TACHS Quiz: Unit Conversion

13 questions · exam conditions

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Unit ConversionQuestion 1 of 13

Express $3.25\text{ km}$ in meters.

325 m

3 250 m

32 500 m

3 250 000 m

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TACHS Quiz

TACHS Quiz: Unit Conversion

Practice Unit Conversion in TACHS 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 Conversion, giving you a quick way to practice the rules, question types, and explanations that matter most for TACHS.

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

Express $3.25\text{ km}$ in meters.

325 m
3 250 m (correct answer)
32 500 m
3 250 000 m

Explanation: When converting between metric units, you need to understand the relationship between kilometers and meters. Since "kilo" means 1,000, one kilometer equals 1,000 meters. To convert

3.25 \text{ km}

to meters, multiply by 1,000:

3.25 \times 1,000 = 3,250 \text{ meters}

You can think of this as moving the decimal point three places to the right when converting from a larger unit (km) to a smaller unit (m). Looking at the wrong answers: Choice A (325 m) represents dividing by 10 instead of multiplying by 1,000 — this shows confusion about conversion direction. Choice C (32,500 m) comes from multiplying by 10,000 instead of 1,000, possibly confusing kilometers with some other unit conversion. Choice D (3,250,000 m) results from multiplying by 1,000,000, which would be the conversion factor from kilometers to millimeters, not meters. The correct answer is B: 3,250 m. Study tip: Remember the metric conversion pattern: when going from a larger unit to a smaller unit, you multiply (and the decimal moves right). When going from smaller to larger, you divide (decimal moves left). For km to m, always multiply by 1,000. A helpful memory device: there are more of the smaller units, so the number gets bigger.

Question 2

Express $72\text{ fluid ounces}$ in quarts.

1.75 qt
2.00 qt
2.25 qt (correct answer)
2.50 qt

Explanation: Unit conversion problems like this test your ability to work with different measurement systems and apply conversion factors accurately. When converting between fluid ounces and quarts, you need to know the relationship between these units. To solve this, start with the key conversion: 1 quart = 32 fluid ounces. You can set up a proportion or use dimensional analysis to convert 72 fluid ounces to quarts:

\frac{72 \text{ fl oz}}{1} \times \frac{1 \text{ qt}}{32 \text{ fl oz}} = \frac{72}{32} = 2.25 \text{ qt}

You can also think of this as division:

72 \div 32 = 2.25

quarts. Looking at the wrong answers: Choice A (1.75 qt) likely results from using an incorrect conversion factor, perhaps confusing quarts with pints (16 fl oz = 1 pint would give

72 \div 16 = 4.5

pints, but that's not what's being asked). Choice B (2.00 qt) suggests rounding

72 \div 32

incorrectly or using 36 fl oz per quart instead of 32. Choice D (2.50 qt) might come from miscalculating the division or using an entirely wrong conversion factor. The correct answer is C) 2.25 qt. Study tip: Memorize these liquid measurement conversions: 8 fl oz = 1 cup, 2 cups = 1 pint, 2 pints = 1 quart. This gives you 32 fl oz = 1 quart. Always double-check your conversion factor direction—you want the unwanted units to cancel out.

Question 3

Convert $9\text{ square feet}$ to square inches.

864 sq in
1 152 sq in
1 296 sq in (correct answer)
1 440 sq in

Explanation: When converting between square units, you're dealing with area measurements, which means you need to square the linear conversion factor. This is a crucial distinction from converting simple length measurements. To convert from square feet to square inches, start with the basic linear conversion:

1 \text{ foot} = 12 \text{ inches}

. Since you're working with square units, you must square this relationship:

1 \text{ square foot} = 12 \times 12 = 144 \text{ square inches}

. Now multiply:

9 \text{ square feet} \times 144 \frac{\text{square inches}}{\text{square foot}} = 1{,}296 \text{ square inches}

. This confirms answer choice C is correct. Let's examine why the other options are wrong. Choice A (864 sq in) results from incorrectly using 96 as the conversion factor—this might come from mixing up different unit conversions. Choice B (1,152 sq in) uses 128 as the conversion factor, which has no basis in the foot-to-inch relationship. Choice D (1,440 sq in) suggests using 160 as the conversion factor, another arbitrary number that doesn't relate to the correct conversion. The most common error students make is forgetting to square the linear conversion factor. If you incorrectly used just 12 instead of 144, you'd get 108 square inches—far too small and not even among the choices, which should signal the mistake. Remember: when converting square units, always square the linear conversion factor. For square feet to square inches, it's always

144

, not

12

Question 4

$1\,500\text{ cm}^3$ is equivalent to how many milliliters?

