**Samacheer Kalvi Class 7 Maths Term 2 Chapter 1 Number System Solutions**

Welcome to NCTB Solutions. Here with this post we are going to help 7th class students by providing Solutions for Samacheer Kalvi Class 7 Maths Term 2 chapter 1 Number System. Here students can easily find all the solutions for Number System Exercise 1.1, 1.2, 1.3, 1.4 and 1.5. Also here our Expert Maths Teacher’s solved all the problems with easily understandable methods with proper guidance so that all the students can understand easily. Here in this post students will get chapter 1 solutions. Here all the solutions are based on Tamil Nadu State Board latest syllabus.

**Number System Exercise 1.1 Solutions : **

**Number System Exercise 1.1 Solutions :**

**(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) We know, 1 mm = 1/10 cm

Therefore,

5 mm = 5/10

= 0.5 cm

(ii) We know, 1 mm = 1/10 cm

Therefore,

9 mm = 9/10

= 0.9 cm

(iii) We know, 1 mm = 1/10 cm

Therefore,

42 mm = 42/10

= 4.2 cm

(iv) We know, 1 mm = 1/10 cm

Therefore,

9 mm = 9/10 = 0.9 cm

Thus, 8 cm 9 mm = 8 + 0.9 = 8.9 cm

(v) We know, 1 mm = 1/10 cm

Therefore,

375 mm = 375/10

= 37.5 cm

**(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) We know, 1 cm = 1/100 m

Therefore, 16 cm = 16/100

= 0.16 m

(ii) We know, 1 cm = 1/100 m

Therefore, 7 cm = 7/100

= 0.07 m

(iii) We know, 1 cm = 1/100 m

Therefore, 43 cm = 43/100

= 0.43 m

(iv) We know, 1 cm = 1/100 m

Therefore, 6 cm = 6/100

= 0.06 m

Thus, 6 m 6 cm

= 6 + 0.06

= 6.06 m

(v) We know, 1 cm = 1/100 m

Therefore, 54 cm

= 54/100

= 0.54 m

Thus, 2 m 54 cm

= 2 + 0.54

= 2.54 m

**(4) Expand the following decimal numbers.**

**(i) 37.3**

**(ii) 658.37**

**(iii) 237.6**

**(iv) 5678.358**

**Solution : **

(i) 37.3

= 30 + 7 + 3/10

(ii) 658.37

= 600 + 50 + 8 + 3/10 + 7/100

(iii) 237.6

= 200 + 30 + 7 + 6/10

(iv) 5678.358

= 5000 + 600 + 70 + 8 + 3/10 + 5/100 + 8/1000

**(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) 5 3 6 1

(ii) 2 6 3 2 7 1

(iii) 1 7 3 9

(iv) 9 6 5 7

(v) 4 9 7 2 0 6 8

(i) The place value of 6 in 53.61 is Tenth.

(ii) The place value of 2 in 263.271 is Tenth.

(iii) The place value of 9 in 17.39 is Hundredths.

(iv) The place value of 5 in 9.657 is Hundredths.

(v) The place value of 8 in 4972.068 is Thousandths.

**Objective Type Question Solution : **

**(6) The place value of 3 in 85.073 is** ___.

**(i) tenths**

**(ii) hundredths**

**(iii) thousands**

**(iv) thousandths**

**Solution : **

Correct option → (iv)

The place value of 3 in 85.073 is thousandths.

**(7) To convert grams into kilograms, we have to divide it by**

**(i) 10000**

**(ii) 1000**

**(iii) 100**

**(iv) 10**

**Solution : **

Correct option → (ii)

To convert grams into kilograms, we have to divide it by 1000

**(8) The decimal representation of 30 kg and 43 g is __ kg.**

**(i) 30.43**

**(ii) 30.430**

**(iii) 30.043**

**(iv) 30.0043**

**Solution : **

Correct option → (iii)

The decimal representation of 30 kg and 43 g is 30.043 kg.

**(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**

**Solution : **

Correct option → (ii)

It is equal to 2.64 m.

