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If characteristic of three numbers a, b ...

If characteristic of three numbers a, b and c and 5, -3 and 2, respectively, then find the maximum number of digits in N = abc.

Text Solution

Verified by Experts

The correct Answer is:
7
According to the given information,
` log a = 5+p`
` log b =- 3+ q`
` log c = 2 + r`
where p,q and r are mantissas.
`:. P,q,r in [0, 1)`
Adding the above equations, we get
` log(abc) = 4 + (p+q+r)`
` (p+q+r) in [0, 3)`
` :. log (abc) in [4, 7)`
`rArr log N in [4, 7)`
` :. ` Maximum possible characteristic of log N = 6
`:. ` Maximum number of digits in `N = 6 +1 = 7`
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