Convert 10.213 (213 repeating decimal) into a fraction. Please show all steps of how to do this?

Write down the number (call it x):
x = 10.213213213...

Since you have a repeat of 3 decimals, you want to multiply both sides by 10^3 = 1000:
1000x = 10213.213213213...

Now subtract the two equations:
1000x = 10213.213213213...
...... x = ..... 10.213213213...
---------- . ------------
999x = 10203

Divide both sides by 999:
x = 10203/999

Reduce that fraction by dividing top and bottom by 3:
x = 3401/333

If they want a mixed number, divide and note the remainder:
10 71/333

Now that you have seen it the long way, the shortcut is to just write the repeating portion over the same number of nines.
... ___
10.213

= 10 213/999

Answer:
10 71/333