lnternational System of Units

Sf comes from the French, Le Sysfdm e lnternational d'Unit6s which translates to International System of Units'

This is the modern form of the metric system and is devised around mutliples of ten. lt is the world's most

used system of mebsurement. Below is a list of some common quantities and their Sl units'

Metric ConversionsA prefix may be added to a unit to produce a multiple of the original unit. All multiples are in powers of ten'The prefix in OotO are the most commonly used ones in science. The shaded boxes are those multiples where

a prefix does not exist.

How many times largar compared to unit? Given that unit = 1, what equates to it?

Mega M 106=1000000 0.000001 megaunit

105 = 100 000

104 = 10 000

Kilo k 103 = 1000 0.001 kilo unit

Hecta h 102 = 100 0.01 hectaunit

Deca da 101 = 10 0.1 decauni t

Unit 100 = 1 1 unit

Deci d 10-1 = 0.1 10 deciuni t

Centi c 10-2 = 0.01 100 centiunit

Mil l i m 10-" = 0.001 1 000 mi l l iuni t

10-a * 0.000 1

104 * 0.000 01

Micro F 10€ = 0.000 001 1 000 000 microunit

10"7 * 0.000 000 1

10{ = 0.000 000 01

Nano n 10-e = 0.000 000 001 1 000 000 000 nanounit

ketvin

Luminous intensitY

Prefix Length Mass Volume

Unit 100 m 259 5L

The above unit is equalto..

Mega 0.0001 Mm a.5 x tO€Hg5 x to-bHuKilo O.l Km o,ofs K9 o.oo5 KL

Hecta lhm o,e5 hg o,o5 hL

Deca lO dam 2,5 dog o.5 daL

Deci I ooo dm a6o dq 5o at-Centi loooo cm 35o ca 5oo cLMil l i lx tO5 mm 35ooo mg 5@o cnL

Micro lx tOr pm t .5 x tortrg 5 x tot" trltNano lx [Or l nm t.5 y to'ong Sxto9nL

Practice: With each of the given unit below, practicethe conversions by completing the chart.

Practice:

Practice: Convert the following using scientificnotation.

From To

4.45 x 104 ng L{.r{S X IO-a mg

3x103L 3xtOe dL

2.5 x 104 pg 3.5 xtot mg

5.25 x 102 g S,es x lo- l kg

3.80 x 102 mg 3.Eo x lO-a das

6.52 x 102 mL b.6) x lO- l 1

2.5 x 103 kL a.5 xtos L

1.50 x 102 km 1.5 x lO7 cm

9.03 x 1o-3 L q. 03 X loo mL

3.5'x 10-2 hg 3.Sx loo g

2.56 x 1o-3 kL a .56 r loq nL

3.5 x 101 dam 3,5 / lot cm

scientific notation.

13.

14.

15.

16.

17.

18.

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20.

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22.

23.

24,

25.

26.

27.

28.

: Convert thr followino and if appropriate change toFrom To Scientific notation

192 cm lq ?O mm l .qaor l03 mm

170 000 m | -1O km t . - to r lo2 km

500 m o. ooos Mm 5 x tO-t Mm

0.42 dam O. OOLta km q.a x lo-3 km

51 000 hm 5 loo km 5,1 r to3 km

4125 dm t {1a.5 m q.t35x lOa m

705 000 pm 705 mm -1 .oS x loa mm

421 mg o. I {a l s A.at x lo- ' s18 m |SOO cm 1.8 xto3 cm

0.0035 m 3 5@ ooo nm 3.5 x lo l" nm

420 cm L{aoo mm r{ .3 x tO3 mm

0.421 km LI2l m q.el x loa m

0,32 ks 33o s 3.a X loa s

3ns o. ooo oo3 ms 3.O x lO-6 ms

100 Mm loo ooo 696 m lx tOs m

5ms 6ooo ps 5 r lo3 ps

Area ConversionsArea is calculated by multiplying units twice such that the final unit is squared (e.g' 10 cm2)'Changing one area unit to another means that the conversion must be performed twice.

