Unit Conversions - SAT Math

Convert $2.75$ hours to seconds. (Students may assume $60\text{ min}=1\text{ hr}$ and $60\text{ s}=1\text{ min}$ .)
Answer: 9,900 s We need to convert 2.75 hours to seconds. Set up the conversion using two steps: hours to minutes, then minutes to seconds. First convert to minutes: 2.75 hr × 60 min/hr = 165 minutes. Then convert to seconds: 165 min × 60 s/min = 9,900 seconds. The dimensional analysis shows: 2.75 hr × (60 min/1 hr) × (60 s/1 min) = 2.75 × 3600 = 9,900 s. A common error is multiplying by 60 only once instead of twice. Remember that going from hours to seconds requires two conversion factors.
A recipe needs $3.5$ quarts of broth. How many gallons is this? Use $4\text{ quarts}=1\text{ gallon}$ .
Answer: 0.875 gal We need to convert 3.5 quarts to gallons using 4 quarts = 1 gallon. Set up the conversion: 3.5 quarts × (1 gallon / 4 quarts). Divide: 3.5 ÷ 4 = 0.875 gallons, with quart units canceling. The key error to avoid is multiplying by 4 instead of dividing - since gallons are larger than quarts, we expect fewer gallons than quarts. When converting to a larger unit, divide by the conversion factor.
A recipe needs 2.5 gallons of water. How many cups is this, using $1 \text{ gal}=4 \text{ qt}$ and $1 \text{ qt}=4 \text{ cups}$ ?
Answer: 40 cups The question asks how many cups are in 2.5 gallons of water, using conversions $1 \text{ gallon} = 4 \text{ quarts}$ and $1 \text{ quart} = 4 \text{ cups}$ . Set up the conversion factors as $4 \text{ quarts per 1 gallon}$ and $4 \text{ cups per 1 quart}$ . Start with $2.5 \text{ gal} \times (4 \text{ qt} / 1 \text{ gal}) \times (4 \text{ cups} / 1 \text{ qt})$ , where gallons cancel to quarts, and quarts cancel to cups. First, $2.5 \times 4 = 10$ quarts, then $10 \times 4 = 40$ cups; alternatively, $2.5 \times 16 = 40$ cups since $4 \times 4 = 16$ . A key error might be using only one conversion factor instead of both, leading to incorrect units. For multi-step conversions, write out each factor with units to track cancellation properly.
A fish tank holds $15{,}000\text{ mL}$ of water. Convert this volume to liters using $1{,}000\text{ mL}=1\text{ L}$ . Which answer is correct?
Answer: 15 L We need to convert 15,000 mL to liters using 1,000 mL = 1 L. Set up the conversion: 15,000 mL × (1 L / 1,000 mL). Divide: 15,000 ÷ 1,000 = 15 L, with mL units canceling. A common error is mishandling the thousands separator or decimal placement when dividing by 1,000. Remember that liters are larger than milliliters, so the numerical value should decrease.
A recipe needs $3.5$ quarts of soup. How many gallons is this? Use $4\text{ quarts}=1\text{ gallon}$ .
Answer: 0.875 gal We need to convert 3.5 quarts to gallons using the fact that 4 quarts = 1 gallon. Set up the conversion: 3.5 qt × (1 gal/4 qt) = 3.5/4 = 0.875 gallons. The dimensional analysis shows: quarts × (gallons/quarts) = gallons, with quarts canceling out. A common error is multiplying by 4 instead of dividing by 4, which would give 14 gallons. Remember: when converting to a larger unit, you divide by the conversion factor.
A water tank holds $18$ quarts. How many gallons is this? Use $1\text{ gallon}=4\text{ quarts}$ .
Answer: 4.5 gal We need to convert 18 quarts to gallons using 1 gallon = 4 quarts. Set up the conversion: 18 quarts × (1 gallon/4 quarts) = 18/4 gallons = 4.5 gallons. The dimensional analysis shows quarts canceling with quarts, leaving gallons. Since we're converting to a larger unit (gallons are larger than quarts), we expect a smaller number. A common error is multiplying by 4 instead of dividing, which would give 72 gallons. Remember: when converting to larger units, divide by the conversion factor.
A hiking trail is marked as 2.6 miles long, but a map legend uses feet. Using $1\text{ mile}=5280\text{ ft}$ , how many feet long is the trail?
