Question

If ${\log }_{10}A=\alpha +\beta$, where $\alpha$ is an integer and $\beta \in [0,1)$, then the correct statement(s) among the following is/are

• A. If $\alpha +\beta =8.65$, then characteristic is $8$
• B. If $\alpha +\beta =-9.63$, then mantissa is $0.37$
• C. If $\alpha +\beta =3.46$, then the number of digits in $A$ is $4$
• D. If $\alpha =4$, then the possible number of integral values of $A$ is $89999$

Answer 1

Answer: (A), (B), (C)

If $\alpha +\beta =3.46$, then the number of digits in $A$ is $4$

If $\alpha +\beta =8.65$
$8.65=8+0.65$
Characteristic is $8$

If $\alpha +\beta =-9.63$
$-9.63=-10+0.37$
Mantissa is $0.37$

If $\alpha +\beta =3.46$
Characteristic is $3$
$\therefore A$ is a $4$ digit number.

If $\alpha =4$
Characteristic is $4$
So, $A$ is a $5$ digit number.
Therefore, $A\in [10000,100000)$
Hence, the possible number of integral values of $A$ is $90000$