Example 1

Gonvert:

Known:

Therefore:

Practice

29.

30.

31.

32.

5 cm2 to mmz

1cm=10mm

lcmxlcm=10mmx10mm1 cm2 = 100 mm2

5cmz x 10 mm x 10 mm = 500 mm21cm 1cm

5cm2x(10mm)2=500mm2( 1cm ) '

5 cm2 x 100 mT2 = 500 mm21 cm'

OR

followitheFrom To

250 m2 ?.5 x toe mm2

6.5 cm2 6.5 x tOe mm2

4000 km2 4 x lol3 cm2

1.2 cm2 l .a x lot pm2

From To

I cm2 8 XtO-q m2

25 m2 a.5 x lO-s km2

I x 106 pm2 8 x loo mm2

0.05 mm2 5 x to' t f cm2

Practice

37.

38.

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42.

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JJ.

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35.

36.

Volume ConversionsVolume is calculated by multiplying units three times such that the final unit is tripled (e.g. 10 cm3).

Chanqinq one volume unit to another means that the conversion must be performed three times.

i;r-;;i";, i md = t rt thus it is possible to change a cubic length measurement to a volume measurement'

theFrom To

500 mm3 o,5 mL

5 cm3 5x to-3 L

0.5 L 5oo cm3

50 cm3 5 x loa mm3

0.05 mL 5 x to-8 m'

5000 m3 5xlO9 mL

55 mm3 5.5 x lo-s L

200 mmz to m2

Known: 1 m = 1000 mm OR 1 mm = 0.001 m

1mx1m=1000mmx1000mm1 m2 = 106 mmz oR

1 mmx 1 mm =0.001 m x0.001 m1 mmz = 10{ m2

200mm2x 1m x 1m =0.002m21000 mm 1000 mm

200 mm2 x 0.001 m x 0.001 fn = 0.002 m21mm 1mm

200mm2x 1m',=0.002m210o mm'

200 mm2 x 10€ m2 = 0.002 m2

Example 3 ^Convert: 1 m" to L

Known:

Therefore:

Solve:

Conclusion:

1m=100cm1cm3=1mL1 mL = 0.001 L

1 mx1 mx1 m=100cmx100cmx100cm1 m3 = 1000000 cmt = 106 cm3

1 m3 = 106 cm3106 cm3 = 1oo mL106 mL x 0.001 L = 1000 L

1mL

1m3=1000L

Scientific NotationExamples:Change the following into scientific notation.

(a) 465 = 4.65 x 10'toi o.oogz =3.2x 1o-3

Practice:1. Express the following into scientific notation'

(a) 3 400 = 3,1{ x lo5 (h) 35 500 = 3, 55 x lo4

(b) 0.000 75 = 7.5 x tO-{ ( i ) 2 000 000 = 3 x lob

(c) 0.000 019 = t .9 x to- s ( j ) 69 = 6 'q x lo l

(d)654000 = o.5r l x los (k)0.147 = l . {Jxl0- l

(e) 1.23 = 1.33 x to l (D 5'8 = 5 '8 x loo

(0 0.000 104 = l .Or{ x lO-* (m)100.2 = | .Ooa x loa

(g) 0.00000003= 3xtO-8 (n)0'015 = l ,5XlO-Q

2. Write the following numbers in expanded form'(a)3x10-2 = o.o3

(b)2.5x103 = 35@

(c)5.21 x10-5 = O.oooo5al

(d) 5.21x 106 = 5 ato ooo

(e) 2.5 x 10-3 = O.oO?5

3. Write the power of 10 necessary to make the following statements correct.3

(a) 3 000 = 3 x 10--- l

(b) 0.27 = 21 x 10- 'o

(c) 7.5 =7.5 x 10-

(d) 480 = 4.8x 104

(e) 0.000 64 = 6.4x 10:5

(0 780 000 = 7.8 x 105-

(gj o.ooo ez1 =2.t x to:5