150 mL
500 mL
1 500 mL (correct answer)
15 000 mL

Explanation: When you encounter volume conversion problems, remember that cubic centimeters and milliliters have a direct 1:1 relationship. This is one of the most useful conversions in science and math because

1 \text{ cm}^3 = 1 \text{ mL}

exactly. To solve this problem, you simply need to recognize this fundamental relationship. Since

1\,500 \text{ cm}^3

needs to be converted to milliliters, and each cubic centimeter equals exactly one milliliter, the answer is

1\,500 \text{ mL}

. This makes choice C correct. Let's examine why the other options are wrong. Choice A (150 mL) suggests you divided by 10, which might happen if you confused this conversion with a different metric conversion. Choice B (500 mL) appears to result from dividing by 3, which has no basis in volume conversion. Choice D (15,000 mL) indicates you multiplied by 10, possibly confusing this with conversions involving different units like liters to milliliters. The key trap here is overthinking the conversion. Many students expect volume conversions to be more complicated than they actually are between cubic centimeters and milliliters. Unlike other metric conversions that involve powers of 10, this particular conversion is straightforward because both units measure the same thing in equivalent ways. Remember this rule:

\text{cm}^3 = \text{mL}

always. When you see cubic centimeters to milliliters (or vice versa), the numbers stay the same—just change the units. This direct relationship makes these conversions much simpler than they appear.

Question 5

How many milliliters are in $0.5\text{ liter}?$

5 mL
50 mL
500 mL (correct answer)
5 000 mL

Explanation: This question tests your understanding of metric unit conversions, specifically between liters and milliliters. When converting between metric units, you need to know the relationship between the units and apply the correct multiplication factor. The key relationship here is that 1 liter equals 1,000 milliliters. To find how many milliliters are in 0.5 liters, you multiply:

0.5 \text{ L} \times 1,000 \text{ mL/L} = 500 \text{ mL}

. Think of it this way: if one whole liter contains 1,000 mL, then half a liter (0.5 L) contains half of 1,000 mL, which is 500 mL. Let's examine why the other answers are incorrect. Choice A (5 mL) represents a major error—this would mean 0.5 liters equals just 5 milliliters, which would make a liter smaller than a milliliter. Choice B (50 mL) suggests multiplying by 100 instead of 1,000, confusing the liter-to-milliliter conversion with perhaps centimeters to millimeters. Choice D (5,000 mL) comes from incorrectly multiplying 0.5 by 10,000 instead of 1,000, possibly confusing different metric conversions. Remember the metric conversion pattern: each step up the metric ladder involves multiplying or dividing by powers of 10. For volume, the key conversion to memorize is 1 L = 1,000 mL. When you see decimal amounts like 0.5, multiply that decimal by 1,000 to convert liters to milliliters. This fundamental conversion appears frequently on standardized tests.

Question 6

How many cups are in $5\text{ gallons}?$

40 cups
60 cups
80 cups (correct answer)
100 cups

Explanation: This question tests your ability to convert between units of liquid measurement, specifically from gallons to cups. When you encounter unit conversion problems, always identify the conversion factors you need and work step by step. To convert gallons to cups, you need to know the relationships in the US customary system: 1 gallon = 4 quarts, and 1 quart = 4 cups. This means 1 gallon = 16 cups. For 5 gallons, multiply:

5 \text{ gallons} \times 16 \text{ cups per gallon} = 80 \text{ cups}

Looking at the wrong answers: Choice A (40 cups) represents a common error where students remember that 1 gallon = 4 quarts but forget to convert quarts to cups, stopping at

5 \times 8 = 40

. Choice B (60 cups) might result from incorrectly thinking 1 gallon = 12 cups, perhaps confusing liquid measurements with other unit systems. Choice D (100 cups) suggests the misconception that 1 gallon = 20 cups, which could come from rounding errors or mixing up different conversion factors. The correct answer is C: 80 cups. Study tip: Memorize the key liquid measurement conversions: 1 gallon = 4 quarts = 8 pints = 16 cups. When converting, write out each step rather than trying to do it all mentally—this prevents the calculation errors that create most wrong answer choices in unit conversion problems.

