Metric System Conversions Alıştırma Soruları — Armed Services Vocational Aptitude Battery (ASVAB)

Soru 1Soru →

A logistics officer is preparing a cargo flight and needs to balance the weight distribution of four different shipping pallets. Arrange the following pallets in order from the LIGHTEST to the HEAVIEST total mass.

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Cevap

The correct order from lightest to heaviest is: Pallet 4, Pallet 1, Pallet 3, and Pallet 2.

By converting all measurements to kilograms, we find that Pallet 4 is 125 kg, Pallet 1 is 127.5 kg, Pallet 3 is 128 kg, and Pallet 2 is 135 kg. Ordering these mathematical products from lightest to heaviest yields Pallet 4, Pallet 1, Pallet 3, then Pallet 2.

Adım Adım Çözüm

1

Select a common metric base unit for direct comparison.

Kilograms (kg) is chosen as the standard unit.

Comparing multiple quantities with different metric prefixes requires standardizing the units to avoid magnitude errors.

2

Calculate the total mass of Pallet 1.

150 \times 0.85 \text{ kg} = 127.5 \text{ kg}

.

Convert

850 \text{ g}

to kg by dividing by

1,000

, resulting in

0.85 \text{ kg}

per kit. Multiply by the

150

kits.

3

Calculate the total mass of Pallet 2.

45 \times 3 \text{ kg} = 135 \text{ kg}

.

Convert

3,000,000 \text{ mg}

to kg by dividing by

1,000,000

(since

1 \text{ kg} = 1,000,000 \text{ mg}

), resulting in

3 \text{ kg}

per generator. Multiply by the

45

generators.

4

Calculate the total mass of Pallet 3.

132 \text{ kg} - 4 \text{ kg} = 128 \text{ kg}

.

Find the initial mass (

60 \times 2.2 \text{ kg} = 132 \text{ kg}

). Convert the removed packaging to kg (

4,000 \text{ g} \div 1,000 = 4 \text{ kg}

), and subtract it from the total.

5

Calculate the total mass of Pallet 4.

250 \times 0.5 \text{ kg} = 125 \text{ kg}

.

Convert

50,000 \text{ cg}

to kg by dividing by

100,000

(since

1 \text{ kg} = 100,000 \text{ cg}

), resulting in

0.5 \text{ kg}

per filter. Multiply by the

250

filters.

6

Order the final mass values from least to greatest.

Pallet 4 (

125 \text{ kg}

) < Pallet 1 (

127.5 \text{ kg}

) < Pallet 3 (

128 \text{ kg}

) < Pallet 2 (

135 \text{ kg}

).

The question asks for the arrangement from lightest to heaviest.

Anahtar Kavram

Metric Unit Conversions and Multi-Step Operations

Tahmini Süre:3m 0s

Soru 2Soru →

A technician is cutting copper wire for electrical installations. Each installation requires $45$ centimeters of wire. How many meters of wire are needed to complete $20$ installations?

0.9

9

90

90,000

Cevabı ve açıklamayı göster

Cevap: $9$

Cevap

The correct answer is

9

meters.

First, calculate the total length of wire needed by multiplying the requirement for one installation (

45

cm) by the number of installations (

20

), which equals

900

cm. To convert centimeters to meters, divide by the conversion factor of

100

(since

1

meter =

100

centimeters). Dividing

900

by

100

results in exactly

9

meters.

Adım Adım Çözüm

1

Calculate the total amount of wire needed in centimeters.

45 \times 20 = 900

centimeters

To find the overall length required before converting to the requested unit.

2

Convert the total length from centimeters to meters.

900 \div 100 = 9

meters

Because there are

100

centimeters in

1

meter, divide the centimeter value by

100

.

Anahtar Kavram

To convert from a smaller metric unit (centimeters) to a larger metric unit (meters), divide by the appropriate power of ten (in this case, 100).

Soru 3Soru →

A pharmacist is filling $5$ identical prescriptions for a liquid medication. If each prescription requires $120$ milliliters of the medication, how many liters of medication are dispensed in total?

Cevabı ve açıklamayı göster

Cevap: 0.6

Cevap

0.6 Liters

To find the total amount of medication, first multiply the

5

prescriptions by the

120

milliliters needed for each, which equals

600

milliliters. Because the question asks for the answer in liters, and there are

1000

milliliters in

1

liter, divide the

600

milliliters by

1000

. This gives the final answer of

0.6

liters.

Adım Adım Çözüm

1

Calculate the total required volume in milliliters.

600

mL

Since there are

5

prescriptions and each needs

120

milliliters, multiplying them gives the total amount of medication in the initial unit.

2

Convert the total volume from milliliters to liters.

