PSAT Math Quiz: Unit Conversions

20 questions · exam conditions

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Unit ConversionsQuestion 1 of 20

A swimmer completes $1{,}200$ meters in $15$ minutes. What is the swimmer's speed in kilometers per hour? Use $1000$ m $= 1$ km and $60$ min $= 1$ hr.

0.08 km/hr

4.8 km/hr

8 km/hr

80 km/hr

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PSAT Math Quiz

PSAT Math Quiz: Unit Conversions

Practice Unit Conversions in PSAT Math with focused quiz questions that help you check what you know, review explanations, and build confidence with test-style prompts.

What this quiz covers

This quiz focuses on Unit Conversions, giving you a quick way to practice the rules, question types, and explanations that matter most for PSAT Math.

How to use this quiz

Try each quiz question before looking at the correct answer. Use the explanations to review missed ideas, then come back to similar questions until the pattern feels familiar.

All questions

Question 1

A swimmer completes $1{,}200$ meters in $15$ minutes. What is the swimmer's speed in kilometers per hour? Use $1000$ m $= 1$ km and $60$ min $= 1$ hr.

0.08 km/hr
4.8 km/hr (correct answer)
8 km/hr
80 km/hr

Explanation: The question asks for the swimmer's speed in kilometers per hour, given 1,200 meters completed in 15 minutes, using 1,000 m = 1 km and 60 min = 1 hr. Set up the conversion by finding speed in m/min and applying factors 60 min/hr and 1 km/1,000 m. Speed is 1,200 m / 15 min = 80 m/min. Then, 80 m/min × (60 min/hr) × (1 km/1,000 m) = (80 × 60 / 1,000) km/hr = 4.8 km/hr, with minutes and meters canceling to leave km/hr. A common error is forgetting to convert minutes to hours, leading to 80 m/min × (1 km/1,000 m) = 0.08 km/min, then perhaps multiplying incorrectly. Another mistake is using 100 min/hr instead of 60. Always use dimensional analysis in rate conversions to ensure all units cancel to the desired ones.

Question 2

A hiker walks 3.6 kilometers. How many meters is that? Use $1\text{ km}=1000\text{ m}$ .

360 m
3,600 m (correct answer)
36,000 m
0.0036 m

Explanation: The question asks to convert 3.6 kilometers to meters, using 1 kilometer = 1000 meters. Set up the conversion by multiplying 3.6 km by 1000 m/km. Dimensional analysis: 3.6 km × (1000 m / 1 km) cancels kilometers, leaving meters. The calculation: 3.6 × 1000 = 3,600 m, tracking units. Errors often involve decimal placement, like forgetting to move it for A or adding zeros for C. Dividing instead gives D. Strategy: Recall 'kilo' means 1,000, so shift decimal three places right.

Question 3

A car travels at 66 miles per hour. What is this speed in feet per second? Use $1\text{ mile}=5280\text{ ft}$ and $1\text{ hour}=3600\text{ s}$ . Convert both the distance and the time units.

96.8 ft/s (correct answer)
17.3 ft/s
121 ft/s
348,480 ft/s

Explanation: The question involves converting a speed of 66 miles per hour to feet per second, using 1 mile = 5280 feet and 1 hour = 3600 seconds. Set up the conversion with factors: 66 mi/hr × (5280 ft / 1 mi) × (1 hr / 3600 s) to cancel miles and hours, leaving feet per second. First, compute 66 × 5280 = 348,480, then divide by 3600: 348,480 ÷ 3600 = 96.8 ft/s, with units canceling step-by-step—mi cancels with mi, hr with hr, resulting in ft/s. Dimensional analysis ensures both distance and time are converted correctly by tracking each unit's cancellation. A frequent error is forgetting to convert time, leaving results like 348,480 ft/s, or converting only time, yielding 121 ft/s. Another mistake could be inverting a factor, such as using 3600 s/hr incorrectly, leading to 17.3 ft/s. For tests, break complex conversions into steps and verify units match the desired output before final calculation.

Question 4

A runner completes a $5$ kilometer route in $22$ minutes. What is the runner's average speed in meters per second? Use $1\text{ km}=1000\text{ m}$ and $1\text{ min}=60\text{ s}$ .

