##### Question 1:

Find the multiplicative inverse of the following:

(i) 2^{–4} (ii) 10^{–5} (iii) 7^{–2}

(iv) 5^{–3} (v) 10^{ –100}

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##### Question 2:

Expand the following numbers using exponents:

(i) 1025.63 (ii) 1256.249.

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##### Question 3:

Simplify and write in exponential form:

(i) (–2)^{–3} × (–2)^{–4} (ii) p^{3} × p^{–10}

(iii) 3^{2} × 3^{–5} × 3^{6}

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##### Question 4:

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##### Question 5:

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##### Question 6:

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##### Question 7:

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##### Question 8:

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##### Question 9:

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##### Question 10:

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##### Question 11:

Write the following numbers in standard form:

(i) 0.000000564 (ii) 0.0000021

(iii) 21600000 (iv) 15240000

##### Answer:

(i) 0.000000564

Let decimal to be moved 7 places to the right.

$\therefore $ 0.000000564 = 5.64 × 10^{–7}

(ii) 0.0000021

Let decimal to be moved 6 places to the right:

$\therefore $ 0.0000021= 2.1 × 10^{–6}

(iii) 21600000

Let decimal to be moved 7 places to the left.

$\therefore $ 21600000 = 2.16 × 10^{7}

(iv) 15240000

Let decimal to be moved 7 places to the left.

$\therefore $ 15240000 = 1.524 × 10^{7}

##### Question 12:

Express the following numbers in standard form:

(i) 0.0000000000085 (ii) 0.00000000000942

(iii) 6020000000000000 (iv) 0.00000000837

(v) 31860000000

##### Answer:

(i) 0.0000000000085

Let the decimal to be moved 12 places to
the right.

$\therefore $ 0.0000000000085 = 8.5 × 10^{–12}

(ii) 0.00000000000942

Let the decimal to be moved 12 places to
the right.

$\therefore $ 0.00000000000942 = 9.42 × 10^{–12}

(iii) 6020000000000000

Let the decimal to be moved 15 places to
the left.

$\therefore $ 6020000000000000 = 6.02 × 10^{15}

(iv) 0.00000000837

Let the decimal to be moved 9 places to the
right.

$\therefore $ 0.00000000837 = 8.37 × 10^{–9}

(v) 31860000000

Let the decimal to be moved 10 places to
the left.

$\therefore $31860000000 = 3.186 × 10^{10}

##### Question 13:

Express the following numbers in usual form:

(i) 3.02 × 10^{–6} (ii) 4.5 × 10^{4}

(iii) 3 × 10^{–8} (iv) 1.0001 × 10^{9}

(v) 5.8 × 10^{12} (vi) 3.61492 × 10^{6}

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##### Question 14:

Express the number appearing in the following statements in standard form:

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##### Question 15:

In a stack there are 5 books each of thickness 20 mm and 5 paper sheets each of thickness 0.016 mm. What is the total thickness of the stack ?

##### Answer:

Thickness of 1 book = 20 mm

$\therefore $ Thickness of 5 books = 20 × 5 = 100 mm

Thickness of 1 paper sheet = 0.016 mm

Thickness of 5 paper sheets = (0.016 × 5) m

= 0.08 mm

$\therefore $ Total thickness of stack

= Thickness of books +

Thickness of sheets

= 100 mm + 0.08 mm

= 100.08 mm

= 1.0008 × 10^{2} mm