Page 96 - Start Up Mathematics_7

4. Simplify and express each of the following in exponential form:
3
4
2
2 × 3 × 4 3 × 7 × 11 8
4
7
4
2 3
(a) (b) [(5 ) × 5 ] ÷ 5 (c) 25 ÷ 5 3 (d)
3 × 32 21 × 11 3
3 7
0
0
0
0
0
0
(e) (f) 2 + 3 + 4 (g) 2 × 3 × 4 (h) (3° + 2°) × 5°
4
3 × 3 3
8 3
8
5
2 × a 5 a 5 4 × a b
3
(i) (j) × a 8 (k) (l) (2 × 2) 2
3
5 2
5
4 × a 3 a 3 4 × a b
5. Say true of false and justify your answer.
3
3
5
2
0
2
11
11
(a) 10 × 10 = 100 (b) 2 > 5 (c) 2 × 3 = 6 (d) 3 = (1000) 0
6. Find the number from each of the following expanded forms:
3
1
4
2
(a) 8 × 10 + 6 × 10 + 0 × 10 + 4 × 10 + 5 × 10 0
5
3
2
(b) 4 × 10 + 5 × 10 + 3 × 10 + 2 × 10 0
2
4
(c) 3 × 10 + 7 × 10 + 5 × 10 0
2
5
(d) 9 × 10 + 2 × 10 + 3 × 10 1
Exemplar Problems
1. If 2 1998 – 2 1997 – 2 1996 + 2 1995 = k.2 1995 , then the value of k is:
(a) 1 (b) 2 (c) 3 (d) 4
2. Which of the following has the largest value?
1 1 1
(a) 0.0001 (b) (c) (d) ÷ 0.1
10,000 10 6 10 6
4
2
3. 4 is greater than 2 . (True/False)
4.  4  5 ×  5  5 =  4 + 5  5 (True/False)

 

 
 3   7   3 7 
5. Arrange in descending order:
3 5
2
3
2
2 3
0
2 2 + 3 , (2 ) , 2 × 2 , 3 2 , 3 × 3 , 2 × 5 2
6. Simplify and express each of the following in exponential form:
 a   6 × 10  2 25
6
5
(a)   × a × a 0 (b)  3  ×
2
 a   2 × 5  27
4
n
n
7. If 2 n + 2 – 2 n + 1 + 2 = c × 2 , find the value of c.
8
8. The speed of light in vacuum is 3 × 10 m/s. Sunlight takes about 8 min to reach the earth.
Express distance of sun from the earth in standard form.
3 5 1
9. A student said that is same as . What mistake has the student made?
9 5 3
10. A googol is the number 1 followed by 100 zeros.
(a) How is a googol written as a power?
(b) How is a googol times a googol written as a power?
5
3
11. By what number should (–4) be divided so that the quotient is equal to (–4) ?
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