PSAT Math Quiz: Unit Conversions

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.

Question 1

1. 360 m
2. 3,600 m (correct answer)
3. 36,000 m
4. 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 2

1. 14 cups
2. 56 cups (correct answer)
3. 3.5 cups
4. 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 3

1. 900 lb
2. 3,600 lb (correct answer)
3. 1,800 lb
4. 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 4

1. 240 g
2. 2,400 g (correct answer)
3. 24,000 g
4. 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 5

1. 432 in$^3$
2. 5,184 in$^3$ (correct answer)
3. 1,728 in$^3$
4. 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 6

1. 10 cups
2. 20 cups
3. 40 cups (correct answer)
4. 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 7

1. 0.00375 g
2. 375 g
3. 3,750 g (correct answer)
4. 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 8

1. 7 cups
2. 14 cups (correct answer)
3. 28 cups
4. 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 9

1. 0.875 gal (correct answer)
2. 1.167 gal
3. 14 gal
4. 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 10

1. 19.2 km/h (correct answer)
2. 0.32 km/h
3. 32 km/h
4. 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.

Question 11

1. 540 in$^2$
2. 6,480 in$^2$ (correct answer)
3. 7,776 in$^2$
4. 3,240 in$^2$

Explanation: The question asks for the area of a 45 square foot rectangular garden in square inches, using 1 foot = 12 inches, noting that area requires squaring the conversion. Set up the conversion factor for area as (12 in / 1 ft)^2 = 144 in² per ft². Using dimensional analysis, start with 45 ft² and multiply by (144 in² / 1 ft²), canceling square feet and leaving square inches. Calculate 45 × 144: 40 × 144 = 5,760, plus 5 × 144 = 720, totaling 6,480 in². A key error is forgetting to square the linear conversion, using just ×12 instead of ×144, which might give 540 in². Another mistake could be squaring after multiplying, leading to incorrect results like 7,776. In tests, always remember to adjust conversion factors for squared or cubed units and write out the dimensional analysis to ensure proper unit cancellation.

Question 12

1. 12 ft/s
2. 66 ft/s (correct answer)
3. 79.2 ft/s
4. 118.8 ft/s

Explanation: We need to convert 45 miles per hour to feet per second. Set up the conversion: 45 mi/h × (5280 ft/1 mi) × (1 h/3600 s). First convert miles to feet: 45 × 5280 = 237,600 ft/h. Then convert hours to seconds: 237,600 ÷ 3600 = 66 ft/s. The key is recognizing that converting the denominator from hours to seconds requires division by 3600. A quick check: 60 mph ≈ 88 ft/s, so 45 mph should be about 3/4 of that.

Question 13

1. 26.4 ft/s (correct answer)
2. 9.5 ft/s
3. 95.0 ft/s
4. 7.3 ft/s

Explanation: We need to convert the cyclist's speed from miles per hour to feet per second. Set up the conversion using the given factors: 18 miles/hour × (5280 ft/1 mile) × (1 hour/3600 s). When we multiply, the miles cancel and hours cancel: 18 × 5280 ft ÷ 3600 s = 95,040 ft ÷ 3600 s = 26.4 ft/s. A common error is dividing by 5280 or multiplying by 3600 instead of dividing, which would give incorrect results. For quick estimation, remember that 1 mph ≈ 1.47 ft/s, so 18 mph should be about 26-27 ft/s.

Question 14

1. 0.03 qt/min (correct answer)
2. 0.3 qt/min
3. 1.8 qt/min
4. 108 qt/min

Explanation: The question asks for a leak rate of 0.45 gallons per hour in quarts per minute, using 1 gal = 4 qt and 60 min = 1 hr. Set up the conversion: multiply by 4 qt/1 gal and then by 1 hr/60 min (or divide by 60 for per minute). Calculate 0.45 gal/hr × (4 qt/1 gal) = 1.8 qt/hr, gallons canceling; then 1.8 qt/hr × (1 hr/60 min) = 0.03 qt/min, hours canceling to per minute. This dimensional analysis tracks the rate units properly. A key error is forgetting the time conversion, leaving 1.8 qt/hr. Another mistake is multiplying by 60 instead of dividing, yielding 108 qt/min. In rate conversions, ensure the denominator unit is converted inversely to the numerator.

