A man earned $1.80 per hour for time worked up to 40 hours and 1 ½ as much for all the time worked over 40 hours. The amount of money he earned during one week when he worked 52 hours was:

The man worked 40 regular hours and 12 overtime hours (52-40=12).

For the regular hours, he earned 40*$1.80=$<<40*1.8=72>>72.
For the overtime hours, he earned 12*(1.5*$1.80)=32.4.
Therefore, he earned a total of $72+$32.4=$<<72+32.4=104.4>>104.4. Answer: \boxed{104.4}.

To calculate the amount of money earned during one week when he worked 52 hours, we need to find the earnings for the first 40 hours and the earnings for the remaining 12 hours.

1. Earnings for the first 40 hours:
He earns $1.80 per hour for the first 40 hours, so the total earnings for this period is:
40 hours * $1.80/hour = $<<40*1.80=72>>72

2. Earnings for the remaining 12 hours:
For all the time worked over 40 hours, he earns 1 ½ as much as the regular rate. So, his hourly rate for these 12 hours is 1.5 * $1.80 = $<<1.5*1.80=2.70>>2.70.
Therefore, the total earnings for the additional 12 hours is:
12 hours * $2.70/hour = $<<12*2.70=32.40>>32.40

3. Total earnings for the week:
Adding the earnings for the first 40 hours and the additional 12 hours gives us:
$72 + $32.40 = $<<72+32.40=104.40>>104.40

Therefore, the man earned $104.40 during the week when he worked 52 hours.