Question

write \\(\frac{42}{11}\\) as a decimal. if necessary, use a bar to indicate which digit or group of digits repeats.

Explanation:

Step1: Divide 42 by 11

To convert the fraction $\frac{42}{11}$ to a decimal, we perform the division: $42 \div 11$.

Step2: Perform the long division

11 goes into 42 three times (since $11\times3 = 33$), with a remainder of $42 - 33 = 9$. We then add a decimal point and a zero, making it 90. 11 goes into 90 eight times (since $11\times8 = 88$), with a remainder of $90 - 88 = 2$. We add another zero, making it 20. 11 goes into 20 once (since $11\times1 = 11$), with a remainder of $20 - 11 = 9$. Now we see that the remainder 9 has appeared before, so the decimal will repeat from here. So $42\div11 = 3.8181\ldots$

Answer:

$3.\overline{81}$