Question

A number is written in scientific notation as $a\times {10}^b$, where a is the maximum possible integer. When it is converted into standard form, the decimal point is moved to the left by $4$ places. Identify the number in its standard form, and what is the value of $b$?

• A. $9.999,b=4$
• B. $9000,b=-4$
• C. $0.0009,b=-4$
• D. $0.9999,b=4$

Answer 1

The correct option is C $0.0009,b=-4$

Detailed step-by-step solution:
$\because a\times {10}^b$ is in scientific notation.
$\because 1\le a<10,$ and $b$ is an integer.
The value of $“a”$ will be $9.0$ as a is the maximum possible integer and less than $10$.

So, the number written in scientific notation will be $9.0\times {10}^b$.
When it is converted into standard form, the decimal point is moved to the left by $4$ places. Hence, the exponent is negative.
$b=-4$
$\Rightarrow 9.0\times {10}^b=9.0\times {10}^{-4}$

So, the number in the standard form is $\mathrm{0.0009.}$

$\Rightarrow 0.0009,b=-4$

➡Option B is correct.