Quantitative Reasoning : Logarithms
How many digits will the number 3200
have if the value of log10
3 = 0.4771?
Choice (3). 96 digits
The logarithm of any number has two components. The characteristic and the mantissa.
Take for example, log10
3, the value of log10
3 = 0.4771.
Here, the 0 in the integral part is known as the characteristic and the value .4771 is known as the mantissa.
The value of log10
30 is 1.4771.
Notice that the value of mantissa remained the same while that of the characteristic changed from 0 to 1.
Given the log of a number, we will be able to find out the number of digits that the original number had by knowing the value of the characteristic.
If the characteristic is '0', then the number is a single digit number
If the characteristic is '1', then the number is a two-digit number
If the characteristic is '5', then the number is a six-digit number
In the given problem, we need to find the number of digits of 3200
If we take log we get log10
3) = 200 (0.4771) = 95.42.
Here, the characteristic is 95. Therefore, the number will have 96 digits.
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