Time — Clock & Calendar • Topic 3 of 6

Units of Time

The units of time form a clear ladder, and converting between rungs is pure multiply-or-divide once you know the factors. Going down the ladder (larger to smaller) you multiply; going up (smaller to larger) you divide. The base unit is the second: 60 seconds make a minute, 60 minutes make an hour (so an hour is 3600 seconds), 24 hours make a day (1440 minutes, 86400 seconds), and 7 days make a week. Above that, 12 months make a year, with the common year holding 365 days and a leap year 366; 10 years is a decade, 100 a century, 1000 a millennium. The months themselves carry 28, 29, 30 or 31 days, and the reliable memory aids are the rhyme 'Thirty days has September, April, June and November' and the knuckle method — knuckles are 31-day months, the dips between them are the shorter ones, with February the odd one out at 28 (or 29 in a leap year). The single biggest error here is decimal contamination: treating 1 minute as 100 seconds or 1 hour as 100 minutes. Time is base-60 for seconds and minutes, base-24 for hours and base-7 for the week, so every addition or subtraction has to carry or borrow at those boundaries, not at 10 or 100.

✅ Solved examples

1. How many seconds are there in 2 hours 30 minutes?
2 hours 30 minutes = 150 minutes (2 x 60 + 30). Each minute is 60 seconds, so 150 x 60 = 9000 seconds.
2. Convert 4 days into hours, and then into minutes.
1 day = 24 hours, so 4 days = 4 x 24 = 96 hours. Each hour is 60 minutes, so 96 x 60 = 5760 minutes.
3. A fortnight is how many hours?
A fortnight is 2 weeks = 14 days. Each day has 24 hours, so 14 x 24 = 336 hours.
4. A child writes that 180 seconds equals 1 minute 80 seconds. Correct the error.
Moving from seconds to minutes you divide by 60: 180 / 60 = 3 minutes exactly. The child treated time as decimal; 80 seconds is impossible because 60 seconds already make a full minute.

✏️ Practice — try these, take hints as needed

1. How many minutes are there in a full day?
1 day = 24 hours.
Each hour has 60 minutes.
1440 minutes
2. Convert 300 seconds into minutes.
Smaller to larger means divide.
Divide by 60.
5 minutes
3. Which months have exactly 30 days?
Use the rhyme or the knuckle dips.
There are four of them.
April, June, September and November
4. How many days are there in a common (non-leap) year, and how many weeks plus extra days is that?
Common year is not 366.
365 / 7 = 52 remainder 1.
365 days = 52 weeks + 1 day

📝 Topic test — 8 questions

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