Samacheer Kalvi 7th Maths Solutions Term 2 Chapter 1 Number System Ex 1.1

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Tamilnadu Samacheer Kalvi 7th Maths Solutions Term 2 Chapter 1 Number System 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 cm using decimals.
(i) 5 mm
(ii) 9 mm
(iii) 42 mm
(iv) 8 cm 9 mm
(v) 375 mm
Solution:
(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

Question 3.
Express the following in metres using decimals.
(i) 16 cm
(ii) 7 cm
(iii) 43 cm
(iv) 6 m 6 cm
(v) 2 m 54 cm
Solution:
(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

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 × 10¹ + 7 × 10⁰ + 3 × 10^-1

(ii) 658.37 = 600 + 50 + 8 + \(\frac { 3 }{ 10 } \) + \(\frac { 7 }{ 100 } \)
= 6 × 10² + 5 × 10¹ + 8 × 100 + 3 × 10^-1 + 7 × 10^-2

(iii) 237.6 = 200 + 30 + 7 + \(\frac { 6 }{ 10 } \)
= 2 × 10² + 3 × 10¹ + 7 × 10⁰ + 6 × 10^-1

(iv) 5678.358 = 5000 + 600 + 70 + 8 + \(\frac { 3 }{ 10 } \) + \(\frac { 5 }{ 100 } \) + \(\frac { 8 }{ 1000 } \)
= 5 × 10³ + 6 × 10² + 7 × 10¹ + 8 × 10⁰ + 3 × 10^-1 + 5 × 10^-2 + 8 × 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
Solution:
(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 g = 1 kg; 1 g = \(\frac { 1 }{ 1000 } \) 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 × 10 + 5 × 1 + 0 × \(\frac { 1 }{ 10 } \) + 7 × \(\frac { 1 }{ 100 } \) + 3 × \(\frac { 1 }{ 1000 } \)

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

Question 9.
A cricket pitch is about 264 cm wide. It is equal to _____ m.
(i) 26.4
(ii) 2.64
(iii) 0.264
(iv) 0.0264
Answer:
(ii) 2.64
Hint: 264 cm = \(\frac { 264 }{ 100 } \) m = 2.64 m