Sexagesimal system

Sexagesimal system, add, subtarct, types of angels, time, convert, sexagesimal to decimal, decimal to sexagesimal

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AnglesConverting to another systemAdding and SubtractingExercises
Sexagesimal system
Matematicas 2
o
E.S.O.
Alberto Pardo Milanes
-

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1Angles2Time3Converting4Adding and Subtracting5Exercises
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Angles
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Angles
What's an angle? Measure an angle
Given two intersecting lines, the point of
intersection is called the vertex and the
amount of rotation about the vertex re-
quired to bring one line into correspondence
with the other is called the angle between
them.
There are several ways to measure the size of an angle. One way is
to use units of degrees: In a complete circle there are three hundred
and sixty degrees (one full rotation corresponds to360degrees).
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Angles
Some angles
Half a full rotation is called a straight angle that is180de-
grees, and a quarter of a full rotation is called a right angle
(90degrees). An angle less than90degrees is called an acute
angle, an angle greater than90degrees and less than180
degrees is called an obtuse angle, and an angle greater than
180degrees and less than360degrees is called a reex angle.
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Angles
Using the proctartor
Acute angleRight angleObtuse angleStraight angle
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Angles
Express an angle
You can express angles to any precision using decimal numbers.
Example:4degrees and a half=4.5degrees.
There is another way to state the size of an angle, and that is by
subdividing a degree. The degree is divided into sixty parts called
minutes. These minutes are further divided into sixty parts called
seconds.
In a full circle there are360degrees, each degree is split up into60
parts called minutes (each part being1=60of a degree), each
minute is split up into60parts called seconds (each part being
1=60of a minute).
Examples:1degree is60minutes, so;5degrees=;560 = 30
minutes, so4.5degrees is equal to4degrees and30minutes.
14degrees,22minutes and55seconds is usually written this
way:14
o
22
0
55
00
.
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Time
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To measure time we can use hours: In a day there are twenty-four
hours.
You can express time to any precision using decimal numbers.
There is another way to state the amount of time, subdividing an
hour. The hour is divided into sixty parts called minutes. These
minutes are further divided into sixty parts called seconds.
In a day there are24hours, each hour is split up into60parts
called minutes (each part being1=60of an hour), each minute is
split up into60parts called seconds (each part being1=60of a
minute).
Example:18hours,51minutes and42seconds is usually written
this way:18hr51min42sec.
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Converting
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Converting
Sexagesimal to decimal
To convert sexagesimal format to decimal format divide the
seconds by three thousand six hundred, then add it to the minutes
divided by sixty, and nally add the degrees. To convert time do
the same.
Example:22
o
54
0
18
00
is written in the sexagesimal system. To
convert it to decimal:18=3600+54=60+22 = 0;005+0;9+22 =
22;905
o
.
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Converting
Decimal to sexagesimal
To convert decimal format to sexagesimal format the whole units
of degrees will remain the same, then multiply the decimal by 60,
the whole number becomes the minutes, take the remaining
decimal and multiply by 60, the resulting number becomes the
seconds. Seconds can remain as a decimal. Take your three sets of
numbers and put them together, using the symbols for degrees (
o
),
minutes (
0
), and seconds (
00
). To convert time do the same.
Example:35;245
o
is written in the decimal system. To convert it
to sexagesimal:35are the degrees,0;24560 = 14;7so14are the
minutes,0;760 = 42so42are the seconds.35;245degrees are
35
o
14
0
42
00
.
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Adding and Subtracting
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Adding and Subtracting
To add or subtract angles or time, you must add or subtract the
units separately. But you may need to do some adjusting:
the hours can not end up 24 or more,
the degrees can not end up 360 or more,
the minutes can not end up 60 or more,
and the seconds can not end up 60 or more.
Negative numbers can not be used.
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Adding and Subtracting
Adding
Add the hours. If the hours are24or more, then you have to
subtract24from the hours and increase the number of days by
one. Add the minutes. If the minutes are60or more, subtract60
