**Exponents and Powers**

**1. Write the following numbers in the expanded forms:**

**279404**

**Solution:-**

The expanded form of the number 279404 is,

= (2 × 100000) + (7 × 10000) + (9 × 1000) + (4 × 100) + (0 × 10) + (4 × 1)

Now we can express it using powers of 10 in the exponent form,

= (2 × 10^{5}) + (7 × 10^{4}) + (9 × 10^{3}) + (4 × 10^{2}) + (0 × 10^{1}) + (4 × 10^{0})

**3006194**

**Solution:-**

The expanded form of the number 3006194 is,

= (3 × 1000000) + (0 × 100000) + (0 × 10000) + (6 × 1000) + (1 × 100) + (9 × 10) + 4

Now we can express it using powers of 10 in the exponent form,

= (3 × 10^{6}) + (0 × 10^{5}) + (0 × 10^{4}) + (6 × 10^{3}) + (1 × 10^{2}) + (9 × 10^{1}) + (4 × 10^{0})

**2806196**

**Solution:-**

The expanded form of the number 2806196 is,

= (2 × 1000000) + (8 × 100000) + (0 × 10000) + (6 × 1000) + (1 × 100) + (9 × 10) + 6

Now we can express it using powers of 10 in the exponent form,

= (2 × 10^{6}) + (8 × 10^{5}) + (0 × 10^{4}) + (6 × 10^{3}) + (1 × 10^{2}) + (9 × 10^{1}) + (6 × 10^{0})

**120719**

**Solution:-**

The expanded form of the number 120719 is,

= (1 × 100000) + (2 × 10000) + (0 × 1000) + (7 × 100) + (1 × 10) + (9 × 1)

Now we can express it using powers of 10 in the exponent form,

= (1 × 10^{5}) + (2 × 10^{4}) + (0 × 10^{3}) + (7 × 10^{2}) + (1 × 10^{1}) + (9 × 10^{0})

**20068**

**Solution:-**

The expanded form of the number 20068 is,

= (2 × 10000) + (0 × 1000) + (0 × 100) + (6 × 10) + (8 × 1)

Now we can express it using powers of 10 in the exponent form,

= (2 × 10^{4}) + (0 × 10^{3}) + (0 × 10^{2}) + (6 × 10^{1}) + (8 × 10^{0})

**2. Find the number from each of the following expanded forms:**

**(a) (8 ×10) ^{4} + (6 × 10)^{3} + (0 × 10)^{2} + (4 × 10)^{1} + (5 × 10)^{0}**

**Solution:-**

The expanded form is,

= (8 × 10000) + (6 × 1000) + (0 × 100) + (4 × 10) + (5 × 1)

= 80000 + 6000 + 0 + 40 + 5

= 86045

**(b) (4 ×10) ^{5} + (5 × 10)^{3} + (3 × 10)^{2} + (2 × 10)^{0}**

**Solution:-**

The expanded form is,

= (4 × 100000) + (0 × 10000) + (5 × 1000) + (3 × 100) + (0 × 10) + (2 × 1)

= 400000 + 0 + 5000 + 300 + 0 + 2

= **405302**

**(c) (3 ×10) ^{4} + (7 × 10)^{2} + (5 × 10)^{0}**

**Solution:-**

The expanded form is,

= (3 × 10000) + (0 × 1000) + (7 × 100) + (0 × 10) + (5 × 1)

= 30000 + 0 + 700 + 0 + 5

= **30705**

**(d) (9 ×10) ^{5} + (2 × 10)^{2} + (3 × 10)^{1}**

**Solution:-**

The expanded form is,

= (9 × 100000) + (0 × 10000) + (0 × 1000) + (2 × 100) + (3 × 10) + (0 × 1)

= 900000 + 0 + 0 + 200 + 30 + 0

= **900230**

**3. Express the following numbers in standard form:**

**(i) 5,00,00,000**

**Solution:-**

The standard form of the given number is 5 × 10^{7}

**(ii) 70,00,000**

**Solution:-**

The standard form of the given number is 7 × 10^{6}

**(iii) 3,18,65,00,000**

**Solution:-**

The standard form of the given number is 3.1865 × 10^{9}

**(iv) 3,90,878**

**Solution:-**

The standard form of the given number is 3.90878 × 10^{5}

**(v) 39087.8**

**Solution:-**

The standard form of the given number is 3.90878 × 10^{4}

**(vi) 3908.78**

**Solution:-**

The standard form of the given number is 3.90878 × 10^{3}

**4. Express the number appearing in the following statements in standard form.**

**(a) The distance between Earth and Moon is 384,000,000 m.**

**Solution:-**

The standard form of the number appearing in the given statement is 3.84 × 10^{8}m.

**(b) Speed of light in vacuum is 300,000,000 m/s.**

**Solution:-**

The standard form of the number appearing in the given statement is 3 × 10^{8}m/s.

**(c) Diameter of the Earth is 1,27,56,000 m.**

**Solution:-**

The standard form of the number appearing in the given statement is 1.2756 × 10^{7}m.

**(d) Diameter of the Sun is 1,400,000,000 m.**

**Solution:-**

The standard form of the number appearing in the given statement is 1.4 × 10^{9}m.

**(e) In a galaxy there are on an average 100,000,000,000 stars.**

**Solution:-**

The standard form of the number appearing in the given statement is 1 × 10^{11} stars.

**(f) The universe is estimated to be about 12,000,000,000 years old.**

**Solution:-**

The standard form of the number appearing in the given statement is 1.2 × 10^{10} years old.

**(g) The distance of the Sun from the centre of the Milky Way Galaxy is estimated to be 300,000,000,000,000,000,000 m.**

**Solution:-**

The standard form of the number appearing in the given statement is 3 × 10^{20}m.

**(h) 60,230,000,000,000,000,000,000 molecules are contained in a drop of water weighing 1.8 gm.**

**Solution:-**

The standard form of the number appearing in the given statement is 6.023 × 10^{22} molecules.

**(i) The earth has 1,353,000,000 cubic km of sea water.**

**Solution:-**

The standard form of the number appearing in the given statement is 1.353 × 10^{9} cubic km.

**(j) The population of India was about 1,027,000,000 in March, 2001.**

**Solution:-**

The standard form of the number appearing in the given statement is 1.027 × 10^{9}.