If F13 = "no", then F13>0.01 returns TRUE. In fact, any string would be considered greater than any number.
So, your formula is =F10*TRUE. Since TRUE is calculated as a 1 and FALSE is calculated as a 0, your formula =F10*("no">0.01) will return =F10*1, or just F10.
If F13 has a value, then your formula =F10*(F13>0.01) will either return 0(if F13 <= 0.01) or F10 (if F13 > 0.01).