0.26 m/s
3.79 m/s (correct answer)
13.6 m/s
227 m/s

Explanation: The question asks for a runner's average speed in meters per second for completing 5 kilometers in 22 minutes, using 1 km = 1000 m and 1 min = 60 s. Set up conversions for distance to meters and time to seconds, then divide distance by time. Using dimensional analysis for speed, convert 5 km × (1000 m / 1 km) = 5,000 m, and 22 min × (60 s / 1 min) = 1,320 s, then speed = 5,000 m / 1,320 s ≈ 3.7879 m/s, rounding to 3.79 m/s. Ensure units align: meters in numerator, seconds in denominator. A common error is forgetting to convert minutes to seconds, leading to meters per minute instead. Another mistake could be inverting the division. For tests, convert all units before calculating and use dimensional analysis to confirm the final unit is correct.

Question 5

A moving company charges by weight in pounds, but a scale reads ounces. A box weighs 88 ounces. Using $16\text{ oz}=1\text{ lb}$ , what is the box's weight in pounds?

5.5 lb (correct answer)
1,408 lb
72 lb
0.1818 lb

Explanation: The question asks to convert a box weight of 88 ounces to pounds, using 16 ounces = 1 pound. Set up the conversion by dividing 88 oz by 16 oz/lb to reach pounds. Dimensional analysis: 88 oz × (1 lb / 16 oz) cancels ounces, leaving pounds. The calculation: 88 / 16 = 5.5 lb, tracking units to confirm. Common errors include multiplying instead of dividing, yielding large numbers like B or C. Reversing the factor might give fractions like D. For test-taking, think of everyday examples: 16 oz = 1 lb, so 80 oz is 5 lb, plus 8 oz is 0.5 lb.

Question 6

A runner completes $5$ kilometers in $25$ minutes. What is the runner's average speed in meters per second? Use $1$ km $= 1000$ m and $60$ s $= 1$ min.

3.33 m/s (correct answer)
12 m/s
0.2 m/s
333 m/s

Explanation: The question asks for a runner's average speed in meters per second after completing 5 kilometers in 25 minutes, using 1 km = 1000 m and 60 s = 1 min. Set up the conversion with speed = distance/time, converting distance to meters and time to seconds using factors 1000 m/1 km and 60 s/1 min. First, convert distance: 5 km × (1000 m/1 km) = 5000 m; then time: 25 min × (60 s/1 min) = 1500 s; now speed = 5000 m / 1500 s = 3.333 m/s, with units canceling to m/s. Rounding to two decimals gives 3.33 m/s. A key error is converting time to seconds but forgetting to convert kilometers to meters, leading to 5 / 1500 = 0.0033 km/s. Another mistake is using minutes in the denominator without conversion, yielding km/min. In rate problems, perform all conversions before dividing to track units via dimensional analysis.

Question 7

A car's fuel economy is rated at 30 miles per gallon. What is the equivalent rating in kilometers per liter? (1 mile = 1.609 km and 1 gallon = 3.785 L)

8.5 km/L
10.5 km/L
12.8 km/L (correct answer)
15.0 km/L

Explanation: Unit conversion problems require you to set up conversion factors that cancel unwanted units while preserving the desired ones. When converting fuel economy from miles per gallon to kilometers per liter, you need to convert both the numerator (miles to kilometers) and denominator (gallons to liters). Start with 30 miles per gallon and set up your conversion factors:

30 \frac{\text{miles}}{\text{gallon}} \times \frac{1.609 \text{ km}}{1 \text{ mile}} \times \frac{1 \text{ gallon}}{3.785 \text{ L}}

The "miles" units cancel, and the "gallon" units cancel, leaving kilometers per liter:

30 \times \frac{1.609}{3.785} = 30 \times 0.425 = 12.75 \text{ km/L}

Rounding to one decimal place gives 12.8 km/L, which is answer choice C. Looking at the wrong answers: Choice A (8.5 km/L) likely results from incorrectly dividing instead of multiplying by one of the conversion factors. Choice B (10.5 km/L) suggests an error in the arithmetic or using approximate conversion factors incorrectly. Choice D (15.0 km/L) probably comes from flipping one of the conversion ratios, such as using 3.785 km per mile instead of 1.609. For unit conversion success on the PSAT, always write out your conversion factors as fractions and verify that unwanted units cancel before calculating. Double-check that your conversion factors are oriented correctly—the unit you want to eliminate should appear in both a numerator and denominator.

