LEMMA

Foundations

Unit conversions

ALEKS · foundation repairTEAS math

Multiply by fractions equal to 1, arranged so the unwanted units cancel.

What this covers

value×old unitnew unit​
  • Write the given quantity as a fraction over 1.
  • Choose a conversion factor with the old unit on the bottom.
  • Cancel units diagonally the way you cancel numbers.
  • When the 1 of a conversion factor sits on the bottom you multiply; when it sits on top you divide. The units decide, not the sizes.
  • Chain as many factors as needed until only the target unit remains.

Worked example

Worked example

Convert 45 miles per hour to feet per second.

  1. 1hr45mi​⋅1mi5280ft​⋅3600s1hr​Each factor equals 1 and cancels one unwanted unit.
  2. 360045⋅5280​=66Miles and hours cancel, leaving feet per second.
Another worked example

Convert 125 cm to meters.

  1. 125cm⋅100cm1m​100 cm and 1 m describe the same length. The old unit cancels.
  2. 100125​m=1.25mMeters are larger units, so the numerical count becomes smaller.

A common mistake

A mistake Lemma catches

From 72hkm​⋅1km1000m​⋅3600s1h​

72⋅1000⋅360072⋅1000÷3600

“The hours factor went in upside down. km/h has hours on the bottom, so the factor that cancels them has hours on top: 1 h / 3600 s, which divides by 3600: 72 · 1000 ÷ 3600 = 20 m/s. Multiplying by 3600 leaves h² on the bottom and gives 259,200,000 — not a speed in m/s.”

Try one

Sample problem

180 inches is how many feet? Enter the number of feet.

180 in= ? ft

Practice units free

No account, no email. Every line you type is checked by the same computer algebra system as the worked example above.

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