# UNIT 6: THE METRIC DECIMAL SYSTEM 6.1 Measurement

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```UNIT 6: THE METRIC DECIMAL SYSTEM
6.1 Measurement
Different units of measurement have been used in the past, some of them
are still in use in UK and USA, but in most places is used the Metric
System of Measurements. The metric units are:
Length metre
Volume cubic metre
Mass or weight gram
Area square metre
Capacity litre
6.2 Measuring length:
The base unit of length is the metre(m).
The multiples of the meter are:
The divisors of the metre are:
* Decametre(dam)
1dam=10m
* Decimetre(dm)
1dm=0,1m
* Hectometre (hm)
1hm= m
* Centimetre(cm)
1cm=
m
* Kilometre(km)
1km=
m
*Millimetre(mm)
1mm=
m
Km
hm
4
dam
0
m
0
dm
0
cm
0
mm
Exercise:
a) How many cm are there in 400m? 400 m = 40.000cm
b) How many dam are there in 1 km?
c) How many cm are there in 2hm?
d) How many hm are there in 1 dam?
6.3. Measuring Capacity
The base unit of capacity is the litre(l).
The multiples of the litre are:
The divisors of the litre are:
* Decalitre(dal)
* Decilitre(dl)
* Hectolitre (hl)
* Centilitre(cl)
* Kilolitre(kl)
*Millilitre(ml)
Kl
hl
dal
4
l
0
dl
0
Exercise:
a) How many dl are there in 40 l ? 40 l = 400dl
b) How many ml are there in 67 hl ?
c) How many l are there in 0,08 hl?
d) How many dl are there in 17 ml ?
6.4 Measuring Weight
The base unit of weight is the gram( g).
cl
ml
The multiples of the gram are:
* Decagram(dag)
* Hectogram (hg)
* Kilogram (kg)
The divisors of the gram are:
* Decigram (dg)
* Centigram (cg)
*Milligram(mg)
Kg
hg
dag
g
dg
0
0
6
Exercise:
a) How many kg are 6dag ? 6dag= 0,06 kg
b) How many dag are 250 hg ?
c) How many hg are 0,04 kg ?
d) How many kg are 25 g ?
cg
mg
6.5. Measuring Area
The base unit of area is the square metre(m 2 ).
The multiples of the m 2 are:
The divisors of the m 2 are:
* S. Decametre(dam 2 )
* S.Decimetre(dm 2 )
*S. Hectometre (hm 2 )
*S. Centimetre(cm 2 )
* S. Kilometre(km 2 )
*S. Millimetre(mm 2 )
km 2
hm 2
6
8
dam 2
0
0
m2
dm 2
cm 2
mm 2
Exercise:
a) How many dam 2 are there in 68 hm 2 ? 68 hm 2 = 6.800 dam 2
b) How many dm 2 are there in 2.340 hm 2 ?
c) How many cm 2 are there in 60 m 2 ?
d) How many m 2 are there in 200 dam 2 ?
6.6. Measuring Volume
The distinction between 'Volume' and 'Capacity' is artificial and kept here
only for historic reasons. A cubic metre is 1000 litres
The multiples of the m 3 are:
The divisors of the m 3 are:
* C. Decametre(dam 3 )
* C.Decimetre(dm 3 )
* C. Hectometre (hm 3 )
*C. Centimetre(cm 3 )
* C. Kilometre(km 3 )
*C. Millimetre(mm 3 )
km 3
hm 3
2
5
dam 3
0 0
m3
dm 3
cm 3
0
Exercise:
a) How many dam 3 are there in 25 hm 3 ? 25 hm 3 = 25.000 dam 3
b) How many dm 3 are there in 128 hm 3 ?
mm 3
c) How many hm 3 are there in 60 m 3 ?
ACTIVITIES
1. Answer the following questions
a) How many dl are there in 1 hl?
b) How many cl are there in 3 dal?
c) How many mm are there in 1 dam?
d) How many m are there in 6 cm?
e) How many dam are there in 80mm?
f) How many kg are 6 dag?
