If 1 day was 10 metric hours, 1 metric hour was 10 metric minutes, and 1 metric minute was 10 metric seconds, what time would it really be if your metric clock reads 8: 9: 2? similarly, convert 5: 56: 48 a.m. to metric time. you may assume that each new day starts at midnight.

Step-by-step explanation:

A. From metric time to normal

In normal time,  

1 min = 60 s

   1 h = 60 min = 3600 s

1 day = 24 h      = 1440 min = 86 400 s

A time of 8:9:2 corresponds to 0.892 day.

0.892 day = 0.892 × 86 400 s = 77 069 s

1. Seconds to hours

2. Seconds to minutes

So, 0.892 day = 21 h + 24 min + 29 s

In international notation, the time is 21:24:29 (about 9:24 p.m.).

B. From normal time to metric

In metric time,

    1 h = 0.1 day

1 min = 0.1 h      = 0.01 day

    1 s = 0.1 min = 0.01 h = 0.001 day

So, the hours, minutes and seconds are tenths, hundredths, and thousandths of a day.

1. Convert the time to seconds

5:56:48 = (5 × 3600 + 56 × 60 + 48) s = (18 000 + 3360 + 48) s = 21 408 s

2. Calculate the fraction of a day