**Number System Exercise 1.2 Solutions : **

**Number System Exercise 1.2 Solutions :**

**(1) Fill in the following place value table.**

Sr. No. |
Decimal form |
Hundreds(100) |
Tens (10) |
Ones (1) |
Tenths (1/10) |
Hundredths (1/100) |
Thousandths (1/1000) |

1. |
320.157 | 3 | 0 | 1 | 5 | 7 | |

2. |
103.709 | 1 | 0 | 3 | 0 | 9 | |

3. |
4.003 | 4 | 0 | 4 | 0 | ||

4. |
360.805 | 3 | 8 | 0 |

**Solution : **

(1) Tens = 2

(2) Tenths = 7

(3) Hundredths = 0

Thousandths = 3

(4) Tens = 6

Ones = 0

Thousandths = 5

**(2) Write the decimal numbers from the following place value table.**

**Solution : **

Decimal form :

(1) = 801.562

(2) = 932.056

(3) = 47.509

(4) = 503.007

(5) = 680.310

(6) = 109.908

**(3) Write the following decimal numbers in the place value table.**

**(i) 25.178**

**(ii) 0.025**

**(iii) 428.001**

**(iv) 173.178**

**(v) 19.54**

**Solution : **

(i) 25.178

Hundreds = 0

Tens = 2

Ones = 5

Tenths = 1

Hundredths = 7

Thousandths = 8

(ii) 0.025

Hundreds = 0

Tens = 0

Ones = 0

Tenths = 0

Hundredths = 2

Thousandths = 5

(iii) 428.001

Hundreds = 4

Tens = 2

Ones = 8

Tenths = 0

Hundredths = 0

Thousandths = 1

(iv) 173.178

Hundreds = 1

Tens = 7

Ones = 3

Tenths = 1

Hundredths = 7

Thousandths = 8

(v) 19.54

Hundreds = 0

Tens = 1

Ones = 9

Tenths = 5

Hundredths = 4

Thousandths = 0

**(4) Write each of the following as decimal numbers**

**(i) 20 + 1 + 2/10 + 3/100 + 7/1000**

**(ii) 3 + 8/10 + 4/100 + 5/1000**

**(iii) 6 + 0/10 + 0/100 + 9/1000**

**(iv) 900 + 50 + 6 + 3/100**

**(v) 6/10 + 3/100 + 1/1000**

**Solution : **

(i) 20 + 1 + 2/10 + 3/100 + 7/1000

= 21+ 0.2+0.03 + 0.007

= 21.237

(ii) 3 + 8/10 + 4/100 + 5/1000

= 3 + 0.8 + 0.04 + 0.005

= 3.845

(iii) 6 + 0/10 + 0/100 + 9/1000

= 6 + 0.0+ 0.00 + 0.009

= 6.009

(iv) 900 + 50 + 6 + 3/100

= 956 + 0.03

= 956.03

(v) 6/10 + 3/100 + 1/1000

= 0.6 + 0.03 + 0.001

= 0.631

**(5) Convert the following fractions into decimal numbers**

**(i) 3/10**

**(ii) 3 1/2**

**(iii) 3 3/5**

**(iv) 3/2**

**(v) 4/5**

**(vi) 99/100**

**(vii) 3 19/25**

**Solution : **

(i) 3/10

= 0.3

(ii) 3 1/2

= 7/2

= 7×5/2×5

= 35/10

= 3.5

(iii) 3 3/5

= 18/5

= 18×2/5×2

= 36/10

= 3.6

(iv) 3/2

= 3×5/2×5

= 15/10

= 1.5

(v) 4/5

= 4 × 2/5 × 2

= 8/10

= 0.8

(vi) 99/100

= 0.99

(vii) 3 19/25

= 94/25

= 94×4/25×4

= 376/100

= 3.76

**(6) Write the following decimals as fractions.**

**(i) 2.5**

**(ii) 6.4**

**(iii) 0.75**

**Solution : **

(i) 2.5

= 25/10

(ii) 6.4

= 64/10

(iii) 0.75

= 75/100

**(7) Express the following decimals as fractions in lowest form.**

**(i) 2.34**

**(ii) 0.18**

**(iii) 3.56**

**Solution : **

(i) 2.34

= 234/100

= 234 ÷ 2/100 ÷ 2

= 117/50

(ii) 0.18

= 18/100

= 18 ÷ 2 /100 ÷ 2

= 9/50

(iii) 3.56

= 356/100

= 356÷4/100÷4

= 89/25

**Objective Type Question Solutions : **

**(8) 3 + 4/100 + 9/1000 = ?**

**(i) 30.49**

**(ii) 3049**

**(iii) 3.0049**

**(iv) 3.049**

**Solution : **

3 + 4/100 + 9/1000 = 3.049

Hence, alternative (iv) 3.049 is the correct answer to this question.

