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Find the characteristic of logarithm of following numbers :(i) 1270(ii) 20.125(iii) 7.985(iv) 431.5(v) 0.02(vi) 0.02539(vii) 70(viii) 0.000287(ix) 0.005(x) 0.00003208(xi) 0.000485(xii) 0.007(xiii) 0.0005309 |
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Answer» (i) Number 1270 is 4 digit number. So, characteristic of its logarithm will be 4 – 1 = 3. (ii) In 20.125, integral part is 20 which contains 2 digit. So, characteristic of its logarithm will be 2 – 1 = 1. (iii) In 7.985, integral part is 7 which contains 1 digit. So, characteristic of its logarithm will be 1 – 1 = 0. (iv) In 431.5, integral part is 431 which contains 3 digit. So, characteristic of its logarithm will be 3 – 1 = 2. (v) In 0.02, there are 1 zero between decimal point and first significant digit. So, characteristic of its logarithm will be – (1 + 1) = – 2 or \(\bar{2}\) . (vi) In 0.02539, there are zero between decimal point and first significant digit. So, characteristic of its logarithm will be – (1 + 1) = – 2 or \(\bar{2}\). (vii) Number 70 is 2 digit number. So, characteristic of its logarithm will be 2 – 1 = 1. (viii) In 0.000287, there are 3 zero between decimal point and first significant digit. So, characteristic of its logarithm will be -(3 + 1) = -4 or \(\bar{4}\). (ix) In 0.005, there are 2 zero between decimal point and first significant digit. So, characteristic of its logarithm will be – (2 + 1) = – 3 or \(\bar{3}\). (x) In 0.00003208, there are 4 zero between decimal point and first significant digit. So, characteristic of its logarithm will be – (4 + 1) = – 5 or \(\bar{5}\) . (xi) In 0.000485, there are 3 zero between decimal point and first significant digit. So, characteristic of its logarithm will be – (3 + 1) = -4 or \(\bar{4}\). (xii) In 0.007, there are 2 zero between decimal point and first significant digit. So, characteristic of its logarithm will be – (2 + 1) = – 3 or \(\bar{3}\). (xiii) In 0.0005309, there are 3 zero between decimal point and first significant digit. So, characteristic of its logarithm will be – (3 + 1 ) = – 4 or \(\bar{4}\). |
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