📝 Make Unit Conversions in the Metric System (28 MCQs)

📖 From Digital SAT Algebra • 1. Basics of Algebra • 28 questions available

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What is Make Unit Conversions in the Metric System?

Definition:
Making unit conversions in the metric system involves changing between metric units (e.g., meters to kilometers, grams to milligrams) using powers of ten, as the system is based on decimals, where each unit differs by a factor of 10, 100, or 1000, making conversions straightforward.

Working:
Use the metric prefixes (kilo-, hecto-, deca-, deci-, centi-, milli-) and their corresponding powers of ten; multiply or divide by the appropriate power of ten to convert, moving the decimal point to the right for larger units to smaller, or left for smaller to larger.

Example:
Convert 2.5 kilometers to meters.
Solution: $1 \text{ km} = 1000 \text{ m}$ ; so $2.5 \text{ km} \times 1000 = 2500 \text{ m}$ .

Reason:
Metric conversions are simpler due to the base-10 system, and they are widely used in science and international contexts, so mastering them is essential for algebraic applications involving scientific notation and measurements.

Easy

Medium

Hard

📝 All Make Unit Conversions in the Metric System MCQs

Q1. A science bottle contains $2.75$ L of solution. A student records the amount in milliliters. Which value is correct, and why?

27.5

mL because liters are divided by

100

275

mL because liters are multiplied by

100

2750

mL because liters are multiplied by

1000

✅

27500

mL because liters are multiplied by

10000

💡 Difficulty: easy | ✅ Correct: C

📖 Explanation: One liter equals $1000$ milliliters, so converting $2.75$ L to milliliters requires multiplying by $1000$ . Thus $2.75\times1000=2750$ mL. The other choices reflect common errors involving incorrect powers of ten.

Q2. A laboratory scale shows $0.048$ kg for a sample. Another student claims this is $48$ g, while a third claims it is $480$ g. Which evaluation is correct?

A.Both students are correct because kilograms and grams have equivalent numerical values

B.The first student is correct because

1

kg equals

1000

g ✅

C.The second student is correct because

1

kg equals

10000

D.Neither is correct because kilograms cannot be converted to grams

💡 Difficulty: medium | ✅ Correct: B

📖 Explanation: Since $1$ kg equals $1000$ g, $0.048$ kg becomes $0.048\times1000=48$ g. The $480$ g answer results from shifting the decimal one place too far, a realistic place-value misconception.

Q3. A water tank holds $3.6$ kL. A technician wants the volume in liters and then in milliliters. Which sequence gives the correct final amount?

3.6

=360

=360000

3.6

=3600

=3600000

mL ✅

3.6

=36000

=36000000

3.6

=36

=36000

💡 Difficulty: medium | ✅ Correct: B

📖 Explanation: A kiloliter is $1000$ liters, so $3.6$ kL equals $3600$ L. Each liter equals $1000$ milliliters, giving $3600000$ mL. This requires two linked conversions and careful tracking of powers of ten.

Q4. A runner's distance is recorded as $8450$ cm. She wants to express it in meters. A student divides by $10$ and obtains $845$ m. What is the error?

A.Centimeters should be multiplied by

100

to obtain meters

B.Centimeters should be divided by

100

, giving

84.5

m ✅

C.Centimeters should be divided by

1000

, giving

8.45

D.Centimeters and meters cannot be directly converted

💡 Difficulty: medium | ✅ Correct: B

📖 Explanation: There are $100$ centimeters in one meter. Therefore, converting $8450$ cm to meters requires division by $100$ : $8450\div100=84.5$ m. Dividing by $10$ confuses the centimeter-to-meter relationship with a single metric step.

Q5. A graph shows the same mass represented at four points: $0.002$ kg, $2$ g, $2000$ mg, and $0.000002$ Mg. Which conclusion best explains the graph?

A.The values represent different masses because their numerical values differ

B.Only

2

g and

2000

mg represent the same mass

C.All four values represent the same mass ✅

D.Only

0.002

kg and

0.000002

Mg represent the same mass

💡 Difficulty: hard | ✅ Correct: C

📖 Explanation: Each value represents $2$ grams: $0.002$ kg equals $2$ g, $2$ g is already in grams, $2000$ mg equals $2$ g, and $0.000002$ Mg also equals $2$ g. The graph tests whether students distinguish numerical size from physical quantity.