**(9) 3/5 = ___**

**(i) 0.06**

**(ii) 0.006**

**(iii) 6**

**(iv) 0.6**

**Solution : **

3/5 = 0.6

Thus, the correct option is – (iv)

**(11) The simplest form of 0.35 is**

**(i) 35/1000**

**(ii) 35/10**

**(iii) 7/20**

**(iv) 7/100**

**Solution : **

The simplest form of 0.35 is 7/20

Hence, the correct answer is – (iii)

**Number System Exercise 1.3 Solutions : **

**Number System Exercise 1.3 Solutions :**

**(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) Given numbers 2.08, 2.086.

The whole number parts of the two decimal numbers are equal.

The digits at tenths and hundredths place are also equal.

Now, the digits at Thousandths place are 0 and 6.

Here, 0 < 6

Hence, 2.08 is smaller number than 2.086

(ii) Given numbers 0.99 and 1.9

Comparing the whole number part, we get 0 < 1

Therefore, 0.99 3

Therefore, 3.53 > 3.35

Hence, 3.35 is smaller number than 3.53

(iv) Given numbers 5.05 and 5.50

The whole number parts of the two decimal numbers are equal.

The digits at tenths are 0 and 5

Here, 0 < 5

Therefore, 5.05 0

Therefore, 123.5 > 12.35

Hence, 12.35 is smaller number than 123.5

**(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

Given, numbers 2.35, 2.53, 5.32, 3.52, 3.25

Since, 5.32 > 3.52 > 3.25 > 2.53 > 2.35

Therefore, the ascending order is 2.35, 2.53, 3.25, 3.52 and 5.32.

(ii) 123.45, 123.54, 125.43, 125.34, 125.3

Given numbers 123.45, 123.54, 125.43, 125.34, 125.3

Since, 125.43 > 125.34 > 125.3 > 123.54 > 123.45

Therefore, the ascending order is 123.45,123.54,125.3,125.34 and 125.45

**(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) Given numbers 24.5 and 20.32

The digits at one place are 4 and 0

Here 4 > 0

Therefore, 24.5 > 20.32

Hence, 24.5 is greater number than 20.32

(ii) Given numbers 6.95, 6.59

The digit at one place are equal.

Now, the digit at tenths place are 9 and 5

Here, 9 > 5

Therefore, 6.95 > 6.59

Hence 6.95 is greater than 6.59

(iii) Given numbers 17.3 & 17.8

The whole number parts of the two decimal numbers are equal.

Now, the digit at tenths place are 3 and 8

Here, 3 < 8

Therefore, 17.3 < 17.8

Hence 17.8 is greater than 17.3

(iv) Given numbers 235.42 and 235.48

The whole number parts of the two decimal numbers are equal.

the digit at tenths place are equal.

the digit at hundredths place are 2 & 8

Here, 2 < 8

Therefore, 235.42 < 235.48

Hence, 235.48 is greater than 235.42

(v) Given numbers 0.007 and 0.07

The whole number parts of the two decimal numbers are equal.

the digit at tenths place are equal.

the digit at hundredths place are 0 and 7

Here, 0 < 7

Therefore, 0.007 < 0.07

Hence, 0.07 is greater than 0.007

(vi) Given numbers 4.571 and 4.578

The whole number parts of the two decimal numbers are equal.

the digit at tenths and hundredths place are equal.

the digit at thousandths place are 1 and 8

Here, 1 < 8

Therefore, 4.571 < 4.578

Hence, 4.578 is greater than 4.571

**(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

Given numbers 17.35, 71.53, 51.73, 73.51, 37.51.

Since, 17.35 < 37.51 < 51.73 < 71.53 < 73.51 < 37.51 < 17.35

Therefore, the descending order is 73.51, 71.53, 51.73,

(ii) 456.73, 546.37, 563.47, 745.63 457.71

Given numbers 456.73, 546.37, 563.47, 745.63 457.71

Since, 456.73 < 457.71 < 546.37 < 563.47 < 745.63

Therefore, the descending order is 745.63, 563.47, 546.37, 457.71, 456.73.