g) How many g are 89mg
2. Write in metres:
a)18 km =
b) 16 dm =
c) 500 cm =
d) 2.340 mm=
e) 5,6 dam =
f) 0,4 hm =
3. Write in metres:
a) 6 Km 4 hm 8 dam
b) 1m 8dm 2cm 6mm
4. Write in cm :
a) 0,006 hm
b) 1,8 m
g) 76,89 dm=
h) 16, 6 mm=
i) 0,59 cm =
c) 3m 4 cm 7 mm
d) 4 m 2 dm 8 mm
c) 23dm
d) 0,7 dm
5. Complete :
a) 1,68 kl= ….. dal
b)5,4 hl=……l
c) 0,58 l=……..dl
d) 76 cl=……….l
e) 235 ml=…..dl
e) 89 mm
f) 0,76 dm
j) 45 dam =
k) 36,8 km=
l) 0,88 dam=
e) 5hm 3m 6cm
f) 7dam 2dm 8cm
g) 876 mm
h)2,87 dam
f) 2,75 kl=…….l
g)456 cl=………l
h) 30 dl =…..dal
i) 2600 ml=…..dal
j) 0,01 hl=……dl
k)12 l= ….dl
l)876 l= ….hl
m)5 ml =……dl
n)54,89 hl=……kl
&ntilde;)987dal =……..kl
6.Write in cl:
a) ( 2l 6dl 7cl) + ( 5dl 9cl 3 ml)=
b) 56 dal + 2,5 hl + 575 l =
7. Write in grams:
a) 5.600 mg
c) 3 cg
b) 23 dag
d) 0,8 hg
8. Complete:
a) 3kg=……g
b) 1,4 hg=….dag
c) 35 dg=……mg
d) 234 g=……kg
e) 3,98 Kg
f) 45 dg
e) 23,7 dg=……g
f) 345 mg=…….cg
g) 2mg=……..dag
h) 2,69hg=…….kg
9.Write in grams
a) ( 7kg 5hg 4g) + ( 7hg 5dag 8g)
g) 5,97 dag
h) 66mg
i) 0,456 kg=…….dag
j) 98,4 dg=…..mg
l) 56,8cg =…..g
m) 76,9 mg= …..hg
b) ( 6dag 2 g 5cg) &middot; 4
c) ( 8dag 5g 6dg) + ( 3g 5dg 7cg)
d) 2kg 4dag 9g
2
10. Write in m :
a) 0,006 km
e) 7,9 hm
2
b) 38 dam
2
2
c) 12455 cm
f) 798,77 dm
2
2
d) 6.987.890 mm
g) 0,006 hm
2
h) 23876 cm
2
2
11. Complete:
2
a) 34.400 mm =……… dm
2
2
d) 7,8 km =…….. hm
2
b) 34.567 m =………… dam
2
c)477 hm = …….. km
2
2
2
2
e)0,008 hm = ……. m
2
2
2
f)832 cm =……… mm
12. Complete:
3
a) 34.450 mm =……… dm
3
3
3
d) 17,8 km =…….. hm
b) 44.567 m =………… dam
3
3
3
3
e) 0,00008 hm = ……. m
3
3
c) 1477 hm = …….. km
f) 5832 cm =……… mm
3
3
13. Write in cubic metres:
a)18 km
3
b) 16 dm
3
=
3
c) 500 cm
d) 2.340 mm =
=
3
e) 5,6 dam
=
f) 0,4 hm
3
3
=
=
3
g) 76,89 dm =
j) 45 dam
i) 0,59 cm
3
k) 36,8 km =
=
l) 0,88 dam =
3
14. How many perfume bottles of 22cl will I be able to fill up with 15litres of perfume?
2
15.A field has an area of 13,98 ha. We have planted corn in an area of 4 hm 15 dam
2
56 m . What’s the area left?
16. A tanker truck is carrying 3kl 5 hl 2dal of petrol. It has just served an order of
9hl 7dal 5dl. How many litres are left?
17. A runner’s stride is 1,5m. How many strides will be if he runs 1 km?
CHECK YOURSELF
1) Complete:
a) 38,8 m =….hm
b) 0,058 hm = …..cm
c) 39,78 dam =…..m
d) 0,887 dam =….. mm
e) 0,030 Km =…... m
f) 3456,93 dm =….. Km
2) Complete:
a) 8998 km
b) 38 m
2
2
=…… dm
=…… dm
2
2
=
3
h) 16, 6 mm =
3
3
d) 3,88 mm
2
=…… m
2
e) 0,05 km
2
=….. m
2
2
c) 150 hm
2
=…. cm
2
f) 3456,93 mm
2
=…… dm
2
3) Express the following in….:
a) 27,88
cm 3  ... mm3
b) 0,008 Km
c) 0,08
3
dam 3
 ... dm 3
 .... dm 3
4) Express the following in…:
a) 2,75 kl =……l
b)950l =…. dal
c)3,6 ml =….. cl
5) Complete:
a) 4,08 Kg =….. g
b) 58 dg =…..dag
c) 33,7 hg=…..cg
mm3  ... dm 3
3
e) 1256 dam
 ... hm 3
3
f) 3456,93 cm
 ... m 3
d) 388,7
d)0,01 hl =…..dl
e) 0,008 dal =….ml
f)5 ml =….. hl
d) 2 cg =…. hg
e) 0,05 dag =…. dg
f) 3456,944 mg =….g
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