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Home , Decimal time

Turning and into and Back

As you probably know, there are 60 in a and 60 minutes in an . We’re really familiar with this but adding or subtracting amounts of can often cause problems for people.

This is because when we do normal calculations, we use Base 10. All that means is that when we get to 10 we start again –

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29

With time, we use Base 60. We count up to 59 minutes and then start again. (I can’t fit all 60 minutes on the page so I’ll just put in every 5 minutes)

0 5 10 15 20 25 30 35 40 45 50 55 1h 1h 5m 1h 10m 1h 15m 1h 20m 1h 25m 1h 30m 1h 35m 1h 40m 1h 45m 1h 50m 1h 55m (60m) (65m) (70m) (75m) (80m) (85m) (90m) (95m) (100) (105m) (110m) (115m) 2h 2h 5m 2h 10m 2h 15m 2h 20m 2h 25m 2h 30m 2h 35m 2h 40m 2h 45m 2h 50m 2h 55m (120m) (125m) (130m) (135m) (140m) (145m) (150m) (155m) (160m) (165m) (170m) (175m)

☞ People often write time as 1:40 meaning 1 hour 40 minutes. Don’t confuse : with a point!

I expect you know all this. But what happens when you try to add two amounts of time together?

1

Here’s the sum – 2 hours 45 minutes + 1 hour 59 minutes.

See if you can tell what’s wrong with this sum…

Hours Minutes 2 45 + 1 59 4 014 X

First of all you can do a rough estimate to see if the answer is right or not. 1 hours 59 minutes is very close to 2 hours. So you can see that the answer is going to be around 4 hours 45 minutes.

But this person has got 4 hours and 4 minutes. Can you see what went wrong? They forgot they were working in hours and minutes – Base 60 – and did the addition using our normal Base 10.

☞ If you are working in hours and minutes you must remember you are using Base 60.

You are less likely to go wrong if you turn the hours and minutes into minutes.

Minutes 165 + 119 2814

But then you have to turn this back into hours and minutes, and Base 10 can mess you up here as well…

2 To find out how many hours in 274 minutes you have to divide by 60 (as we are working in Base 60).

Here’s the division – 284 minutes divided by 60.

4.73 60 284.000 240 440 420 200 180

So the answer is 4 hours 73 minutes??? Or 5 hours 15 minutes??? Noooooo!!! You’ve turned the time into a decimal. ☞ If you want the time in hours and minutes, stop when you’ve found out the whole number – the remainder is the minutes.

So…

4 remainder 44 60 284 240 44

So 284 minutes is 4 hours 44 minutes.

3 Turning Time into Decimal Time

Very often it’s easier to turn hours and minutes into decimals – now you know how to do it. You just divide the minutes by 60. Minutes are a fraction of an hour (60 minutes), for example 18/60. And to convert any fraction to a decimal you divide the top by the bottom.

0.3 60 18.0 Try it yourself: So 18 minutes is 0.3 of an hour a/ 9 hours 8 minutes b/ 5 hours 47 minutes c/ 9 hours 21 minutes

Turn Decimal Time into Hours and Minutes To turn a decimal time into minutes, you just do the opposite. You multiply by 60. So 6.1 hours is 6.1 x 60 = 366 minutes. Turn this into hours and minutes by dividing with a remainder (we can guess the whole number will be 6…)

6 remainder 6 60 366

So 6.1 hours is 6 hours and 6 minutes. Try it yourself: a/ 4.65 hours b/ 27.23 hours c/ 1.79 hours

4 Answers:

Turning Time into Decimal Time

a/ 9 hours 8 minutes = 548 minutes = 9.1333… hours

b/ 5 hours 47 minutes = 347 minutes = 5.7833.. hours

c/ 9 hours 21 minutes = 561 minutes = 9.35 hours

Turn Decimal Time into Hours and Minutes

a/ 4.65 hours = 279 minutes = 4 hours 39 minutes b/ 27.2 hours = 1632 minutes = 27 hours 12 minutes c/ 1.7 hours = 102 minutes = 1 hour 42 minutes

You may have just gone straight to multiplying the numbers beyond the decimal point by 60. For example:

4.65 hours = 4 hours and 0.65 x 60 = 39 minutes, so 4 hours 39 minutes. Either method is fine as long as you get it right! 5