calculate the decimal number for each fraction and identify the ascending numerical order of the decimal numbers: 5/8, 1/4, 3/8, 2/3, 6/7

To calculate the decimal number for each fraction, divide the numerator by the denominator:

5/8 = 0.625
1/4 = 0.25
3/8 = 0.375
2/3 = 0.6666 (rounded to 4 decimal places)
6/7 = 0.8571 (rounded to 4 decimal places)

Now, let's identify the ascending numerical order of the decimal numbers:

0.25 < 0.375 < 0.625 < 0.6666 < 0.8571

Therefore, the ascending numerical order of the decimal numbers is: 1/4, 3/8, 5/8, 2/3, 6/7.