Solving Decimal Division: $0.000033 \div 0.11$

This problem requires us to calculate the result of dividing a small decimal number by another decimal number. We need to find the value of $\frac{0.000033}{0.11}$.

Step-by-Step Calculation

To make the division easier, we can eliminate the decimal in the divisor ($0.11$). We do this by moving the decimal point to the right until the number becomes a whole number. In this case, we move the decimal point two places to the right in $0.11$ to get $11$.

To keep the division problem equivalent, we must perform the same operation on the dividend ($0.000033$). We also move its decimal point two places to the right.

• Original problem: $0.000033 \div 0.11$
• Move decimal 2 places right in the divisor: $0.11 \times 100 = 11$
• Move decimal 2 places right in the dividend: $0.000033 \times 100 = 0.0033$

The problem is now simplified to:

$0.0033 \div 11$

Now, we can perform the division:

When we divide $0.0033$ by $11$, we get:

• $0 \div 11 = 0$
• Bring down the decimal point.
• The next digit is $0$. $0 \div 11 = 0$.
• The next digit is $3$. $3 \div 11 = 0$.
• The next digit is $3$. We now have $33$. $33 \div 11 = 3$.

So, the calculation looks like this:

$ \require{enclose} \begin{array}{r} 0.0003 \\ 11 \enclose{longdiv}{0.0033} \\ \underline{0} \phantom{0000} \\ 0 \phantom{000} \\ \underline{0} \phantom{000} \\ 00 \phantom{00} \\ \underline{00} \phantom{00} \\ 33 \phantom{0} \\ \underline{33} \phantom{0} \\ 0 \end{array} $

Therefore, $0.0033 \div 11 = 0.0003$.

Final Result

The result of the division $0.000033 \div 0.11$ is $0.0003$. This matches one of the given options.