Basic Mathematics Form One Notes – Units
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UNITS
A unit ~ is defined as a symbol or sign which is assigned to a number to describe a kind of
measurement made
Units of Length
Convertion of One Unit of Length to Another
Convert one unit of length to another
The conversion of one unit to another is done by considering the arrangement below
km 1
hm 1 0
dam 10 0
m £2 Oo 0
dm 1000 0
cm 100 00 0
mm 000 00 0
“a
Example, from the above we get
1km = 1,000,000 mm
1hm = 100,000 mm
1dam = 1000 cm
lm=100cm
Computations on Metric Units of Length
Perform computations on metric units of length
Example 1
Convert
(a) 12cm to dm
(b) 2,500mm to m
(c) 87km tocm
Solution
4s
(a) 12cm to dm
1dm=10 cm
TS 120m
By cross multiplication, we get
1dm x 12cm_ 12
– Span ig am = 12am
(b) 2,500 mm to m
1m 1000 mm
PS 2500 mn
By cross multiplication, we get
_1m x2500mm _ 2500 _
~~~qo00mm 1000″ “?TM
(c) 87km tocm
1km= 100 000 cm
aries?
By cross multiplication, we get
87km x 100000cm 8700000
>= = em = 8700 000 cm
1km 1
Unit of Mass
Convertion of One Unit of Mass to Another
Convert one unit of mass to another
The conversion of one unit to another is done by considering the arrangement below
46
kg 1
hg 1 0
dag 10 0
g 100 0
dg 1000 0
cog 10000 0
m 00000 0
Example, from the above
1kg = 1,000,000 mg
1hg = 100,000 mg
1 dag = 1000 cg
lg=100cg
The conversion of tonneto other units is done converting it to kilogramfirst and then
fromkilogramto the required unit
I tonne = 1000kg
Computation on Metric Units of Mass
Perform computation on metric units of mass
Example 2
a7
Convert (i) 8500g to kg
(ii) 0.000025 kg to mg
(iii) 4.67cg to dg
Solution
(i) 8500g to kg
1kg = 1000 g
2 =85009
1kg x8500g _ 8500
=—“To00g 1000 #9 = 85ko
(ii) 0.000025 kg to mg
1kg = 1000 000 mg
0.000025 kg = ?
0.000025 kg x 1000000mg 25 _ 9.
= Tkg Og EN,
(iii) 4.67cg to dg
1dg =10cg9
2 =467¢9
_ldg x 46769 _ 467 4g agra,
~—F0eg. ~~ «10 ad
Units of Time
The units of time are of two types, smaller and larger units of time Smaller units of time includes
seconds, minutes, hours and days Larger units of time includes week, month, year, decade,
century millennium.
Convertion of One Unit of Time to another
Convert one unit of time to another
The conversion of units of time to another can be done by considering the arrangement below
48
year
day
hour
minute
second
Example, from the circle above
Also
lyear = 365 x 24 x 60 x60 seconds
ldays = 24 x 60x 60 seconds
lhour = 60 x 60 seconds
1 minute = 60 seconds
Example 3
Convert
(i) 54,000 seconds to minutes
(ii) 7,200 minutes to hours
(iii) 6 hours to seconds
Solution
49
(i) 54,000 seconds to minutes
1 min = 60 sec
2 =54000 sec
min x 54000sec _ 54000 900
= —— = Zp min = 900 minutes
(ii) 7,200 minutes to hours
1 hour = 60 minutes
2 =7 200 minutes
hour x 7200 minutes _ 7200
= = — hours = 120 hours
60 minutes 60
(iii) 6 hours to seconds
1 hour = 60 x 60 sec
6hours= ?
Lhours x 60x 60sec _ 3600
=———__— =~ seconds = 3 600 seconds
Thour 1
Convertion of Unit Time of 12 Hour Clock to 24 Hour Clock and Vice Versa
Read and convert unit time of 12 hour clock to 24 hour clock and vice versa
The hours can exist in two systems: 12- hour clock and 24 – hour clock.
A 12- hour clock has 12 hours between midnight and midday(a.mand 12 hours between midday
and midnight(p.m).
