Write the numbers in scientific notation and perform the operations. $\frac { 0.00000184 } { 0.0004 }$ Give the answer in scientific notation and in standard notation.
A) $4.6 \times 10 ^ { - 4 } , 0.00046$
B) $0.46 \times 10 ^ { - 3 } , 0.00046$
C) $0.46 \times 10 ^ { - 2 } , 0.0046$
D) $4.6 \times 10 ^ { - 2 } , 0.046$
E) $4.6 \times 10 ^ { - 3 } , 0.0046$

Question

Quizplus · Accepted Answer

To convert both numbers to scientific notation, we move the decimal point until there is only one non-zero digit to the left of the decimal point. For the numerator, we move the decimal point 6 places to the right, resulting in $1.84	imes 10^{-6}$. For the denominator, we move the decimal point 3 places to the right, resulting in $4	imes 10^{-4}$.

To divide, we subtract the exponent of the denominator from the exponent of the numerator: \begin{align*}
1.84	imes 10^{-6} \div 4	imes 10^{-4} &= 1.84	imes 10^{-6-(-4)} \
&= 1.84	imes 10^{-6+4} \
&= 1.84	imes 10^{-2} \
&= 0.0184\quad (	ext{in standard notation})
\end{align*} The only answer choice that matches this result is E.

Write the Numbers in Scientific Notation and Perform the Operations 0.000001840.0004\frac { 0.00000184 } { 0.0004 }0.00040.00000184​

Write the Numbers in Scientific Notation and Perform the Operations $\frac { 0.00000184 } { 0.0004 }$