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

For 5/8: 5 ÷ 8 = 0.625
For 1/4: 1 ÷ 4 = 0.25
For 3/8: 3 ÷ 8 = 0.375
For 2/3: 2 ÷ 3 = 0.666666... (recurring)
For 6/7: 6 ÷ 7 = 0.857142857... (recurring)

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

0.25 < 0.375 < 0.625 < 0.666666... < 0.857142857...