Mathematics (Core)Exam code: 0580
Time, Currency and Conversions
Number
Conversions to know
- Time does not use the decimal system, so its conversions have to be learned rather than derived
| Unit | Equals |
|---|---|
| 1 minute | 60 seconds |
| 1 hour | 60 minutes |
| 1 day | 24 hours |
| 1 week | 7 days |
| 1 year | 12 months, taken as 365 days |
- This specification treats a year as 365 days unless a question states otherwise
- Month lengths are needed for date calculations: April, June, September and November have 30 days, February has 28 (29 in a leap year), and the remaining seven have 31
Minutes are not decimals of an hour
- Sixty minutes make an hour, so a part-hour written as a decimal is a fraction of 60, not of 100
- 15 minutes is 0.25 h, 30 minutes is 0.5 h, and 45 minutes is 0.75 h
- Writing 2 hours 30 minutes as 2.30 hours is wrong; it is 2.5 hours
Worked example
Changing a decimal time into hours and minutes
A calculation gives a journey time of 2.458 hours. Write it in hours and minutes, to the nearest minute. Another gives a time of 1427 seconds. Write it in minutes and seconds.
Solution:
- The whole hours stay as they are: 2 hours
- Only the decimal part is a fraction of an hour, so multiply it by 60: 0.458 × 60 = 27.48 minutes
- Round at this last step: the journey takes 2 h 27 min
- Rounding 2.458 to 2.46 first would give 0.46 × 60 = 27.6, which rounds to 28 minutes, one minute out
- For the seconds, find the whole minutes first: 1427 ÷ 60 = 23.78…, so 23 whole minutes
- Those 23 minutes are 23 × 60 = 1380 seconds, leaving 1427 − 1380 = 47 seconds
- The time is 23 min 47 s, not 23 min 78 s