## DECIMALS

**EXERCISE – 8.1**

**EX 8.1 QUESTION 1.**

**Write the following as numbers in the given table.**

**Solution:**

Rows | Hundreds | Tens | Ones | Tenths |

a | 0 | 3 | 1 | 2 |

b | 1 | 1 | 0 | 4 |

**EX 8.1 QUESTION 2.**

**Write the following decimals in the place value table.**

**(a) 19.4**

**(b) 0.3**

**(c) 10.6**

**(d) 205.9**

**Solutions:**

Hundreds | Tens | Ones | Tenths | |

19.4 | 0 | 1 | 9 | 4 |

0.3 | 0 | 0 | 0 | 3 |

10.6 | 0 | 1 | 0 | 6 |

205.9 | 2 | 0 | 5 | 9 |

**EX 8.1 QUESTION 3.**

** Write each of the following as decimals:**

**(a) Seven-tenths**

**(b) Two tens and nine-tenths**

**(c) Fourteen point six**

**(d) One hundred and two ones**

**(e) Six hundred point eight**

**Solutions:**

(a) Seven-tenths = 7 / 10 = 0.7

(b) Two tens and nine-tenths = 20 + 9 / 10 = 20.9

(c) Fourteen point six = 14.6

(d) One hundred and two ones =100 + 2 = 102.0

(e) Six hundred point eight = 600.8

**EX 8.1 QUESTION 4.**

** Write each of the following as decimals:**

**(a) 5 / 10**

**(b) 3 + 7 / 10**

**(c) 200 + 60 + 5 + 1 / 10**

**(d) 70 + 8 / 10**

**(e) 88 / 10**

**(f) **

**(g) 3 / 2**

**(h) 2 / 5**

**(i) 12 / 5**

**(j) **

**(k) **

**Solutions:**

**(a) **5 / 10 = 0.5

(b) 3 + 7 / 10 = 3 + 0.7

= 3.7

(c) 200 + 60 + 5 + 1 / 10 = 265 + 0.1

= 265.1

(d) 70 + 8 / 10 = 70 + 0.8

= 70.8

(e) 88 / 10 = 80 / 10 + 8 / 10

= 8 + 0.8

= 8.8

(f)

(g) 3 / 2 = (2 + 1) / 2

= 2 / 2 + 1 / 2

= 1 + 0.5

= 1.5

(h) 2 / 5 = 0.4

(i) 12 / 5 = (10 + 2) / 5

= 10 / 5 + 2 / 5

= 2 + 0.4

= 2.4

(j)

(k)

**EX 8.1 QUESTION 5.**

**Write the following decimals as fractions. Reduce the fraction to lowest form.**

**(a) 0.6**

**(b) 2.5**

**(c) 1.0**

**(d) 3.8**

**(e) 13.7**

**(f) 21.2**

**(g) 6.4**

**Solutions:**

**(a) **0.6 = 6 / 10

= 3 / 5

(b) 2.5 = 25 / 10

= 5 / 2

(c) 1.0 = 1

= 1

(d) 3.8 = 38 / 10

= 19 / 5

(e) 13. 7 = 137 / 10

(f) 21.2 = 212 / 10

= 106 / 5

(g) 6.4 = 64 / 10

= 32 / 5

**EX 8.1 QUESTION 6.**

**Express the following as cm using decimals.**

**(a) 2 mm**

**(b) 30 mm**

**(c) 116 mm**

**(d) 4 cm 2 mm**

**(e) 162 mm**

**(f) 83 mm**

**Solutions:**

We know that

1 cm = 10 mm

1 mm = 1 / 10 cm

(a) 2 mm = 2 / 10 cm

= 0.2 cm

(b) 30 mm = 30 / 10 cm

= 3.0 cm

(c) 116 mm = 116 / 10 cm

= 11.6 cm

(d) 4 cm 2 mm = [(4 + 2 / 10)] cm

= 4.2 cm

(e) 162 mm = 162 / 10 cm

= 16.2 cm

(f) 83 mm = 83 / 10 cm

= 8.3 cm

**EX 8.1 QUESTION 7.**

**Between which two whole numbers on the number line are the given numbers lie? Which of these whole numbers is nearer the number?**

**(a) 0.8**

**(b) 5.1**

**(c) 2.6**

**(d) 6.4**

**(e) 9.1**

**(f) 4.9**

**Solution:**

(a) 0.8 lies between 0 and 1.

(a) 5.1 lies between 5 and 6.

(b) 2.6 lies between 2 and 3.

(c) 6.4 lies between 6 and 7.

(d) 9.1 lies between 9 and 10.

(e) 4.9 lies between 4 and 5.

**EX 8.1 QUESTION 8.**

**Show the following numbers on the number line.**

**(a) 0.2**

**(b) 1.9**

**(c) 1.1**

**(d) 2.5**

**Solution:**

**EX 8.1 QUESTION 9.**

**Write the decimal number represented by the points A, B, C, D on the given number line.**

**Solution:**

Point A represents 0.8

Point B represents 1.3

Point C represents 2.2

Point D represents 2.9

**EX 8.1 QUESTION 10.**

**(a) The length of Ramesh’s notebook is 9 cm 5mm. What will be its length in cm?**

**(b) The length of a young gram plant is 65 mm. Express its length in cm.**

**Solution:**

** **The length of Ramesh notebook is 9 cm 5 mm

The length in cm is [(9 + 5 / 10)] cm

= 9.5 cm

(b) The length of a gram plant is 65 mm

Hence, the length in cm is 65 / 10

= 6.5 cm