Question

Use long division to convert 6 7/20%0D%0A6%0D%0A7%0D%0A20%0D%0A to a decimal.(1 point)%0D%0AResponses%0D%0A%0D%0A0.35%0D%0A0.35%0D%0A%0D%0A6.35%0D%0A6.35%0D%0A%0D%0A6.72%0D%0A6.72%0D%0A%0D%0A6.285714

Answer 1

To convert \(6 \frac{7}{20}\%\) to a decimal using long division, we follow these steps:

1. Convert the mixed number to an improper fraction:
\[
6 \frac{7}{20} = \frac{6 \times 20 + 7}{20} = \frac{120 + 7}{20} = \frac{127}{20}
\]

2. Convert the percentage to a decimal by dividing by 100:
\[
\frac{127}{20} \div 100 = \frac{127}{20} \times \frac{1}{100} = \frac{127}{2000}
\]

3. Perform long division for \(\frac{127}{2000}\):
- Divide 127 by 2000.
- Since 127 is less than 2000, the integer part is 0. Now we consider it as 127.000.
- Now perform the division:
- 2000 into 1270 (the first three decimal places) goes 0 times.
- 2000 into 12700 goes 6 times (since \(2000 \times 6 = 12000\)).
- Subtract \(12000\) from \(12700\) to get 700.
- Bring down the next 0 to make it 7000.
- 2000 into 7000 goes 3 times (since \(2000 \times 3 = 6000\)).
- Subtract \(6000\) from \(7000\) to get 1000.
- Bring down another 0 to make it 10000.
- 2000 into 10000 goes 5 times (since \(2000 \times 5 = 10000\)).
- Subtract \(10000\) from \(10000\) to get 0.

Thus, the division gives us \(0.0635\). This means:
\[
6 \frac{7}{20}\% = 0.0635
\]

Since \(6 \frac{7}{20}\%\) is equivalent to \(6.35%\), it is equal to \(0.0635\) in decimal form.

So, the converted decimal is \(0.0635\), and considering the values you provided, the appropriate choice based on valid options would be:
- None of the provided options are correct since \(0.0635\) is not listed, but the expression \(6.35\%\) simply evaluated is not among them.

Confirming the original question context to clarify that the hundred applies to the original percentages listed, making any provided decimal (like options \(0.35\) or \(6.35\)) incorrect for \(6 \frac{7}{20}\%\), leads us back to basic clarity that:

The answer can't align accurately, while being interpreted checking against visible options listed. If finding the decimal link is preferred for precision, highlighting a reconsideration or correcting context for those options stands justified.