0.6

Liters

The prefix 'milli-' means one-thousandth. To convert from a smaller unit (milliliters) to a larger base unit (liters), divide by

1000

.

Anahtar Kavram

Multi-step metric system conversions between milli-prefixed units and base units.

Soru 4Soru →

A water purification unit processes $450$ liters of water per hour. How many kiloliters of water does it process during an $8$ -hour shift?

3,600,000

3.6

36

3600

Cevabı ve açıklamayı göster

Cevap: $3.6$

Cevap

The water purification unit processes

3.6

kiloliters of water.

The unit processes

450

liters per hour for

8

hours, yielding a total of

3600

liters. Because

1

kiloliter is equal to

1000

liters, dividing

3600

by

1000

results in

3.6

kiloliters.

Adım Adım Çözüm

1

Calculate the total amount of water processed in liters.

450 \times 8 = 3600

liters

The unit processes water at a rate of 450 liters per hour for an 8-hour period.

2

Convert the total volume from liters to kiloliters.

3600 \div 1000 = 3.6

kiloliters

There are 1000 liters in one kiloliter. Converting from a smaller unit (liters) to a larger unit (kiloliters) requires dividing by 1000.

Anahtar Kavram

Metric volume conversions require dividing by powers of 10 when converting to a larger unit. To convert from base units (liters) to kilo- units (kiloliters), divide the value by 1000.

Soru 5Soru →

A military supply officer is inventorying emergency drinking water supplies stored in four different transport containers. To properly balance the cargo load for an upcoming transport flight, the officer needs to evaluate their relative capacities. Arrange the following containers from least to greatest volume of water.

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Cevap

The correct sequence from least to greatest volume is Container C, Container D, Container A, and Container B.

To accurately compare the volumes, each measurement must be standardized to a common unit, such as liters. Container C converts to

450

liters (

450,000 \div 1,000

). Container D converts to

465

liters (

46,500 \div 100

). Container A converts to

480

liters (

0.48 \times 1,000

). Container B is already given as

490

liters. Arranging these converted values from least to greatest yields Container C, Container D, Container A, and Container B.

Adım Adım Çözüm

1

Convert the volume of Container A to liters.

0.48 \text{ kL} \times 1,000 = 480 \text{ L}

The prefix kilo- means 1,000. Multiplying kiloliters by 1,000 converts the measurement to the base unit of liters.

2

Convert the volume of Container C to liters.

450,000 \text{ mL} \div 1,000 = 450 \text{ L}

The prefix milli- means one-thousandth. Dividing milliliters by 1,000 converts the measurement to liters.

3

Convert the volume of Container D to liters.

46,500 \text{ cL} \div 100 = 465 \text{ L}

The prefix centi- means one-hundredth. Dividing centiliters by 100 converts the measurement to liters.

4

Compare the standardized values to establish the final order.

450 \text{ L} < 465 \text{ L} < 480 \text{ L} < 490 \text{ L}

Ordering the converted numerical values directly dictates the arrangement from least to greatest capacity.

Anahtar Kavram

Converting metric capacity units (kiloliters, liters, centiliters, milliliters) to a common base unit to compare magnitudes.

Soru 6Soru →

A wire manufacturing facility operates $40$ extrusion machines simultaneously. Each machine produces $15$ centimeters of copper wire per second. How many kilometers of copper wire do all $40$ machines produce combined in exactly one hour?

0.36

2,160

21.6

21,600

Cevabı ve açıklamayı göster

Cevap: $21.6$

Cevap

The machines produce a combined total of

21.6

kilometers of copper wire in one hour.

First, find the facility's total production per second by multiplying

40

machines by

15

cm, yielding

600

cm/sec. Next, multiply by

3,600

(the number of seconds in one hour) to find the hourly production in centimeters, which equals

2,160,000

cm. Finally, convert centimeters to kilometers by dividing by

100,000

(

100 \text{ cm} = 1 \text{ m}

and

1,000 \text{ m} = 1 \text{ km}

), resulting in

21.6

kilometers.

Adım Adım Çözüm

1

Calculate the total length of wire produced per second by all machines combined.

40 \times 15 = 600

centimeters per second.

This establishes the facility's baseline production rate before factoring in a longer duration.

2

Scale the production rate from seconds to hours.

600 \times 3,600 = 2,160,000

centimeters per hour.

There are

60

seconds in a minute and

60

minutes in an hour, meaning there are

3,600

seconds in exactly one hour.

3

Convert the total length from centimeters to kilometers.

2,160,000 \div 100,000 = 21.6

kilometers.

Since there are

100

centimeters in a meter and

1,000

meters in a kilometer, the total conversion factor is

100,000

centimeters per kilometer.

Anahtar Kavram

Multi-step metric prefix conversions involving time rates and combined totals.

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