from the minutes and increase the number of hours by one. Add
the seconds. If the seconds are60or more, subtract60from the
seconds and increase the number of minutes by one. To add angles
do the same method.
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Adding and Subtracting
Adding
Example:To add18hr55min +9hr21min:
18hr55min
+9hr21min
27hr76min
1day3hr76min
1day4hr16min
Add the hours:18 + 9 = 27. The hours are24or more, so we
subtract24from the hours (2724 = 3hr) and increase the
number of days by one. Add the minutes:55 + 21 = 76. The
minutes are60or more, so subtract60from minutes (7660 =
16min) and increase the number of hours by one (3 + 1 = 4hr).
So18hr55min +9hr21min=1day4hr16min.
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Adding and Subtracting
Subtracting
Subtract the hours, if the hours are negative, add 24 to the hours
and subtract 1 from the days. Subtract the minutes, if the minutes
are negative, add 60 to the minutes and subtract 1 from the hours.
Subtract the seconds, if the seconds are negative, add 60 to the
seconds and subtract 1 from the minutes.
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Adding and Subtracting
Subtracting
Example:To subtract12hr30min -7hr55min:
12hr30min
-7hr55min
11hr90min
-7hr55min
4hr35min
Subtract the hours:127 = 5. Subtract the minutes:3055 =
25. The minutes are negative, so subtract1from hours and
increase the number of minutes by sixty (30 + 60 = 90min). So
12hr 30min - 7hr 55min =
=11hr90min -7hr55min=4hr35min.
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Exercises
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Exercises
Exercise 1
Find ve objects in your classroom that have all kind of angles
angles but no right angles.
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Exercises
Exercise 2
Using a set square is easy to draw a right angle, a30
o
angle, a45
o
angle or a60
o
angle. Use a set square to draw a15
o
angle and a
75
o
angle.
30
o
angle45
o
angle60
o
angle
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Exercises
Exercise 3
Measure these angles:
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Exercises
Exercise 4
Write down the following amounts:
12
o
11
0
12
00
:
145
o
23
0
3
00
:
3hr25min28sec:
16hr46min50sec:
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Exercises
Exercise 5
Jane works six hours a day from Monday till Friday, and one hour
less on Saturday. How many hours does she work a week?
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Exercises
Exercise 6
At13:45AM, Peter went to have lunch at his friend Paul's house.
His mother told him to be back in two and a half hours. At what
time does Peter have to be home?
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Exercises
Exercise 7
Thirty days have September, April, June, and November; All the
rest have thirty-one, Save February, with twenty-eight days clear,
And twenty-nine each leap year. How many days are there in one
leap year? How many hours? How many minutes? How many
seconds?
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Exercises
Exercise 8
Two angles are complementary if the sum of their measures is90
o
.
Find two complementary angles measuring exactly the same.
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Exercises
Exercise 9
Two angles are supplementary if the sum of their measures is180
o
.
Find two supplementary angles being the measure of the big one
three times the measure of the small one.
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Exercises
Exercise 10
Charles rode his bike on Monday and Thursday. He spend1hr
36min48sec riding on Monday and1hr32min25sec riding on
Thursday How much time did he ride over the two days in total?
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Exercises
Exercise 11
The interior angles of a triangle always add up to180
o
. If two
angles of a triangle measure21
o
24
0
and86
o
49
0
. What is the
measure of the third angle?
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Exercises
Exercise 12
Spencer got on the train to get to the airport at11:23. He spent
42min in the train. It took him25min to get his plane ticket and
He spent1h6min waiting for the plane to take o. At what time
did the plane take o?
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Exercises
Exercise 13
A tv show started at20:25and it ended at23:30. How long did
the show last for?
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Exercises
Exercise 14
School ended at15:15. Al arrived home just in time to watch a
movie. If the movie started at16:05, how long did it take for Al to
get home?
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Exercises
Exercise 15
A bus runs from around half past six in the morning until around
00:45at night. How many hours does the drivers use the bus? How
many minutes? If it rides the same route sixty times a day, how
much time does the route need to be covered?
Alberto Pardo Milanes Sexagesimal system