in metres
8 m + \(\frac { 30 }{ 100 } \) m = 8 m + 0.30 m = 8.30 m
(ii) 24 km 200 m in kilometres
24 km + \(\frac { 200 }{ 1000 } \) km = 24 km + 0.200 km = 24.200 km

(i) \(\frac { 23 }{ 10000 } \) = 0.0023
(ii) \(\frac { 421 }{ 100 } \) = 4.21
(iii) \(\frac { 37 }{ 10 } \) = 3.7

(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 = \(\frac { 5 }{ 1000 } \) = \(\frac{5 \div 5}{10000 \div 5}\) = \(\frac { 1 }{ 2000 } \)

0.07 lies between 0.0 and 0.1
The unit space between 0 and 0.1 is divided into 10 equal parts and 7th 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 7th part is taken.

(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.

Given measures are 1 km and \(\frac { 9 }{ 10 } \) km. i.e., 1 km and 0.9 km.
Difference = 1.0 – 0.9 = 0.1 km.
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