What Time is It?

Ever since time began, humans have measured it. We needed to know when it would be day or night, winter or summer, when to plant, when to harvest, when to stock up on food to eat during the cold season -- and like all our early measuring systems, we used natural objects and events to measure time. Our first chronometers ( instruments to measure time) were designed to measure the apparent movement of the Sun, Moon, Planets and Stars in the sky.

All this began when the Ancient Babylonians noticed the circular path of the sun in the day sky and divided it into 360 degrees. Each degree was then divided into 60 minutes. Later, once we transfered the approach to the 12 hour clock, and we needed intervals smaller than an hour which was 30 degrees, it was divided into 60 minutes each of which was divided into 60 seconds.

The basic units of time measurement are necessarily determined by natural events.
A day is the time it takes the Earth to rotate once on its axis.
An hour is one twenty-fourth of a day.
Days, Hours, Minutes and Seconds are the time intervals we measure on a clock.

Longer intervals are measured on a calendar. A year is the time it takes the Earth to travel around the sun. A month is one-twelfth the time it takes the Earth to complete an orbit about the sun. A season is one quarter of that time.

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Measuring "Clock" Time

Sundial

The sundial was one of the earliest devices for measuring the time of day. It only works in sunlight, as the shadow of the sun moves around a circular surface, marked off in equal intervals. We can still buy sundials that will tell the right time, to the minute if we position them correctly -- on a flat surface, aligned with the axis of the Earth.

Hourglass or Sand Glass

Time can also be measured accurately by letting sand trickle through the narrow opening of a sand or hourglass. Fancy sand glasses like this one were used to mark the passage of minutes and hours. When we flip the glass, the sand falls though its narrow central hole, in a fixed period of time. Hourglasses measured time quite accurately.

Though we generally call them hourglasses, because an hour was their standard setting, they could be made to measure almost any period of time, by changing the amount of sand or the size of the hole. Today, we sometimes use them in old-fashioned kitchens, to time the cooking of our soft-boiled eggs, and in board games to time our turn at the board. Our computers show us a small hourglass image to tell us they're busy.

In our attempts to find more accurate ways to measure time than sand glasses and sundials, we have progressed from watching the Sun, Moon, and stars move across the sky, to constructing ingenious mechanical devices to measure ever smaller intervals of time. Today, we can measure microseconds.

Big Ben in London

Clocks and watches

This clock is world famous. It is called Big Ben. For many years it has stood in the tower high above London, England -- helping Brits get to work on time. Big Ben is an analog clock. It has 2 hands, one longer than the other -- to indicate minutes and hours -- that turn around on a circular face, sectioned into 12 equal intervals called hours. The hands are moved by a mechanical device made of huge gears and weights known as clockworks. The photo on the left was taken at twenty-five past one (1: 25 p.m.) and the one on the right was taken at twenty-five to eleven -- also known as ten thirty-five.

Until the age of batteries, transistors, and computer chips, almost all clocks and watches were analog. Today we have digital clocks that display the time and other data with digits (of course!).

Digital Clock showing the time, date and temperature.

People such as pilots and timekeepers (at sports events), use specialized watches. A pilot uses a watch like this one that tells him the time in the plane he's flying and at his destination. Some, like this one, even tell him the time at his 2nd destination, if there is one. This pilot's watch has a 24 hour face like a military watch.

Time keepers at sporting events use stopwatches -- that measure time in units as small as a hundredth of a second.

Time Units Measured on a Clock

Most of us use a 12 hour clock -- but there are 24 hours in a day -- so we divide it into two 12 hour intervals that begin and end at midnight and noon. To tell them apart, we use the letters a.m. to mean before noon -- and p.m. to mean after noon. These abbreviations stand for antemeridian and postmeridian. The word meridian means middle -- in this case, middle of the day or noon. "Ante" is a prefix that means "before" and "post" means "after", so a.m. stands for before noon and p.m. means after noon.

The minute (longer) hand of an analog clock makes a full turn of the face every hour. There are 12 hour intervals, so each one represents 5 minutes, as well as 1 hour. The hour (shorter) hand, moves one-twelfth ( 1/12 ) of the way around each hour, so it takes 12 hours to make a full turn. The second hand (if there is one) circles the clock face every minute.

Note how we write the time with colons ( : ) to separate the hours, minutes and seconds.

Comparing the 1st and 2nd clocks here, we see the hour hand didn't move. The minute hand moved 5 minutes (from 12 to 1) and the second hand moved ¾ of the way round the clock -- which is 45 seconds (¾ of 60). In the 3rd clock, the hour hand moved from 2 to 3 -- that's an hour, the minute hand moved from 1 to 2 -- that's 5 minutes, and the second hand moved ½ way round the clock or 30 seconds. The time difference between the 2nd and 3rd clocks is
1 hour, 5 minutes and 30 seconds.

The time units we measure on a clock are seconds, minutes, hours and days.

60 seconds = 1 minute

60 minutes = 1 hour

24 hours = 1 day

Changing or Converting Units of Time

As always, when we change from big units to small, we multiply -- because one big unit contains lots of small ones. When we change from small units to big ones, we divide -- because a whole lot of small units count as 1 big one.

