Foundations of Math 10 - UNIT 1 Date.~Ke=---..!..~_·/__

NOTES 1.3 - Convertin2 Between SI and Imperial Systems

When solving problems with measurements, it is really important thatwe work in the same units. We can convert between SI units andImperial units by using:

- unit analysis (multiplying by conversion factors)- proportional reasoning Se.-+ Q... -*', (\.~-5 CAS e ttLA.ct \

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We need to know the relationship between SI units and Imperial units.Our data pages show several conversions. Let's have a look:

\ N\\\ e. .~ \' bO ~ \< yY'\ k::- (A PP(Q x \{Y\ a--\<...;\ j J. = O. q \L·ti.\- m i-«: ~ClC.+\.ft - 0 \~O4:~ m\ \ (\ -::: Q \5~ L-m

A "=" sign shows an "exact conversion".. .' .-* 'to\.\ vJ \\ \ \.AU -\'h IS O+~('\ .

Example: \1 yd = 0.914mj 1 yd = 3 ft. 3ft = 0.9144 m

How many metres (m) are in 1 ft? (*Use unit analysis):

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Foundations of Math 10 - UNIT 1 Date _

A ({~"sign shows an "approximate conversion".

Example: 1 m is often given as 1.094 yd.

Is this conversion exact? (*Use proportional reasoning):'(J-t W\\\ l.tSt an -f.({)cJ ConV-lx.s~O(\ ~ ~0+ ,+:

~4-m (;;OtVf1{' \A~11S)

~ _ X j J. h-\- "~" l'e.prdUnf .,j}j olsCross enu \\-;~21~ (')\q\ !.l- 4- m \ N\

(\)(.\')-::«»o ,q \L.\- 4-') t L'" ~ \/ 0 (q\ L-\-L\- ~ \l · 0q 3 b I ·... .

Since we have to round our answer, the conversion 1m - 1.094 ydis ao-\- \\ -e)<. tl C+ il .~ .

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When estimating between measurement systems, you can useapproximate values (1 in ~ 2.5 em, 1.6 kIP ~ Imi). We can also round \values to make things simpler when we are estimating. (\ ('\ ...\Ih.e.. (a\ t

When an exact conversion is needed, use 1 yd = 0.9144 m to find aconversion between the required units. ~~

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Foundations of Math 10 - UNIT 1 Date _

Problems

Example 1: Convert between SI and Imperial Units:

The speed of light in a vacuum is defined as 299 792 458 ta]».

a) Estimate the speed oflight in mil s (miles per second): \ 0°1a2 boo \<- .~ \ '" \\ e.-?( \ (boq kr(\ me+r \'c.~ ((\t

firs-\- Gon\l.e(-r m --7 kro : ((Y\)

--.s<J- ~ q~ '11.. L\S'l ty( 1- \ \<.m ':0- 9-q q iQz..'45»No\).) \<m ~ ro' .~ S \000 =~ \<m

~ ~ IY' z: ~ q q 1 9 2- \(rn.m\ =- Bqq '1Q2 \<A <. \ r<'\ \ z: l<31 310 \ ~OUIOO'.s s \\bDq~ ~

b) Predict whether the actual speed of light, in mues per second;is greater than your estimate. Justify your prediction.

11\ mj e.s+\ ('(\ a-\L I I r OIAI\cJ....e.d -\-De ~ped d.ou).0 .So)-\Y\t e.S+i mo.4i \s \ e ~s ~h an ~e Utc-htal s~J .

c) Calculate the speed oflight to the nearest mile per second.NOTE: We are calculating not estimating! We cannot useapproximate conversions! ~

We. YY\\,lS+ U$.t e((ac* (»f\\J~v.si()(\S'. \~~ ~\ ffi\t ~

Co'(\"le(t ~ ..ill. ~ ~ -? .'n'li.s -5 S

~ yY"\\" ~ aC\q l ql, 4~~1l1. 'f. ~

6 _ s n \ Ct\ L.\4 r0~ }~ h ~ 16 ~ • 3 q 1--\ n'\l-- ~ -S

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