Question 7

How many feet are equivalent to $7\text{ yards}?$

14 ft
21 ft (correct answer)
24 ft
28 ft

Explanation: Unit conversion problems like this test your knowledge of measurement relationships and your ability to apply conversion factors accurately. When you see yards being converted to feet, you need to recall the fundamental relationship between these units. To convert yards to feet, you multiply by the conversion factor:

1 \text{ yard} = 3 \text{ feet}

. So for 7 yards, you calculate:

7 \text{ yards} \times 3 \text{ feet/yard} = 21 \text{ feet}

. This makes choice B correct. Let's examine why the other options are wrong. Choice A (14 ft) represents a common error where students might think there are only 2 feet in a yard, possibly confusing this with other measurement relationships. Choice C (24 ft) suggests the student might have mistakenly used 24 ÷ 7 or confused yards with a different unit that has a different conversion factor. Choice D (28 ft) appears to come from multiplying 7 by 4, which shows confusion about the yards-to-feet relationship. The key strategy here is memorizing core conversion factors. For length measurements, remember: 12 inches = 1 foot, 3 feet = 1 yard, and 5,280 feet = 1 mile. These are fundamental relationships you'll see repeatedly on standardized tests. Always set up your conversion with units that cancel properly—write "7 yards × 3 feet/yard" so you can see the yards cancel out, leaving you with feet as your final unit.

Question 8

$9\,000\text{ g}$ equals how many kilograms?

0.9 kg
9 kg (correct answer)
90 kg
900 kg

Explanation: This question tests your ability to convert between metric units of mass, specifically from grams to kilograms. When converting within the metric system, you need to understand the relationship between units and which direction to move the decimal point. The key relationship here is that 1 kilogram equals 1,000 grams. To convert from grams to kilograms, you divide by 1,000 (or move the decimal point three places to the left). Starting with

9,000\text{ g}

, you calculate:

9,000 \div 1,000 = 9\text{ kg}

. This confirms that answer B is correct. Looking at the wrong answers: Choice A (0.9 kg) results from dividing by 10,000 instead of 1,000, suggesting confusion about the conversion factor. Choice C (90 kg) comes from dividing by only 100, which would be the conversion factor from centimeters to meters, not grams to kilograms. Choice D (900 kg) happens when you multiply by 0.1 instead of dividing by 1,000, showing a fundamental error in the conversion direction. For metric conversions, remember the phrase "King Henry Died By Drinking Chocolate Milk" (kilometer, hectometer, dekameter, meter, decimeter, centimeter, millimeter). Each step represents a factor of 10. Since grams to kilograms involves moving three decimal places (milli- to kilo-), you always divide by 1,000 when converting from the smaller unit (grams) to the larger unit (kilograms). Practice recognizing that larger units mean smaller numbers.

Question 9

A package weighs $132\text{ ounces}$ . What is its mass in pounds?

7.25 lb
7.5 lb
8.25 lb (correct answer)
8.75 lb

Explanation: Unit conversion problems require you to know the relationship between different units of measurement and apply it correctly. When converting between ounces and pounds, you need to remember that there are 16 ounces in 1 pound. To convert 132 ounces to pounds, you divide by 16:

132 \div 16 = 8.25

pounds. You can verify this by multiplying back:

8.25 \times 16 = 132

ounces, which confirms our answer. Let's examine why the other options are incorrect. Choice A (7.25 lb) would equal

7.25 \times 16 = 116

ounces, which is 16 ounces short of our target. Choice B (7.5 lb) gives us

7.5 \times 16 = 120

ounces, still 12 ounces too light. Choice D (8.75 lb) would equal

8.75 \times 16 = 140

ounces, which is 8 ounces too heavy. These wrong answers likely represent common calculation errors or confusion with the conversion factor. The correct answer is C) 8.25 lb. For unit conversion success on the TACHS, memorize key conversion factors like 16 ounces = 1 pound, 12 inches = 1 foot, and 3 feet = 1 yard. Always double-check your work by converting back to the original unit. If you're unsure about a conversion factor during the test, you can sometimes work backwards from the answer choices to determine which one makes sense.

Question 10

Write $3\text{ ft }9\text{ in}$ as a single measurement in feet.

3.45 ft
3.60 ft
3.75 ft (correct answer)
3.90 ft

Explanation: When you see mixed units like feet and inches, you need to convert everything to a single unit. Since the question asks for the answer in feet, you'll convert the inches to feet and add them to the whole feet. To convert inches to feet, remember that there are 12 inches in 1 foot. So 9 inches equals

\frac{9}{12}

feet. Simplify this fraction by dividing both numerator and denominator by 3:

\frac{9}{12} = \frac{3}{4} = 0.75

feet. Now add this to the 3 feet:

3 + 0.75 = 3.75

feet. Let's examine why the other answers are wrong. Choice A (3.45 ft) would result from incorrectly converting 9 inches as

\frac{9}{20} = 0.45

feet, perhaps confusing the conversion factor. Choice B (3.60 ft) comes from treating 9 inches as if there were 15 inches in a foot (

\frac{9}{15} = 0.60

), which is incorrect. Choice D (3.90 ft) results from the common mistake of simply placing the 9 after the decimal point without any conversion, treating "3 ft 9 in" as "3.90 ft." Remember this key fraction conversion: when converting inches to decimal feet, you'll often see these common fractions: 3 inches = 0.25 ft, 6 inches = 0.50 ft, 9 inches = 0.75 ft. Memorizing these quarter-foot increments will help you work faster on similar problems.

