Question

multi - step conversions
chain conversion factors: start × factor1 × factor2 = final answer
example: multi - step
convert 5.2 miles to centimeters: 5.2 mi×1609 m/1 mi×100 cm/1 m = 836,680 cm
more practice problems

1. convert 15 gallons to liters
2. a recipe calls for 250 ml of milk. you only have a measuring cup marked in fluid ounces. how many fluid ounces do you need? (1 fl oz = 29.57 ml)
3. a marathon is 26.2 miles long. how many kilometers is this?
4. your cars gas tank holds 18.5 gallons. how many liters is this?
5. the speed limit is 65 mph. what is this in meters per second? (use: 1 mile = 1609 m, 1 hour = 3600 s)
6. a swimming pool is 25 yards long, 12 yards wide, and 4 feet deep. what is its volume in cubic meters?

answer key
basic problems:

1. 350 cm
2. 0.75 kg
3. 2500 ml
4. 72 in
5. 1.2 m
6. 72 oz

more basic:

1. 850 m
2. 0.35 l
3. 4,022,400 mm
4. 3,856 g
5. 56.8 l
6. 8.45 fl oz

word problems:

1. 42.2 km
2. 70.0 l

challenge:

1. 29.1 m/s
2. 110 m³

study tips:

• always write units in every step
• check that unwanted units cancel out
• use conversion factors that equal 1
• practice with real - world examples daily
• double - check by converting back to original units

Explanation:

Step1: Convert 15 gallons to liters

We know that 1 gallon is approximately 3.78541 liters. So, we multiply 15 by 3.78541.
$15\times3.78541 = 56.78115\approx56.8$ L

Step2: Convert 250 mL of milk to fluid - ounces

Given that 1 fl oz = 29.57 mL, we divide 250 by 29.57.
$\frac{250}{29.57}\approx8.45$ fl oz

Step3: Convert 26.2 miles to kilometers

Since 1 mile = 1.609 km, we multiply 26.2 by 1.609.
$26.2\times1.609 = 42.1558\approx42.2$ km

Step4: Convert 18.5 gallons to liters

Using the conversion factor 1 gallon = 3.78541 liters, we multiply 18.5 by 3.78541.
$18.5\times3.78541=70.020085\approx70.0$ L

Step5: Convert 65 mph to meters per second

First, convert miles to meters: 1 mile = 1609 m, so 65 miles = $65\times1609$ m.
Then convert hours to seconds: 1 hour = 3600 s.
The speed in m/s is $\frac{65\times1609}{3600}=\frac{104585}{3600}\approx29.1$ m/s

Step6: Convert the dimensions of the swimming - pool to meters and find the volume

1 yard = 0.9144 m, so the length $l = 25$ yards $=25\times0.9144 = 22.86$ m, the width $w = 12$ yards $=12\times0.9144 = 10.9728$ m.
1 foot = 0.3048 m, so the depth $h = 4$ feet $=4\times0.3048 = 1.2192$ m.
The volume $V=l\times w\times h=22.86\times10.9728\times1.2192\approx110$ $m^{3}$

Answer:

1. 56.8 L
2. 8.45 fl oz
3. 42.2 km
4. 70.0 L
5. 29.1 m/s
6. 110 $m^{3}$