Examples: Convert:

Reading and Writing the Time

Here is how we read or say the times shown here:

a) ........b) .............c)

a) 10 minutes to (before) 2 o'clock

b) 10 minutes past (after) 10

c) 22 minutes after 6 o'clock

We write these times as:

a) 1: 50 : 56

b) 10 : 10 : 53

c) 6 : 22 : 44

If we know whether it's morning or afternoon, we add a.m. and p.m. We rarely say or write the seconds value in everyday life, but people who work in radio or TV, pay close attention to the seconds, because every second counts and costs in broadcasting.

Elapsed Time or How Long Has It Been?

When we measure elapsed time, we find how long it has been between the start and the end of some event or happening. If we leave home at 10 a.m. and arrive at Granny's house at 11:30 a.m., our trip took us an hour and a half or 1 hour and 30 minutes. We could also say it took us 90 minutes to get to Granny's house.

To find elapsed time, we subtract the start time of the event from the end time.

The thing to remember with time however, is that it's not a decimal system based on 10. It is a sexagesimal system, based on 60, so when we have to carry, or borrow (regroup) hours into minutes or minutes into seconds, we use multiples of 60.

Example: Find how much time elapsed between 7: 15 a.m. and 9: 10 a.m.

We need to find 9: 10 - 7: 15 but 0:10 - 0:15 doesn't go, so we borrow an hour (60 minutes) from the 9. Now, 9 : 10 becomes 8 : 70, and we can subtract. We get:

We do the same thing when we add units of time.
We carry multiples of 60 to the next biggest unit.

Example: Richard promised his Mom he'd meet her at exactly 6:15 p.m. for their weekly supper. At 4: 25 p.m. he still had 2 packages to deliver on his courrier route. The first would take
1 hour and 10 minutes to do, the other would take just 40 minutes, if the traffic wasn't too bad.
Richard needs only 20 minutes to get to his Mom's from the 2nd delivery address.
Will he make it to Mom's on time? If not, how late will he be?

Solution: We have to add the time he'll need for the deliveries and his drive to Mom's to
4: 25 p.m. . Then we'll know if Richard will be late.

When we add 4: 25 + 1: 10 + 0: 40 + 0: 20 , we get 6: 35 p.m since
40 minutes + 20 minutes = 1 hour and 4: 25 + 1: 10 = 5: 35
1 hour after 5 : 35 is 6: 35 p.m.
so Richard will be 20 minutes late arriving at his mother's house.

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We add the start time to the elapsed time, to find the end time.

We subtract the elapsed time from the end time, to find the start time.

We subtract the start time from the end time, to find elapsed time.

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Now get a pencil, an eraser and a note book, copy the questions,
do the practice exercise(s), then check your work with the solutions.
If you get stuck, review the examples in the lesson, then try again.

Practice Exercise

1) Fill in the blanks:

a) 27 min = ____ sec	b) 1 hr 10 min = ____ min	c) 79 min = ___ hr ____ min
d) 2½ days = ____ hrs	e) 72 hrs = ____ days	f) 4 days 5 hrs = ___ hrs

2) Write the time shown on each clock in words and in digits: (put in a.m. or p.m.)

3) Find the missing start, end or elapsed time.

start time	elapsed time	end time
7: 15 a.m.	4 hrs 53 min	?
?	5 hrs 47 min	7:50 p.m.
10:20 p.m.	?	0: 14 a.m.

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AFTERNOON FLIGHTS FROM ATLANTIC CITY
Destination	departs at	arrives at
Chicago	1: 50	3: 15
Miami	2: 30	4: 05
Los Angeles	3: 15	7:05

4) Use the airline schedule to find the answers:
a) How long is the flying time between Atlantic City and Chicago?
b) How long is the flying time between Atlantic City and Los Angeles?
c) How much longer does it take to fly to Los Angeles than to Miami?
d) How many minutes is this?

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Solutions

1) Fill in the blanks:

a) 27 min = _1620_ sec	b) 1 hr 10 min = _70_ min	c) 79 min = _1_ hr _19_ min
d) 2½ days = _60_ hrs	e) 72 hrs = _3_ days	f) 4 days 5 hrs = _101_ hrs

2) Write the time shown on each clock in words and in digits: (put in a.m. or p.m.)

time in words	time in digits
a) twelve-thirty p.m. or half past noon	12: 30 p.m.
b) ten minutes to five a.m. or four-fifty a.m.	4: 50 a.m.
c) twenty minutes to two p.m. or one-forty p.m.	1: 40 p.m.

3) Find the missing start, end or elapsed time.

start time	elapsed time	end time
7: 15 a.m.	4 hrs 53 min	12: 08 p.m.
2: 03 p.m.	5 hrs 47 min	7:50 p.m.
10:20 p.m.	1 hrs 54 min	0: 14 a.m.

4) Use the airline schedule to find the answers:
a) 3: 15 - 1: 50 = 2: 75 - 1: 50 = 1 hour 25 minutes
b) 7: 05 - 3: 15 = 7: 65 - 3: 15 = 3 hours 50 minutes
c) 3 hours and 50 minutes - 1 hour and 25 minutes = 2 hours and 25 minutes.
d) 2 hours and 25 minutes = 145 minutes

( Primary MathRoom Index )