Question 8

The pressure on the ocean floor being studied is 3.2 atmospheres. What is this pressure in pascals? (1 atm = 101.3 kPa and 1 kPa = 1,000 Pa)

$3.24 \times 10^{4}$ Pa
$3.24 \times 10^{5}$ Pa (correct answer)
$3.24 \times 10^{6}$ Pa
$3.24 \times 10^{7}$ Pa

Explanation: Unit conversion problems require you to work systematically through multiple conversion factors, keeping track of units at each step to ensure they cancel properly. Starting with 3.2 atmospheres, you need to convert to pascals using the given conversion factors. First, convert atmospheres to kilopascals:

3.2 \text{ atm} \times \frac{101.3 \text{ kPa}}{1 \text{ atm}} = 324.16 \text{ kPa}

Next, convert kilopascals to pascals:

324.16 \text{ kPa} \times \frac{1,000 \text{ Pa}}{1 \text{ kPa}} = 324,160 \text{ Pa}

In scientific notation, this is

3.24 \times 10^5 \text{ Pa}

, which is answer choice B. Choice A (

3.24 \times 10^4 \text{ Pa}

) results from forgetting the final conversion from kilopascals to pascals—stopping at 324.16 kPa and incorrectly expressing this as pascals. Choice C (

3.24 \times 10^6 \text{ Pa}

) adds an extra factor of 10, perhaps from misreading one of the conversion factors. Choice D (

3.24 \times 10^7 \text{ Pa}

) compounds multiple errors, likely from both misreading conversion factors and calculation mistakes. When tackling unit conversions, always write out each step with units included, and verify that unwanted units cancel out completely. Double-check that your final answer makes sense—since pascals are much smaller units than atmospheres, you should expect a large number. Setting up conversion factors as fractions helps you see visually whether units will cancel properly.

Question 9

A height of 5 feet 8 inches is measured for a basketball player. What is this height, to the nearest centimeter, if 1 inch equals 2.54 centimeters?

150 cm
163 cm
173 cm (correct answer)
187 cm

Explanation: Unit conversion problems like this require careful step-by-step calculation and attention to detail. You need to convert mixed units (feet and inches) to a single unit, then apply the given conversion factor. First, convert the height to inches only. Since 5 feet 8 inches equals

5 \times 12 + 8 = 60 + 8 = 68

inches, you're working with 68 total inches. Next, apply the conversion factor: 1 inch = 2.54 centimeters. Multiply the total inches by this factor:

68 \times 2.54 = 172.72

centimeters. Finally, round to the nearest centimeter: 172.72 cm rounds to 173 cm, which is answer choice C. Looking at the wrong answers: Choice A (150 cm) is far too small—this would represent someone under 5 feet tall, suggesting a major calculation error or forgetting to include the feet measurement. Choice B (163 cm) is close but still too small; you might get this if you miscalculated the feet-to-inches conversion or made an arithmetic error in the multiplication. Choice D (187 cm) is too large, possibly resulting from adding the feet and inches incorrectly or using the wrong conversion factor. When tackling unit conversion problems, always convert to a single unit first before applying conversion factors. Double-check your arithmetic, especially when dealing with mixed measurements like feet and inches. These problems test both your calculation skills and your ability to work methodically through multiple steps without making careless errors.

Question 10

A recipe uses 5.5 cups of broth. The measuring pitcher is marked in quarts. Using $4\text{ cups}=1\text{ quart}$ , how many quarts of broth are needed? Choose the closest exact value.

1.375 qt (correct answer)
22 qt
0.727 qt
2.25 qt

Explanation: The question requires converting 5.5 cups of broth to quarts, using the factor 4 cups = 1 quart. Set up the conversion as 5.5 cups × (1 quart / 4 cups) to cancel cups and obtain quarts. Calculate by dividing: 5.5 ÷ 4 = 1.375 quarts, with units canceling as cups in numerator and denominator leave quarts. Dimensional analysis helps track this, ensuring the result is in the desired unit without confusion. A key error is multiplying instead of dividing, yielding large values like 22 quarts, or inverting the factor to get 0.727 quarts. Another mistake could be misreading the factor as 4 quarts per cup, leading to incorrect results like 2.25 quarts. For test-taking, choose the closest exact value as instructed, and double-check the conversion direction by considering if the result makes sense—quarts should be fewer than cups here.