Q6. A manufacturer needs $0.75$ m of wire for each device and plans to make $240$ devices. The wire is sold in centimeters. How many centimeters should the manufacturer purchase, assuming no waste?

A.180 cm

B.1800 cm

C.18000 cm ✅

D.180000 cm

💡 Difficulty: medium | ✅ Correct: C

📖 Explanation: Each device requires $0.75$ m, so $240\times0.75=180$ m. Since $1$ m equals $100$ cm, the total is $180\times100=18000$ cm. The problem combines multiplication with unit conversion rather than performing either operation alone.

Q7. A researcher says, 'Because $1$ meter is larger than $1$ centimeter, converting $4.2$ meters to centimeters should make the number smaller.' Another researcher disagrees. Which reasoning is mathematically sound?

A.The first researcher is correct because larger units always produce smaller converted numbers

B.The second researcher is correct because

4.2

m equals

420

cm ✅

C.Both are correct depending on the decimal position

D.Neither is correct because metric conversions require addition

💡 Difficulty: hard | ✅ Correct: B

📖 Explanation: Changing from a larger unit to a smaller unit requires more units to represent the same quantity, so the numerical value increases. Since $1$ m equals $100$ cm, $4.2$ m becomes $420$ cm. The key is preserving the actual quantity.

Q8. A student needs to measure the length of a classroom wall. Which metric unit would give a practical measurement without creating an unnecessarily large or tiny numerical value?

A.Millimeter

B.Centimeter

C.Meter ✅

D.Kilogram

💡 Difficulty: easy | ✅ Correct: C

📖 Explanation: A classroom wall is typically several meters long, making meters the most practical metric unit. Millimeters would produce an unnecessarily large number, while kilograms measure mass rather than length.

Q9. A medicine container holds $750$ mL. A student records its capacity as $7.5$ L. Which statement best evaluates the student's answer?

A.Correct, because

100

mL equals

1

B.Correct, because liters are smaller than milliliters

C.Incorrect, because

750

mL equals

0.75

L ✅

D.Incorrect, because

750

mL equals

75

💡 Difficulty: medium | ✅ Correct: C

📖 Explanation: Since $1000$ mL equals $1$ L, $750$ mL equals $0.75$ L. The student's answer is too large by a factor of $10$ , indicating a likely place-value or conversion-factor error.

Q10. A delivery truck carries $2.4$ tonnes of material. The material is divided equally among $6$ containers. Each container's mass is then recorded in kilograms. What is the mass of each container?

A.40 kg

B.240 kg

C.400 kg ✅

D.4000 kg

💡 Difficulty: medium | ✅ Correct: C

📖 Explanation: First divide $2.4$ tonnes by $6$ , giving $0.4$ tonnes per container. Since $1$ tonne equals $1000$ kg, each container has $400$ kg. The solution requires both division and unit conversion.

Q11. A student claims that $3.5$ kg is less than $850$ g because $3.5$ is a smaller number than $850$ . Which response correctly identifies the mistake?

A.The student should compare the values after converting them to the same unit ✅

B.The student is correct because kilograms always have smaller numbers

C.The student should add

3.5

and

850

before comparing

D.The student should convert grams into meters first

💡 Difficulty: medium | ✅ Correct: A

📖 Explanation: Different units cannot be compared reliably by looking only at their numerical values. Converting $3.5$ kg to grams gives $3500$ g, which is greater than $850$ g. The misconception ignores unit size.

Q12. A graph displays three measurements on a common scale: $0.8$ L, $800$ mL, and $80$ cL. Which interpretation of the graph is correct?

A.The three points represent different capacities

B.Only

0.8

L and

800

mL are equivalent

C.Only

800

mL and

80

cL are equivalent

D.All three points represent the same capacity ✅

💡 Difficulty: hard | ✅ Correct: D

📖 Explanation: Since $1$ L equals $1000$ mL and $1$ L equals $100$ cL, $0.8$ L equals $800$ mL and $80$ cL. Therefore, all three graph points represent the same physical capacity.

Q13. A factory measures a metal rod as $1.25$ m and its mass as $850$ g. It then fills a container with $2.5$ L of liquid. Which set correctly identifies the quantities by type?