‘A 21 – hour has 24 hours in a day.Times in the morning are the same in both systems.For times
in the afternoon, convert by adding or subtracting 12 hours
Example 4
Convert the following times from the 12 – hour clock to 24 – hour clock
50
(i) 5.30a.m
(ii) 1.40 p.m
(iii) 7.15 p.m
Solution
(i) 5.30 a.m = 0530 hrs
(ii) 1.40 p.m= (0140 + 1200) = 1340 hrs
(iii) 7.15 p.m = (0715 +1200) = 1915 hrs
Example 5
Convert the following times from the 24 – hour clock to 12 – hour clock
(i) 0450 hrs
(ii) 1245 hrs
(iii) 2300 hrs
Solution
(i) 0450 hrs = 4.50a.m
(ii) 1245 hrs = 12.45 p.m
(iii) 2300 hrs = (2300 — 1200) = 11.00 p.m
Units of Capacity
Standard Unit of Measuring Capacity
‘State the standard unit of measuring capacity
Capacity is related to the volume
Definitions
5
+ Capacity-is defined as the ability hold or contain something
+ The S.1 unit of capacity is Hire.
+ Volume ~is defined as the amount of space occupied by a substance
+ The S.Lunit of volume is cubic metres (m’)
Capacity is related to the volume as follows:
J litre = 1000cm? = 0.001m? = Idm?
Also J ml = 1 cm?
Other units related to litre are kiloliter (kl), hectoliter (hl), decalitre (dal), litre (1), deciliter (dl),
centiliter (cl) and mililitre (ml).
The conversion of one unit to another is done by considering the arrangement below
kl cl
hl L
dal 10 0
I 100 0
dl 1000 0
cd 10000 0
m 000 00 0
Example, from the above
52
1 kl = 1,000,000 ml
1hl = 100,000 ml
ldal = 1000 cl
11= 100cl
The Litre in Daily Life
Example 6
Convert the following units into
@ ~~ 3500ml
(ii) 0.006 m3
(iii) ~~ 4000 dm?
(iv) 500 mm
Solution
33
(i) Convert first 3500 ml to cm?
1ml = 1cm®
3500ml= ?
3500 ml x 1cm* 3500,
= —____—_ = em? = 5
1Iml if
Then 3500cm® to litres
1 litre = 1000 cm?
? = 3500cm3
_ 3500cm* x 1litre _ 3500 m F
~~ qo00em «1000 |
(ii) 0.006 m3 to litres
1 litre = 0.001 m*
? = 0.006 m
1litre x 0.006 m? 0.006
=e =~ litres}=
0.001 m3 0.001
(it) Convert first 4000 dim? to cm?
Lam = 10 em
(1dim)* = (10.em)? + Adm? = 1000 em?
so
1d = 1000 em’
4000 dm? = ?
4000 di? x 1000em* 4000000, :
= 2000 dn 1000 er _ 4.000000 = 4000 00m
Second, convert 4000 000m? to litres
1 litre = 1000 on?
2 = 4.000 000em?
Litre x 4000 000em? _ 4.000 000
= Litre + $000 000ern 4000 000 eres = 4000 litres
3
(iv) 500 mm*
Convert first 500 mm® to cm®
1em= 10mm
(1em)3 = (10 mm)? > 1. cm? = 1000 mm*
So
Lem = 1000 mm
2 =500 mm?
Lem? x 500mm! _ 500 oy _ yg cma
~~~{000 mms ~ 1000 “TM 9
Second, convert 0.5m? to litres
1 litre = 1000 cm?
2 =05em?
_ Llitre x 05cm? _ 05 avers DUOUEEN
“F000 em ~ oo9 “TES ~ HNN Heres
Measurements can be rounded to a certain number of significant figures Approximation- is a
process of rounding numbers to a certain degree of accuracy.A number can be rounded to a
certain required place value such as to the nearest ten, hundred, and thousand
Rounding Off Numbers
Rounding off Whole Numbers to Given Place Values
Round off whole numbers to given place values
STEPS
+ When rounding a number, stand at the digit of the required place value, then look at the
next digit to the right; if itis or more, round up (i.e, increase the digit of the required place value
by 1) and if it is or less, do not change the digit of the required place value
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