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Question 1: Find the value of:
Solution:
Question 2: Simplify:
Solution:
Thuss,
Question 3: Find the value of m when
Solution: We have
Since base is same on both sides, then their exponents are same.
∴ m – 5 = 3
⇒ m = 3 + 5 = 8
Thus, the required value of m is 8.
Question 4: Simplify:
Solution:
Question 5: Write the following in standard form:
(i) 0.000000456 and (ii) 34500000.
Solution: We have
Thus, 0.000000456 = 4.56 * 10^{–7}
(ii) 34500000 = 345 * 100000
= 3.45 * 100 * 100000
= 3.45 * 10^{2} * 10^{5} = 3.45 * 10^{2+5}
= 3.45 * 107
Thus, 34500000 = 3.45 * 10^{7}
Question 6: Express 2.0001 * 10^{9} in usual form.
Solution: We have
= 20001 * 100000
= 2000100000
Thus, 2.0001 * 10^{9} = 2000100000
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