Question 11

Convert $2\text{ hr }45\text{ min}$ to seconds.

5 400 sec
7 200 sec
9 900 sec (correct answer)
11 400 sec

Explanation: Time conversion problems require you to work systematically through multiple unit conversions. When converting from larger units (hours and minutes) to smaller units (seconds), you'll multiply at each step. Start by converting everything to minutes first. You have

2 \text{ hr } 45 \text{ min}

. Since there are 60 minutes in 1 hour:

2 \text{ hr} = 2 \times 60 = 120 \text{ min}

. Adding the existing minutes:

120 + 45 = 165 \text{ min}

total. Now convert minutes to seconds. Since there are 60 seconds in 1 minute:

165 \text{ min} \times 60 = 9{,}900 \text{ sec}

. This confirms answer C is correct. Looking at the wrong answers: Choice A (5,400 sec) represents a common error where students might convert only the 45 minutes to seconds (

45 \times 60 = 2{,}700

) and then add the hours incorrectly. Choice B (7,200 sec) is exactly 2 hours in seconds (

2 \times 60 \times 60 = 7{,}200

), suggesting the student forgot to include the 45 minutes entirely. Choice D (11,400 sec) likely comes from incorrectly adding

7{,}200 + 45 \times 60 + 45 \times 10

or making similar calculation errors. For time conversion problems, always convert step-by-step to avoid mistakes: first get everything into the same intermediate unit (like minutes), then convert to your target unit. Double-check by working backwards—9,900 seconds ÷ 60 = 165 minutes ÷ 60 = 2.75 hours = 2 hr 45 min.

Question 12

How many miles are in $13\,200\text{ feet}?$

1.5 miles
2.0 miles
2.5 miles (correct answer)
3.0 miles

Explanation: Unit conversion problems require you to know the relationship between different measurements and set up the conversion correctly. When converting between feet and miles, you need to remember that 1 mile equals 5,280 feet. To convert 13,200 feet to miles, divide by 5,280 feet per mile:

\frac{13,200 \text{ feet}}{5,280 \text{ feet per mile}} = 2.5 \text{ miles}

You can verify this by recognizing that 13,200 is exactly 2.5 times 5,280. Since

5,280 \times 2 = 10,560

and

5,280 \times 0.5 = 2,640

, we get

10,560 + 2,640 = 13,200

. Looking at the wrong answers: Choice A (1.5 miles) would equal only 7,920 feet, which is significantly less than 13,200. Choice B (2.0 miles) equals 10,560 feet, which is close but still 2,640 feet short. Choice D (3.0 miles) would equal 15,840 feet, which overshoots by 2,640 feet. These incorrect answers might result from miscalculating the division or confusing the conversion factor. For unit conversion success, always write down the conversion factor clearly (1 mile = 5,280 feet), set up your division so unwanted units cancel out, and double-check by working backwards. Memorizing that 5,280 feet equals one mile is essential for the TACHS exam.

Question 13

Express $48\text{ inches}$ as yards.

1 yard
1,\dfrac14 yards
1,\dfrac13 yards (correct answer)
1,\dfrac12 yards

Explanation: When converting between units of measurement, you need to know the relationship between the units and set up the conversion correctly. For length measurements, remember that 1 yard equals 36 inches. To convert 48 inches to yards, divide by 36:

48 \div 36 = \frac{48}{36}

. You can simplify this fraction by finding the greatest common factor of 48 and 36, which is 12. Dividing both numerator and denominator by 12 gives you

\frac{48}{36} = \frac{4}{3}

. Converting

\frac{4}{3}

to a mixed number: since

4 \div 3 = 1

with remainder

1

, you get

1\frac{1}{3}

yards. Looking at the wrong answers: Choice A (1 yard) would equal only 36 inches, which is 12 inches short of our target. Choice B (

1\frac{1}{4}

yards) equals

1.25 \times 36 = 45

inches, which is 3 inches too small. Choice D (

1\frac{1}{2}

yards) equals

1.5 \times 36 = 54

inches, which overshoots by 6 inches. Therefore, choice C (

1\frac{1}{3}

yards) is correct. Study tip: Memorize key conversion factors like 12 inches = 1 foot and 36 inches = 1 yard. When converting from smaller to larger units, you divide; when converting from larger to smaller units, you multiply. Always double-check by converting your answer back to the original unit.