Question 11

A beverage can is labeled 12.0 fluid ounces. Approximately how many milliliters of liquid does the can contain? (1 fl oz = 29.6 mL)

296 mL
325 mL
355 mL (correct answer)
385 mL

Explanation: Unit conversion problems like this test your ability to set up proportions correctly and perform accurate calculations. When you see a conversion factor given, use it as a bridge between the units. To convert 12.0 fluid ounces to milliliters, set up the conversion using the given factor: 1 fl oz = 29.6 mL. Multiply the given amount by the conversion factor:

12.0 \text{ fl oz} \times \frac{29.6 \text{ mL}}{1 \text{ fl oz}} = 12.0 \times 29.6 = 355.2 \text{ mL}

This rounds to 355 mL, making C the correct answer. Let's examine why the other choices are wrong. Choice A (296 mL) represents what you'd get if you divided instead of multiplied:

\frac{12.0}{29.6} \times 100 ≈ 296

. This is a common error when students flip the conversion factor. Choice B (325 mL) might result from using an incorrect conversion factor or rounding errors during calculation. Choice D (385 mL) is too high and could come from miscalculating

12 \times 29.6

or using the wrong conversion factor entirely. Strategy tip: Always write out your conversion setup clearly with units included. The units should cancel out properly (fl oz cancels, leaving mL), which helps you catch setup errors. Also, do a quick reasonableness check—since 1 fl oz converts to about 30 mL, 12 fl oz should be roughly 12 × 30 = 360 mL, confirming that C is in the right ballpark.

Question 12

A recipe uses 3.5 gallons of broth. How many cups is this? (Use $1\text{ gal}=4\text{ qt}$ and $1\text{ qt}=4\text{ cups}$ .)

14 cups
56 cups (correct answer)
3.5 cups
28 cups

Explanation: We need to convert 3.5 gallons to cups. The conversion path is gallons → quarts → cups. First, convert gallons to quarts: 3.5 gal × (4 qt/1 gal) = 14 qt. Then convert quarts to cups: 14 qt × (4 cups/1 qt) = 56 cups. The key is to multiply by both conversion factors sequentially: 3.5 × 4 × 4 = 56. A common error would be to only use one conversion factor, giving 14 cups (choice A). When converting through multiple units, track each step carefully to avoid missing a conversion.

Question 13

A truck carries 1.8 tons of gravel. How many pounds is that? (Use $1\text{ ton}=2000\text{ lb}$ .)

900 lb
3,600 lb (correct answer)
1,800 lb
36,000 lb

Explanation: We need to convert 1.8 tons to pounds. The conversion is straightforward: multiply tons by the conversion factor. Set up: 1.8 tons × (2000 lb/1 ton) = 3,600 lb. Notice how the ton units cancel, leaving pounds. A common error would be dividing instead of multiplying, which would give 0.0009 lb. Another error might be misplacing the decimal, giving 360 lb or 36,000 lb. Always check that your answer makes sense: since 1 ton = 2000 lb, 1.8 tons should be slightly less than 2 × 2000 = 4000 lb.

Question 14

A bag of rice has a mass of 2.4 kilograms. What is its mass in grams? Use $1\text{ kg}=1000\text{ g}$ .

240 g
2,400 g (correct answer)
24,000 g
0.0024 g

Explanation: The question asks to convert a mass of 2.4 kilograms to grams, using 1 kilogram = 1000 grams. Set up the conversion by multiplying 2.4 kg by 1000 g/kg to shift to the base unit. Using dimensional analysis: 2.4 kg × (1000 g / 1 kg) cancels kilograms, resulting in grams. Calculate 2.4 × 1000 = 2,400 g, with units properly tracked. A typical error is adding extra zeros, like multiplying by 10,000 for C, or dividing for D. Misreading the decimal might lead to A. As a strategy, remember metric prefixes: 'kilo' means thousand, so multiply by 1,000 to get grams.

Question 15

A storage cube has a volume of 3 cubic feet. What is its volume in cubic inches? Use $1\text{ ft}=12\text{ in}$ . (Remember to convert volume units appropriately.)

432 in $^3$
5,184 in $^3$ (correct answer)
1,728 in $^3$
62,208 in $^3$

Explanation: The question asks to convert a volume of 3 cubic feet to cubic inches, using 1 foot = 12 inches, remembering volume needs cubing the factor. Set up by multiplying 3 ft³ by (12 in/ft)³ = 1,728 in³/ft³. In dimensional analysis: 3 ft³ × (1,728 in³ / 1 ft³) cancels cubic feet, resulting in cubic inches. Compute 3 × 1,728 = 5,184 in³, emphasizing cubed units. Common errors include not cubing, using 144 or 12, yielding A or C. Over-cubing might lead to D. As a tip, verify with smaller units: 1 ft³ = 1,728 in³, so multiply by 3.