Question 15

1. 66 ft/s (correct answer)
2. 132 ft/s
3. 33 ft/s
4. 118,800 ft/s

Explanation: The question requires finding the average speed of a train traveling 90 miles in 2 hours in feet per second, using 5280 ft = 1 mi and 3600 s = 1 hr. Set up with factors 5280 ft / 1 mi and 1 hr / 3600 s, first finding 90 mi / 2 hr = 45 mi/hr. Then 45 mi/hr × (5280 ft / 1 mi) × (1 hr / 3600 s) = 45 × 5280 / 3600 ft/s, mi and hr cancel: 45 × 1.4667 ≈ 66 ft/s. Compute 5280 / 3600 = 1.4667, times 45 = 66. This tracks both units. A key error is not converting time, leading to large numbers like 118,800.

Question 16

1. 10 cups
2. 20 cups
3. 40 cups (correct answer)
4. 80 cups

Explanation: The question asks how many cups are in 2.5 gallons of cleaner per day, using conversions 1 gal = 4 qt, 1 qt = 2 pt, and 1 pt = 2 cups. Set up the conversion chain from gallons to cups using factors 4 qt/gal × 2 pt/qt × 2 cups/pt. This gives 1 gal × 4 qt/gal × 2 pt/qt × 2 cups/pt = 16 cups/gal, so 2.5 gal × 16 cups/gal = 40 cups, with gallons, quarts, and pints canceling to leave cups. The multiplication confirms the total. A common error is stopping at quarts (2.5 × 4 = 10 qt) without continuing. Another mistake might be using 1 qt = 4 cups directly, leading to wrong factors. In chained conversions, write the full dimensional analysis to ensure units cancel step by step.

Question 17

1. 0.075 L
2. 0.75 L (correct answer)
3. 7.5 L
4. 75 L

Explanation: We need to convert 750 milliliters to liters. Set up the conversion: 750 mL × (1 L/1000 mL) = 0.75 liters. The milliliter units cancel, leaving liters. Since 'milli' means one-thousandth, we divide by 1000 to convert mL to L. A common mistake is multiplying by 1000, which would give 750,000 L. When converting from a smaller unit to a larger unit, the numerical value decreases.

Question 18

1. 22 oz
2. 44 oz
3. 80 oz
4. 88 oz (correct answer)

Explanation: We need to convert 5½ pounds to ounces. First express the mixed number as a decimal: 5½ = 5.5 pounds. Set up the conversion: 5.5 lb × (16 oz/1 lb) = 88 ounces. The pound units cancel, leaving ounces. A common error is multiplying only the whole number part (5 × 16 = 80 oz) and forgetting the fraction. When working with mixed numbers, convert to decimals or improper fractions first.

Question 19

1. 5.0 km/h
2. 50.0 km/h
3. 64.8 km/h (correct answer)
4. 648 km/h

Explanation: We need to convert 18 meters per second to kilometers per hour. Set up the conversion: 18 m/s × (1 km/1000 m) × (3600 s/1 h). For the distance: 18 × (1/1000) = 0.018 km. For the time: multiply by 3600 to convert seconds to hours: 0.018 × 3600 = 64.8 km/h. A common error is dividing by 3600 instead of multiplying, which would give 0.005 km/h. When converting rates, remember that converting the denominator requires the reciprocal operation.

Question 20

1. 450 m$^2$
2. 4.5 m$^2$ (correct answer)
3. 45 m$^2$
4. 0.45 m$^2$

Explanation: We need to find the area of a rectangle with dimensions 2.5 meters by 180 centimeters, expressing the answer in square meters. First, convert 180 cm to meters: 180 cm × (1 m/100 cm) = 1.8 m. Now calculate the area: 2.5 m × 1.8 m = 4.5 m². A common mistake is multiplying 2.5 × 180 = 450 without converting units first, which gives an incorrect answer in mixed units. Always convert all measurements to the same unit before multiplying when finding area.