A.Length

=1.25

m, mass

=850

g, capacity

=2.5

L ✅

B.Length

=850

g, mass

=1.25

m, capacity

=2.5

C.Length

=2.5

L, mass

=850

g, capacity

=1.25

D.Length

=1.25

m, mass

=2.5

L, capacity

=850

💡 Difficulty: easy | ✅ Correct: A

📖 Explanation: Meters measure length, grams measure mass, and liters measure capacity. Correctly identifying the measurement type prevents invalid comparisons and helps determine which unit conversions are mathematically meaningful.

Q14. A scientist compares $0.006$ kg, $5.5$ g, and $6500$ mg. Which ordering from greatest mass to least mass is correct?

6500

mg,

0.006

kg,

5.5

0.006

kg,

6500

mg,

5.5

6500

mg,

5.5

0.006

0.006

kg,

5.5

6500

mg ✅

💡 Difficulty: hard | ✅ Correct: D

📖 Explanation: Convert all masses to grams: $0.006$ kg is $6$ g, $5.5$ g remains $5.5$ g, and $6500$ mg is $6.5$ g. Therefore, the correct descending order is $0.006$ kg, $6500$ mg, $5.5$ g.

Q15. A water tank contains $4.2$ kiloliters. Which equivalent measurement in liters is correct?

42

420

4200

L ✅

42000

💡 Difficulty: easy | ✅ Correct: C

📖 Explanation: The prefix kilo means $1000$ times the base unit. Therefore, $4.2$ kiloliters equals $4.2\times1000=4200$ liters. The other choices result from incorrectly shifting the decimal or confusing kilo with another metric prefix.

Q16. A technician records a cable length as $7.5$ meters. Another record requires the length in centimeters. Which value should be entered?

0.075

0.75

75

cm ✅

750

💡 Difficulty: medium | ✅ Correct: C

📖 Explanation: The prefix centi represents one hundredth of a base unit, so one meter contains $100$ centimeters. Thus $7.5$ meters becomes $7.5\times100=750$ centimeters. This makes option D correct, not C.

Q17. A student converts $0.84$ meters to millimeters by multiplying by $100$ , obtaining $84$ mm. What is the most important error in the student's reasoning?

A.Milli means one thousandth, so meters must be multiplied by

1000

✅

B.Milli means one hundredth, so meters must be multiplied by

100

C.Meters must be divided by

1000

to obtain millimeters

D.The conversion is impossible because milli is not a metric prefix

💡 Difficulty: medium | ✅ Correct: A

📖 Explanation: The prefix milli means $10^{-3}$ , so $1$ meter equals $1000$ millimeters. Therefore, $0.84$ meters equals $840$ millimeters. The student incorrectly used the factor associated with centi rather than milli.

Q18. A measuring device displays three readings for the same distance: $0.006$ km, $0.06$ hm, and $6$ dam. A graph places these readings at the same physical point. What does this indicate?

A.Only the kilometer and hectometer readings are equivalent

B.Only the hectometer and dekameter readings are equivalent ✅

C.All three readings represent the same distance

D.All three readings must represent different distances

💡 Difficulty: hard | ✅ Correct: B

📖 Explanation: Since $1$ km equals $100$ dam, $0.006$ km equals $0.6$ dam, while $0.06$ hm equals $0.6$ dam. Therefore, the three displayed values are equivalent only if the first value is interpreted carefully; actually $0.006$ km equals $0.6$ dam, not $6$ dam, so the graph cannot place all three at the same physical point.

Q19. A factory needs $35$ dekameters of cable. The cable is sold by the meter. How many meters are needed?

3.5

35

350

m ✅

3500

💡 Difficulty: medium | ✅ Correct: C

📖 Explanation: The prefix deka means $10$ times the base unit. Therefore, $35$ dekameters equals $35\times10=350$ meters. A common misconception is treating deka as $100$ or $1000$ , producing the larger incorrect choices.

Q20. A laboratory sample has a mass of $2.4$ kg. It is divided equally into $8$ portions, and each portion is recorded in grams. What is the mass of one portion?

30

300

g ✅

3000

0.3

💡 Difficulty: medium | ✅ Correct: B

📖 Explanation: First divide $2.4$ kg by $8$ , giving $0.3$ kg per portion. Because kilo represents $1000$ base units, $0.3$ kg equals $300$ g. The problem requires division followed by a prefix-based conversion.

Q21. A designer compares $0.7$ hectometers, $6.5$ dekameters, and $7200$ centimeters. Which measurement is greatest?