Answer: 13,728 ft We need to convert 2.6 miles to feet. Set up the conversion using the given factor: 2.6 miles × (5280 ft/1 mile). When we multiply, the mile units cancel: 2.6 × 5280 = 13,728 ft. The key is to multiply the decimal 2.6 by 5280 without rounding: 2.6 × 5280 = 2 × 5280 + 0.6 × 5280 = 10,560 + 3,168 = 13,728. A common error is rounding 2.6 to 3 or miscalculating the decimal multiplication. For test-taking, write out the dimensional analysis to ensure units cancel properly.
A cyclist rides at $18\text{ miles/hour}$ . What is this speed in feet per second? Use $1\text{ mile}=5{,}280\text{ ft}$ and $1\text{ hour}=3{,}600\text{ s}$ . (Convert both the miles and the hour.)
Answer: 26.4 ft/s We need to convert 18 miles/hour to feet/second, requiring two conversions. Set up: 18 miles/hour × (5,280 ft / 1 mile) × (1 hour / 3,600 s). Calculate step by step: 18 × 5,280 = 95,040 ft/hour, then 95,040 ÷ 3,600 = 26.4 ft/s. The miles cancel with miles and hours cancel with hours, leaving ft/s. A common error is converting only the distance or only the time unit. For compound units, always convert both parts using dimensional analysis.
A car trip takes $2$ hours $45$ minutes. How many minutes is the total time?
Answer: 165 min We need to convert 2 hours 45 minutes to total minutes. First convert the hours: 2 hours × 60 min/hour = 120 minutes. Then add the 45 minutes: 120 + 45 = 165 minutes total. A common error is converting only the 45 minutes portion and forgetting to include the hours, or only converting the 2 hours and forgetting the 45 minutes. Always convert all parts of a mixed measurement to the target unit.
A gasoline container holds $2.5$ gallons. How many cups is that? Use $1\text{ gallon}=4\text{ quarts}$ , $1\text{ quart}=2\text{ pints}$ , and $1\text{ pint}=2\text{ cups}$ . (Don't stop after quarts or pints.)
Answer: 40 cups We need to convert 2.5 gallons to cups through multiple steps. Set up the chain: 2.5 gal × (4 qt/1 gal) × (2 pt/1 qt) × (2 cups/1 pt). Calculate step by step: 2.5 × 4 = 10 quarts, then 10 × 2 = 20 pints, then 20 × 2 = 40 cups. The units cancel in sequence: gal→qt→pt→cups. A common error is stopping at quarts (10) or pints (20) instead of continuing to cups.
How many cups are in 2 quarts?
Answer: 8 cups We need to convert 2 quarts to cups using the US customary system conversion factor. Set up the conversion: 2 quarts × (4 cups/1 quart). Calculate: 2 × 4 = 8 cups, with the quart units canceling out properly. The essential conversion factor is that 1 quart = 4 cups in the US measurement system. Students often confuse this with pints (1 quart = 2 pints) or gallons (4 quarts = 1 gallon). For US liquid measurements, remember the hierarchy: cup → pint → quart → gallon with factors of 2, 2, and 4 respectively.
A hiker walks 3.6 miles along a trail. Using $1\text{ mi}=5280\text{ ft}$ , how many feet does the hiker walk?
Answer: 19,008 ft The question asks how many feet a hiker walks if the distance is 3.6 miles, using the conversion 1 mile = 5280 feet. To convert miles to feet, set up the conversion factor as 5280 feet per 1 mile. Start with 3.6 mi × (5280 ft / 1 mi), where the miles units cancel, leaving feet. Calculate 3 × 5280 = 15,840 and 0.6 × 5280 = 3,168, then add them to get 19,008 feet. A common error is forgetting to multiply the decimal portion or misaligning the multiplication. When doing unit conversions, always track units through dimensional analysis to ensure proper cancellation and avoid calculation mistakes.
A storage bin holds $3$ gallons of paint. How many cups is that? Use $1\text{ gallon}=4\text{ quarts}$ , $1\text{ quart}=2\text{ pints}$ , and $1\text{ pint}=2\text{ cups}$ .
Answer: 48 cups We need to convert 3 gallons to cups using a chain of conversions: gallons to quarts to pints to cups. Set up: 3 gal × (4 qt/1 gal) × (2 pt/1 qt) × (2 cups/1 pt) = 3 × 4 × 2 × 2. Calculate step by step: 3 × 4 = 12 quarts, 12 × 2 = 24 pints, 24 × 2 = 48 cups. The dimensional analysis shows all intermediate units cancel, leaving only cups. A shortcut is to multiply all conversion factors first: 4 × 2 × 2 = 16 cups/gallon, then 3 × 16 = 48 cups.
A metal rod has a mass of $1.8$ kilograms. It is cut into $6$ equal pieces. Using $1000\text{ g}=1\text{ kg}$ , what is the mass of each piece in grams?