**Objective Type Question Solutions : **

**(5) 0.009 is equal to**

**(i) 0.90**

**(ii) 0.090**

**(iii) 0.00900**

**(iv) 0.900**

**Solution : **

Correct option is → (iii)

0.009 is equal to 0.00900

**(6) 37.70** ____** 37.7**

**(i) =**

**(ii) <**

**(iii) >**

**(iv) ≠**

**Solution : **

Correct Option → (ii)

37.70 = 37.7

**(7) 78.56** ____** 78.57**

**(i) <**

**(ii) >**

**(iii) =**

**(iv) ≠**

**Solution : **

Correct option is – (i)

78.56 < 78.57

**Number System Exercise 1.4 Solutions : **

**Number System Exercise 1.4 Solutions :**

**(3) Between which two whole numbers, the following decimal numbers lie?**

**(i) 3.3**

**(ii) 2.5**

**(iii) 0.9**

**Solution : **

(i) 3.3 this decimal number lie between 3 and 4 whole numbers.

(ii) 2.5 this decimal number lie between 2 and 3 whole numbers.

(iii) 0.9 this decimal number lie between 0 and 1 whole numbers.

**(4) Find the greater decimal number in the following.**

**(i) 2.3, 3.2**

**(ii) 5.6, 6.5**

**(iii) 1.2, 2.1**

**Solution : **

(i) Given numbers 2.3, 3.2

Since, 2.3 < 3.2

Therefore, 3.2 is greater than 2.3

(ii) Given numbers 5.6 and 6.5

Since, 5.6 < 6.5

Therefore, 6.5 is greater than 5.6

(iii) Given numbers 1.2 and 2.1

Since, 1.2 < 2.1

Therefore, 2.1 is greater than 1.2

**(5) Find the smaller decimal number in the following.**

**(i) 25.3, 25.03**

**(ii) 7.01, 7.3**

**(iii) 5.6, 6.05**

**Solution : **

(i) Given numbers 25.3, 25.03

Since, 25.3 > 25.03

Therefore, 25.03 is smaller than 25.3

(ii) Given numbers 7.01, 7.3

Since, 7.01 < 7.3

Therefore, 7.01 is smaller than 7.3

(iii) Given numbers 5.6, 6.05

Since, 5.6 < 6.05

Therefore, 5.6 is smaller than 6.05

**Objective Type Question Solutions : **

**(6) Between which two whole numbers 1.7 lie?**

**(i) 2 and 3**

**(ii) 3 and 4**

**(iii) 1 and 2**

**(iv) 1 and 7**

**Solution : **

Correct Option → (iii)

1.7 lie between whole numbers 1 and 2

**(7) The decimal number which lies between 4 and 5 is __**

**(i) 4.5**

**(ii) 2.9**

**(iii) 1.9**

**(iv) 3.5**

**Solution : **

Correct Option → (i)

The decimal 4.5 lies between 4 and 5.

**Number System Exercise 1.5 Solutions : **

**Number System Exercise 1.5 Solutions :**

**(1) Write the following decimal numbers in the place value table.**

**(i) 247.36**

**(ii) 132.105**

**Solution : **

(i) 247.36

Decimal form = 247.36

Hundreds = 2

Tens = 4

Ones = 7

Tenths = 3

Hundredths = 6

Thousandths = 0

(ii) 132.105

Decimal form = 132.105

Hundreds = 1

Tens = 3

Ones = 2

Tenths = 1

Hundredths = 0

Thousandths = 5

**(2) Write each of the following as decimal number**

**(i) 300 + 5 + 7/10 + 9/100 + 2/100**

**(ii) 1000 + 400 + 30 + 2 + 6/10 + 7/100**

**Solution : **

(i) 300 + 5 + 7/10 + 9/100 + 2/100

= 305 + 7/10 + 11/100

= 305 + 70/100 + 11/100

= 305 + 81/100

= 305+0.81

= 305.81

(ii) 1000 + 400 + 30 + 2 + 6/10 + 7/100

= 1432+0.6+0.07

= 1432.67

**(3) Which is greater?**

**(i) 0.888 (or) 0.28**

**(ii) 23.914 (or) 23.915**

**Solution : **

(i) Given numbers are 0.888 and 0.28

The digit of tenths are 8 and 2

Here, 8 > 2

Therefore, 0.888 > 0.28

Hence, 0.888 is greater.

(ii) Given numbers are 23.914 and 23.915

The digit of thousandths are 4 and 5.

