Question

what is the decimal representation of \\(\frac{5}{12}\\)? show your reasoning. submit your work using the tools below. insert image take photo draw graph

Explanation:

Step1: Perform Division

To find the decimal representation of $\frac{5}{12}$, we divide 5 by 12.
We know that $5\div12$. Since 5 is less than 12, we add a decimal point and zeros. So we have $5.0\div12$. 12 goes into 50 four times (because $12\times4 = 48$). Subtract 48 from 50, we get a remainder of 2.

Step2: Continue Division

Bring down a zero to make it 20. 12 goes into 20 once (because $12\times1=12$). Subtract 12 from 20, we get a remainder of 8.

Step3: Continue Division

Bring down a zero to make it 80. 12 goes into 80 six times (because $12\times6 = 72$). Subtract 72 from 80, we get a remainder of 8. Now we see that the remainder 8 repeats, so the decimal will repeat from here.

So putting it all together, $5\div12 = 0.4166\cdots$ or $0.41\overline{6}$.

Answer:

The decimal representation of $\frac{5}{12}$ is $0.41\overline{6}$ (or approximately $0.4167$ if rounded to four decimal places).