I used to do it this way in highschool, but could never remember if it was divide by or multiply by 3.6
Instead I now do it as you have shown, except it all goes in the same expression.
10 km/h * 1000 m/km * 1h/3600s = 2.778 m/s
No need for the extra steps. Slap it all in the same expression and put it in the calculator (being careful to check that the units cancel as intended)