Here, 4 < 5

Therefore, 23.914 < 23.915

Hence, 23.915 is greater.

**(4) In a 25 m swimming competition, the time taken by 5 swimmers A, B, C, D and E are 15.7 seconds, 15.68 seconds, 15.6 seconds, 15.74 seconds and 15.67 seconds respectively. Identify the winner.**

**Solution : **

Given, in a 25 m swimming competition,

The time taken by 5 swimmers A, B, C, D and E are 15.7 seconds, 15.68 seconds, 15.6 seconds, 15.74 seconds and 15.67 seconds respectively.

Since, 15.6 < 15.67 < 15.68 < 15.7 < 15.74

Therefore, swimmer C is winner.

**(5) Convert the following decimal numbers into fractions.**

**(i) 23.4**

**(ii) 46.301**

**Solution : **

(i) 23.4

= 234/10

(ii) 46.301

= 46301/1000

**(6) Express the following in kilometres using decimals.**

**(i) 256 m**

**(ii) 4567 m**

**Solution : **

(i) Given, 256 m

We know, 1m = 1/1000 km

256 m = 256/1000 km = 0.256 km

(ii) Given, 4567 m

We know, 1m = 1/1000 km

4567 m = 4567 /1000 km = 4.567 km

**(7) There are 26 boys and 24 girls in a class. Express the fractions of boys and girls as decimal numbers.**

**Solution : **

Given, there are 26 boys and 24 girls in a class

Total = 26 + 24 = 50

Thus, boys,

= 26/50

= 52/100

= 0.52

And Girls,

= 24/50

= 48/100

= 0.48

**Challenge Problem Solutions : **

**(8) Write the following amount using decimals.**

**(i) 809 rupees 99 paise**

**(ii) 147 rupees 70 paise**

**Solution : **

(i) Given, 809 rupees 99 paise

We know, 1 paise = 1/100 rupees

809 rupees 99 paise

= 809 rupees + 99/100 rupees

= 809 + 0.99

= 809.99 rupees

(ii) Given, 147 rupees 70 paise

We know, 1 paise = 1/100 rupees

147 rupees 70 paise

= 147 rupees + 70/100 rupees

= 147+0.70

= 147.70 rupees

**(9) Express the following in metres using decimals.**

**(i) 1328 cm**

**(ii) 419 cm**

**Solution : **

(i) Given, 1428 cm

We know, 1 cm = 1/100 m

1328 cm = 1328/100 m

= 13.28 m

(ii) Given, 419 cm

We know, 1 cm = 1/100 m

419 cm = 419/100 m

= 4.19 m

**(10) Express the following using decimal notation.**

**(i) 8 m 30 cm in metres**

**(ii) 24 km 200 m in kilometres**

**Solution : **

(i) Given, 8 m 30 cm

We know, 1 cm = 1/100 m

8 m 30 cm = 8 m + 30/100 m

= (8 + 0.30)m

= 8.30 m

(ii) Given, 24 km 200 m

We know, 1m = 1/1000m

24 km 200 m = 24 km + 200/1000 km

= (24 + 0.200) km

= 24.200 km

**(11) Write the following fractions as decimal numbers**

**(i) 23/10000**

**(ii) 421/100**

**(iii) 37/10**

**Solution : **

(i) 23/10000

= 0.0023

(ii) 421/100

= 4.21

(iii) 37/10

= 3.7

**(12) Convert the following decimals into fractions and reduce them to the lowest form.**

**(i) 2.125**

**(ii) 0.0005**

**Solution : **

(i) 2.125 = 2125/1000

= 2125 ÷ 25 /1000 ÷ 25

= 85/40

= 85 ÷ 5/40 ÷ 5

= 17/8

(ii) 0.0005 = 5/10000

= 5 ÷ 5/1000 ÷ 5

= 1/200

**(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.

**(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 this number between 0 to 1

(ii) 3.4 this number between 3 to 4.

(iii) 3.9 this number between 3 to 4.

(iv) 2.7 this number between 2 to 3.

(v) 1.7 this number between 1 to 2.

(vi) 1.3 this number between 1 to 2.

**(16) By how much is 9/10 km less than 1 km. Express the same in decimal form.**

**Solution : **

9/10 km = 0.9 km

Now, 1 km – 0.9 km = 0.1 km

Therefore, 9/10 km is less than 1 km by 0.1 km

**Next Chapter Solution : **