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Wize High School Algebra I Textbook (Common Core) > Quantities and Units

Working with the SI & Imperial Systems

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Converting Lengths Between the SI & Imperial Units

Recall the SI and Imperial units for measuring lengths:

We can convert between SI and Imperial units using the relationship 1 in  =  2.54 cm\boxed{1~in~~=~~2.54~cm}.

Conversion Diagram


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Example: Converting Between SI and Imperial Units

1. Convert 1 ft into cm.

Therefore, 1ft =30.48cm\boxed{1ft~=30.48cm}

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2. Convert 1 yd into m.

Therefore, 1yd = 0.9144m\boxed{1yd~=~0.9144m}

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3. Convert 1mi into km.

Therefore, 1mi ≈ 1.6km\boxed{1mi~\approx~1.6km}

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4. Convert 1m into ft.

Therefore, 1m ≈ 3.28ft\boxed{1m~\approx~3.28ft}

Practice: Converting Between SI and Imperial Units

a) Convert 35 yd into m.

b) Convert 76 km into mi.
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Example: Converting Between SI and Imperial Units

Use these relationships to convert the following:
1in=2.54cm1mm≈0.0394in1ft=30.38cm1cm≈0.3937in1yd=0.9144m1m≈1.094yd1mi≈1.609km1m≈3.281ft1km≈0.6214mi\begin{array}{|cccc|cccc|} \hline 1in&=&2.54cm&&1mm&\approx&0.0394in\\[.3em] 1ft&=&30.38cm&&1cm&\approx&0.3937in\\[.3em] 1yd&=&0.9144m&&1m&\approx&1.094yd\\[.3em] 1mi&\approx&1.609km&&1m&\approx&3.281ft\\[.3em] &&&&1km&\approx&0.6214mi \\ \hline \end{array}

a) Convert 35yd into m.

=35yd×0.9144m1yd=35yd1×0.9144m1yd=35×0.9144m1=32.004m\begin{array}{cl} =&35yd\times\dfrac{0.9144 m}{1yd}\\[1em] =&\dfrac{35\cancel{yd}}{1}\times\dfrac{0.9144 m}{1\cancel{yd}}\\[1em] =&\dfrac{35\times0.9144m}{1}\\[1em] =&32.004m \end{array}

b) Convert 76km into mi.

=76km×1mi1.609km≈76km1×1mi1.609km≈76mi1.609≈47.2mi\begin{array}{cl} =&76km\times\dfrac{ 1mi}{1.609km}\\[1em] \approx&\dfrac{76\cancel{km}}{1}\times\dfrac{1 mi}{1.609\cancel{km}}\\[1em] \approx&\dfrac{76mi}{1.609}\\[1em] \approx&47.2mi \end{array}

OR

=76km×0.6214mi1km≈76km1×0.6214mi1km≈76×0.6214mi1≈47.2mi\begin{array}{cl} =&76km\times\dfrac{ 0.6214mi}{1km}\\[1em] \approx&\dfrac{76\cancel{km}}{1}\times\dfrac{0.6214 mi}{1\cancel{km}}\\[1em] \approx&\dfrac{76\times0.6214mi}{1}\\[1em] \approx&47.2mi \end{array}