0.7

hectometers ✅

6.5

dekameters

7200

centimeters

D.They are all equal

💡 Difficulty: hard | ✅ Correct: A

📖 Explanation: Convert each measurement to meters: $0.7$ hm equals $70$ m, $6.5$ dam equals $65$ m, and $7200$ cm equals $72$ m. Therefore, $0.7$ hectometers is the greatest, requiring comparison after converting unlike prefixes.

Q22. A laboratory records a liquid volume of $3.75$ L. The value must be entered in milliliters. Which decimal movement produces the correct result?

A.Move the decimal

1

place right to get

37.5

B.Move the decimal

2

places right to get

375

C.Move the decimal

3

places right to get

3750

mL ✅

D.Move the decimal

3

places left to get

0.00375

💡 Difficulty: medium | ✅ Correct: C

📖 Explanation: Moving from liters to milliliters changes from a larger unit to a unit that is $1000$ times smaller. Therefore, the decimal moves three places to the right, giving $3.75\times1000=3750$ mL.

Q23. A student converts $0.064$ meters to centimeters and writes $0.64$ cm. Which reasoning best identifies the mistake?

A.The decimal should move two places right, giving

6.4

B.The decimal should move two places left, giving

0.00064

C.The decimal should move one place right, giving

0.64

D.The decimal should move three places right, giving

64

cm ✅

💡 Difficulty: medium | ✅ Correct: D

📖 Explanation: There are $100$ centimeters in one meter, so the decimal must move two places right. Thus $0.064$ m equals $6.4$ cm. The student's answer reflects an incorrect assumption about the number of decimal places.

Q24. A package has a mass of $2.08$ kg. A scale displays grams, and the technician must enter the equivalent value. Which value should appear?

20.8

208

2080

g ✅

20800

💡 Difficulty: easy | ✅ Correct: C

📖 Explanation: The conversion from kilograms to grams requires moving the decimal three places to the right because $1$ kg equals $1000$ g. Therefore, $2.08$ kg becomes $2080$ g, preserving the same physical mass.

Q25. A graph shows measurements of a rod recorded as $0.45$ m, $45$ cm, and $450$ mm. All three points appear aligned at the same physical length. What conclusion is justified?

A.Only

0.45

m and

45

cm are equivalent

B.Only

45

cm and

450

mm are equivalent

C.All three measurements represent the same length ✅

D.The graph must be incorrect because their numerical values differ

💡 Difficulty: hard | ✅ Correct: C

📖 Explanation: Converting $0.45$ m to centimeters gives $45$ cm, while converting $45$ cm to millimeters gives $450$ mm. The different numerical values occur because the units have different sizes, not because the physical lengths differ.

Q26. A recipe requires $1.6$ L of water. The measuring container is marked in deciliters. A student moves the decimal one place left and obtains $0.16$ dL. What should the student have done?

A.Move the decimal one place right to obtain

16

dL ✅

B.Move the decimal two places right to obtain

160

C.Move the decimal one place left to obtain

0.16

D.Leave the decimal unchanged because liters and deciliters are equivalent

💡 Difficulty: medium | ✅ Correct: A

📖 Explanation: A deciliter is one tenth of a liter, so one liter equals ten deciliters. Converting $1.6$ L to deciliters requires moving the decimal one place right, producing $16$ dL. The student's direction was reversed.

Q27. A technician needs to compare $0.0075$ km, $7.5$ m, and $750$ cm. Which statement correctly describes their relationship?

0.0075

km is greatest

7.5

m is greatest

750

cm is greatest

D.All three measurements are equal ✅

💡 Difficulty: medium | ✅ Correct: D

📖 Explanation: Moving from kilometers to meters requires three places right, so $0.0075$ km equals $7.5$ m. Moving from meters to centimeters requires two more places right, so $7.5$ m equals $750$ cm. All represent the same length.

Q28. Three students convert $0.00084$ km to millimeters. Student A gets $0.84$ mm, Student B gets $840$ mm, and Student C gets $840000$ mm. Which evaluation is correct?

A.Student A is correct because the decimal moves three places

B.Student B is correct because the decimal moves six places right ✅

C.Student C is correct because the decimal moves eight places right

D.All three are correct because different decimal movements can represent the same value

💡 Difficulty: hard | ✅ Correct: B

📖 Explanation: Converting kilometers to millimeters requires moving the decimal six places right because $1$ km equals $1,000,000$ mm. Thus $0.00084$ km becomes $840$ mm. Student A stops too early, while Student C moves the decimal too far.

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