Final answer:
The fraction of a clockwise revolution the hour hand turns through depends on the hours it moves. From 3 to 9, it's ½ of a revolution; from 4 to 7, it's ⅔; from 7 to 10, it's ⅔; from 12 to 9, it's ⅔; and from 1 to 10, it's ¾ of a revolution. When starting at given positions and making fractional revolutions, the hand stops at new positions, and when rotating from east, the final direction faced changes accordingly.
Step-by-step explanation:
To determine what fraction of a clockwise revolution the hour hand of a clock turns through for the different specified times, we consider that a full revolution is 360 degrees, which corresponds to 12 hours on a clock. Therefore, each hour on the clock represents 30 degrees (360 degrees divided by 12 hours).
- (a) From 3 to 9, the hour hand moves through 6 hours or 180 degrees, which is ½ of a revolution.
- (b) From 4 to 7, the hour hand moves through 3 hours or 90 degrees, which is ⅔ of a revolution.
- (c) From 7 to 10, the hour hand moves through 3 hours or 90 degrees, which is ⅔ of a revolution.
- (d) From 12 to 9, the hour hand moves through 3 hours or 90 degrees, which is ⅔ of a revolution.
- (e) From 1 to 10, the hour hand moves through 9 hours or 270 degrees, which is ¾ of a revolution.
For the second part of the question, where the clock hand stops after a fractional revolution:
- (a) Starting at 12 and making 1/6 of a revolution clockwise results in the hour hand pointing at 2.
- (b) Starting at 2 and making 1/4 of a revolution clockwise brings the hour hand to 5.
- (c) Starting at 5 and making 3/4 of a revolution clockwise lands the hour hand back at 2.
- (d) Starting at 5 and making 1/3 of a revolution clockwise leads to the hour hand pointing at 9.
If you start facing east and make a rotation:
- (a) A 1/4 revolution clockwise will have you facing south.
- (b) A 1/6 revolution clockwise will position you between south and southeast.