Final answer:
To find the first five digits after the decimal point when 0.372 (with the 2 recurring) is written out in full, multiply 0.372 by 10,000 to get 3,720. Subtract 372 from 3,720 to get 3,348. Divide 3,348 by 9 to get 372 with a remainder of 204, and add a repeating bar over the remainder to get the final answer 0.3722042.
Step-by-step explanation:
When 0.372 is written out in full, the 2 is recurring. To find the first five digits after the decimal point, we can multiply 0.372 by 10,000 (since we want five decimal places) to get 3,720. Then, we subtract 372 from 3,720 to get 3,348. Next, we divide 3,348 by 9 (since 0.372 is equivalent to 372/1000 = 372/999) to get 372 with a remainder of 204. Finally, we add a repeating bar over the remainder to denote the recurring digit, giving us the answer 0.3722042.