3.07 Converting units

We can apply our understanding of ratios and proportional relationships to convert units.

Worked examples

Question 1

Evaluate: The ratio of miles to kilometers is $1:1.6$1:1.6. Use this fact to find out how many kilometers are equal to $5$5 miles.

Think:  The given ratio of $1:1.6$1:1.6 means that $1$1 mile is equal to $1.6$1.6 kilometers.  Set up a ratio problem, identifying by what factor each part of the ratio needs to be multiplied to give $5$5 miles.

Do: 

miles	to	kilometers
$1$1	$:$:	$1.6$1.6
to get $5$5 miles, we need $5$5 lots of  the part representing miles in the ratio		so we also need to multiply the number of kilometers by $5$5
$1\times5$1×5	$:$:	$1.6\times5$1.6×5
$5$5	$:$:	$8$8

So $5$5 miles is equivalent to $8$8 kilometers.

 

Question 2

$1$1 gallon is around $3.8$3.8 liters.

a)  State this as a ratio of liters to gallons, in the form $a:b$a:b. Give your answer in simplest form.

Think: We want a ratio that compares the number of liters to the numer of gallons. 

Do: Liters:Gallons = $3.8:1$3.8:1

Simplest form is without fractions or decimals:

$3.8$3.8	$:$:	$1$1	multiply both parts by $10$10 to remove the decimal
$38$38	$:$:	$10$10	divide both parts by common factor of $2$2
$19$19	$:$:	$5$5	this is in simplest form

This means that $19$19 liters is equivalent to $5$5 gallons.

 

b) How many liters would a $15$15 gallon vat hold?

Think: Use the conversion ratio.

Do: 

Liters	to	Gallons
$19$19	$:$:	$5$5	for $15$15 gallons we need to multiply the $5$5 "gallons" parts by $3$3.
$19\times3$19×3	$:$:	$5\times3$5×3	so we need to multiply both parts of the ratio by $3$3
$57$57	$:$:	$15$15

So $15$15 Gallons is equivalent to $57$57 Liters. 

 

Practice questions

Question 3

Question 4