Answer: 300 g We need to find the mass of each piece when a 1.8 kg rod is cut into 6 equal pieces, with the answer in grams. First, convert the total mass to grams: 1.8 kg × (1000 g/1 kg) = 1800 g. Then divide by 6 to find the mass of each piece: 1800 g ÷ 6 = 300 g per piece. Alternatively, we could divide first (1.8 kg ÷ 6 = 0.3 kg) then convert (0.3 kg × 1000 g/kg = 300 g). Either order gives the same result. When problems involve both unit conversion and other operations, you can often choose the order that seems easiest.
A board is $2.25$ yards long. How many inches long is the board? Use $3\text{ ft}=1\text{ yd}$ and $12\text{ in}=1\text{ ft}$ .
Answer: 81 in We need to convert 2.25 yards to inches using two conversions: yards to feet, then feet to inches. Set up: 2.25 yd × (3 ft/1 yd) × (12 in/1 ft) = 2.25 × 3 × 12. Calculate: 2.25 × 3 = 6.75 ft, then 6.75 × 12 = 81 inches. The dimensional analysis shows: yd × (ft/yd) × (in/ft) = in, with yards and feet canceling. A shortcut is to multiply the conversion factors first: 3 × 12 = 36 in/yd, then 2.25 × 36 = 81 in.
A ribbon is 3.5 yards long. A craft pattern lists lengths in inches. Using $1\text{ yd}=3\text{ ft}$ and $1\text{ ft}=12\text{ in}$ , how many inches long is the ribbon?
Answer: 126 in We need to convert 3.5 yards to inches using two conversion factors. Set up the chain conversion: 3.5 yd × (3 ft/1 yd) × (12 in/1 ft). The yard units cancel with the first conversion, then feet cancel with the second: 3.5 × 3 × 12 = 10.5 × 12 = 126 inches. Notice how dimensional analysis shows the path: yards → feet → inches. A common error is forgetting one conversion step or multiplying 3.5 × 12 directly. When multiple conversions are needed, write each step to track unit cancellation.
A plane flies for $2.5$ hours at an average speed of $480$ miles per hour. Using $1\text{ mile}=5280\text{ ft}$ , how many feet does the plane travel during the flight?
Answer: 6,336,000 ft We need to find the distance traveled in feet when a plane flies at 480 miles per hour for 2.5 hours. First, find the distance in miles: 480 mi/hr × 2.5 hr = 1,200 miles. Then convert to feet: 1,200 mi × (5,280 ft/1 mi) = 6,336,000 feet. The dimensional analysis shows: (mi/hr) × hr × (ft/mi) = ft, with hours and miles canceling. A common error is miscalculating the multiplication of large numbers. When dealing with large results, double-check your arithmetic or use scientific notation.
A factory produces 1.2 tons of material. A report requires the mass in pounds. Using $2000\text{ lb}=1\text{ ton}$ , how many pounds is 1.2 tons?
Answer: 2,400 lb We need to convert 1.2 tons to pounds. Set up the conversion: 1.2 tons × (2000 lb/1 ton). The ton units cancel: 1.2 × 2000 = 2,400 pounds. To multiply: 1.2 × 2000 = 1 × 2000 + 0.2 × 2000 = 2000 + 400 = 2,400. A common error is misplacing the decimal or using 1000 instead of 2000 as the conversion factor. Remember: when converting to smaller units (tons to pounds), multiply to get a larger number.
A square tile has side length $30\text{ cm}$ . What is the tile's area in square meters? Use $100\text{ cm}=1\text{ m}$ . (Area requires squaring the length conversion.)
Answer: 0.09 m $^2$ We need to find the area of a 30 cm × 30 cm square in square meters. First find area in cm²: 30 × 30 = 900 cm². Then convert using (100 cm)² = 10,000 cm² = 1 m²: 900 cm² × (1 m² / 10,000 cm²) = 0.09 m². The key insight is that for area conversions, we must square the linear conversion factor: 100² = 10,000. A common error is using just 100 instead of 10,000 as the conversion factor.
How many centimeters are in 5 meters?
Answer: 500 cm We need to convert 5 meters to centimeters using the metric system conversion factor. Set up the conversion: 5 meters × (100 cm/1 meter). Calculate: 5 × 100 = 500 centimeters, with the meter units canceling out to leave centimeters. The key conversion factor to remember is that 1 meter = 100 centimeters in the metric system. A common mistake is confusing this with millimeters (1000 mm = 1 m) or forgetting the factor of 100. When working with metric conversions, remember that each step up or down the scale involves factors of 10, 100, or 1000.

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