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\ 06-Jan-2025 Bharat Arora Proof-7 Reader’s Sign _______________________ Date __________

Example 7: Write the following in expanded form using exponents of 10.

(a) 425.2394 (b) 76.359898
Solution: (a) 425.2394 = 400 + 20 + 5 + 0.2 + 0.03 + 0.009 + 0.0004
1 1 1 1
3
9
4
= 4 × 100 + 2 × 10 + 5 × 1 + 2 × +× +× +×
10 100 1000 10000
2
0
1
–3
–2
–1
= 4 × 10 + 2 × 10 + 5 × 10 + 2 × 10 + 3 × 10 + 9 × 10 + 4 × 10 –4
(b) 76.359898 = 70 + 6 + 0.3 + 0.05 + 0.009 + 0.0008 + 0.00009 + 0.000008
1 1 1 1
9
8
5
= 7 × 10 + 6 × 1 + 3 × +× +× +× +
10 100 1000 10000
1 1
9 × + 8 ×
100000 1000000
1
–2
–5
–1
0
= 7 × 10 + 6 × 10 + 3 × 10 + 5 × 10 + 9 × 10 + 8 × 10 + 9 × 10 + 8 × 10 –6
–4
–3
Practice Time 11B
1. Find the value of each of the following.
2
–1 3
(a) 2 × (–3) 2 (b) 81 × 3 2 (c) (3 ÷ 3 ) (d) (2 × 3 )
6
3 2
2
–2
–1
0
(e)    11  − 1 (f) 4 × 27 (g) 3 + 3 + 3 1 (h) (6 + 5 ) + (6 – 5 )
0
0
0
0
5 
2. Find the value of
   −   −1 3 8
−3

3
3
8
6
5 2
5
−
0
(a) 7 × 7 ÷ (7 ) (b) 3 × 8 × 4 –2 (c)     (d) 3 × − 3
   2    3
1
−

1
2
–4
2
–3 3
2
–2
–2
(e) (3 ÷ 3 ) (f) (6 × 3 )(6 ÷ 3 ) (g)      − 1 −     − 1
2
3
3. Evaluate the following.      
  5  −3  3 1   1 − 2  1 − 2  − 3
0
–1
–1 0
–1
(a) (2 + 5 + 7 ) (b)   −   (c) (6 + 5 − 1 )× (d)   −   

  9   10 − 2      
7
4
4. Find the reciprocal of the following in the exponential form.
81  −  2 3  3 − 4
(a) (b) (–5) 5 (c)   (d)  
7
256  5   
5. Simplify and express with positive exponents.
4

–1
0
7
–1 –2
–1
0
0
–5
0
(a) (–3) × (–3) –7 (b) (2 × 5 × 7 ) (c) 4 ×   − 7 (d) (2 + 5 + 70 ) ÷ (3 × 7 )
 
5
6. Simplify the following.
5
5
3xy 3 8 × 5 3 25t − 4 3 × 10 × 125
1
−
4
−
−
(a) (b) (c) (d)
3
−
7
×
−
3
18xy 5 2 − 4 5 × 10 t − 8 5 × 6 − 5
7. Express the following in positive exponent only.
1
(
(a) (xy ) (b) a × b × b × c (c) xy) ( xy ) 1
5
–2
2
–1 –2
−2
2
−3 3
  −  9 3  3 4
8. By what number should we multiply     so that the product is equal to  5   ?
−

   2     9 
 5  −3  25 − 2
9. By what number should −   be divided so that the quotient is   4   ?

 2
269 Exponents and Powers