Question 16

A recipe uses $2.5$ gallons of soup. How many cups is this? Use $1\text{ gallon}=4\text{ quarts}$ and $1\text{ quart}=4\text{ cups}$ .

10 cups
20 cups
40 cups (correct answer)
160 cups

Explanation: We need to convert 2.5 gallons to cups. Setting up the conversion with two steps: 2.5 gallons × (4 quarts/1 gallon) × (4 cups/1 quart). First convert to quarts: 2.5 × 4 = 10 quarts. Then convert to cups: 10 × 4 = 40 cups. Notice how the units cancel: gallons → quarts → cups. A common mistake is using only one conversion factor and getting 10 cups. Remember to chain conversions when going through intermediate units.

Question 17

A shipping box has a mass of $3.75$ kilograms. Convert this mass to grams. Use $1\text{ kg}=1000\text{ g}$ .

0.00375 g
375 g
3,750 g (correct answer)
37,500 g

Explanation: We need to convert 3.75 kilograms to grams. Set up the conversion: 3.75 kg × (1000 g/1 kg). Multiply: 3.75 × 1000 = 3,750 grams. The kilogram units cancel, leaving grams. A common mistake is dividing by 1000 instead of multiplying, which would give 0.00375 g. Remember that 'kilo' means 1000, so 1 kilogram equals 1000 grams.

Question 18

A recipe needs 3.5 quarts of soup, but the pot is marked in cups. Using $1\text{ qt}=2\text{ pt}$ and $1\text{ pt}=2\text{ cups}$ , how many cups of soup are needed?

7 cups
14 cups (correct answer)
28 cups
3.5 cups

Explanation: The question asks to convert 3.5 quarts of soup to cups, using 1 quart = 2 pints and 1 pint = 2 cups. Set up the conversion by multiplying 3.5 qt by 2 pt/qt and then by 2 cups/pt to reach the desired unit. In dimensional analysis: 3.5 qt × (2 pt / 1 qt) × (2 cups / 1 pt) shows quarts and pints canceling, leaving cups. Compute 3.5 × 2 = 7, then 7 × 2 = 14 cups, or directly 3.5 × 4 = 14 cups, with units tracking throughout. A frequent error is using only one conversion factor, like just quarts to pints, resulting in 7 cups as in A. Another mistake might be reversing the factors, leading to fractions like D. As a strategy, list all steps with units to catch if intermediate conversions are missed.

Question 19

A recipe needs $3.5$ quarts of broth. How many gallons is this? (Use $4\text{ quarts}=1\text{ gallon}$ .)

0.875 gal (correct answer)
1.167 gal
14 gal
7.5 gal

Explanation: We need to convert 3.5 quarts to gallons using the conversion factor 4 quarts = 1 gallon. Set up the conversion: 3.5 quarts × (1 gallon/4 quarts) = 3.5/4 gallons = 0.875 gallons. The quarts units cancel, leaving gallons. A common error is multiplying by 4 instead of dividing, which would give 14 gallons. When converting to a larger unit (gallons are larger than quarts), your numerical answer should be smaller than what you started with.

Question 20

A runner completes 800 meters in 2.5 minutes. What is the runner's speed in kilometers per hour? Use $1000\text{ m}=1\text{ km}$ and $60\text{ min}=1\text{ hr}$ . Convert both distance and time units.

19.2 km/h (correct answer)
0.32 km/h
32 km/h
4.8 km/h

Explanation: This question requires finding a runner's speed in kilometers per hour from 800 meters in 2.5 minutes, using 1000 meters = 1 kilometer and 60 minutes = 1 hour. Set up the conversion: speed = 800 m / 2.5 min × (1 km / 1000 m) × (60 min / 1 hr) to cancel meters and minutes, leaving km/hr. First, 800 ÷ 2.5 = 320 m/min, then 320 × (60 / 1000) = 320 × 0.06 = 19.2 km/hr, with units canceling properly. Dimensional analysis is essential for rates, showing each factor's role in unit conversion. Common errors include forgetting the time conversion, yielding 0.32 km/min instead of per hour, or inverting factors to get 4.8 km/h. Another mistake is converting distance only, leading to 32 km in some miscalculation. As a strategy, compute speed in original units first, then apply conversions step-by-step, verifying units match the target.