What is the difference between 7 hr 5 min and 6.65 hrs?

Answer 1

1 hr = 60 min

→ 6.65 hrs = 6 hr + 0.65 x 60 min

= 6 hr 39 min

→ difference between 7 hr 5 min (7:05) and 6 hr 39 min (6:39) is:

7:05 - 6:39 = 0:26

= 26 minutes.

I am aware that some people, incorrectly, use the decimal point to separate the hours and minutes of a time.

Time uses sexagesimal (base 60) numbers where each digit can represent the equivalent of the decimal numbers 0-59. Unlike hexadecimal (base 16) numbers, where each digit only has to represent the decimal numbers 0-15 so that the "extra" 6 decimal numbers 10-15 are represented using the letters A-F (or a-f) giving each digit a single character, sexagesimal digits have an additional 50 digits. As a result, sexagesimal digits are written using decimal numbers and each digit is separated by a colon.

For example 1:55:8 in sexagesimal represents the number 1 x 60^2 + 55 x 60 + 8 = 6908 in decimal.

Sexagesimal is (now in the West) only used for time (in hours/minutes/seconds) and measuring angles (in degrees/minutes/seconds - though the separators in this case are unit marks after the digits: degreeso minutes' seconds'', eg 50o 25' 20'' though this can be written as a decimal by adding the fractions together 50 + 25/60 + 20/3600 degrees = 5019/45o ≈ 50.422o).

When dealing with time the colons can also be replaced by unit marks after the digits: H hours M minutes S seconds (or some abbreviation of the units), with any zero digit being dropped with its unit mark, eg 4:0:25 is 4 hours 0 minutes 25 seconds which can be written 4 hours 25 seconds.

However, as we're not really used to sexagesimal numbers, and see each digit as a decimal number, there can be a tendency to for the last digit to include a decimal (fractional) part (of 60). Thus 6.65 represents 6 and (.65 x 60) = 639/60 = 6:39 which depending upon the unit of the whole number could be 6.65 hr = 6 hr 39 min, 6.65 min = 6 min 39 sec, 6.65 sec = 6.65 or 639/60 sec (as we don't use a unit for any smaller time). It is this "misuse" of sexagesimal digits that can cause the confusion if the decimal point (.) is used to separate sexagesimal numbers; thus the colon (:) should always be used.

Another inconsistency with proper sexagesimal numbers is that we also allow the first digit to exceed 59, eg 70 secs = 1 min 10 secs (or 1:10 min), 75 min = 1 hr 15 min (or 1:15 hr) (but this is often used to make calculating with time (slightly) easier, just like mixed numbers are converted to improper fractions to make calculation easier; converting a time of hours and minutes to minutes, calculating with that and converting the result back to hours minutes [seconds] can be easier).

If other digits exceed 59, they should be corrected by subtracting multiples of 60 until they in the range 0-59 and the number of multiples added to the preceding digit (with the same correction if necessary), eg:

6:65 hr = 6 hr 65 min

= 6 hr 60 + 5 min

= 6 + 1 hr 5 min

= 7 hr 5 min

= 7:5 (or 7:05) hr

6:59:121 hr = 6 hr 59 min 123 sec

= 6 hr 59 min 2 x 60 + 3 sec

= 6 hr 59 + 2 min 3 sec

= 6 hr 61 min 3 sec

= 6 hr 1 x 60 + 1 min 3 sec

= 6 + 1 hr 1 min 3 sec

= 7 hr 1 min 3 sec

= 7:1:3 (or 7:01:03) hr