Time
Section: Measurement | Syllabus: Cambridge Primary Mathematics (0845)
Converting Time Intervals: Decimal and Mixed Units
A time interval can be written either as a decimal number of hours (or minutes) or as mixed units combining two measures, such as hours and minutes. Converting between the two works just like converting a decimal into its whole and fractional parts - except here, the fractional part is out of 60, not 100, since there are 60 minutes in an hour and 60 seconds in a minute.
- To convert a decimal number of hours to hours and minutes: keep the whole number of hours, then multiply the decimal part by 60 to find the minutes
- To convert hours and minutes to a decimal number of hours: keep the whole number of hours, then divide the minutes by 60 to find the decimal part
- The same method works for minutes and seconds, since there are also 60 seconds in a minute
0.5 hours is half of 60 minutes, which is 30 minutes - the decimal part always scales against 60, not 100
Worked Example: Decimal Hours to Hours and Minutes
- Question: Convert 2.5 hours to hours and minutes.
- Step 1: The whole number part is 2 hours
- Step 2: Multiply the decimal part by 60: 0.5 × 60 = 30
- Answer: 2 hours 30 minutes
Worked Example: Hours and Minutes to Decimal Hours
- Question: Convert 3 hours 45 minutes to a decimal number of hours.
- Step 1: The whole number part is 3 hours
- Step 2: Divide the minutes by 60: 45 ÷ 60 = 0.75
- Answer: 3.75 hours
Common Mistakes
MistakeTreating the decimal part of an hour as if it were out of 100, e.g. thinking 2.5 hours = 2 hours 50 minutes
Fixan hour splits into 60 minutes, not 100 - multiply the decimal part by 60: 0.5 × 60 = 30, so 2.5 hours = 2 hours 30 minutes
MistakeWriting the minutes straight into the decimal digits, e.g. thinking 3 hours 45 minutes = 3.45 hours
Fixthe minutes must be divided by 60 first: 45 ÷ 60 = 0.75, so 3 hours 45 minutes = 3.75 hours, not 3.45
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