Units of measurement

Overview:

In this article we will learn what units of measurement are, we will know their different types and we will see examples. At the end of the article you will be able to find a table that concentrates all the units of measure.

A1 - Units of measurement

Table of contents:

With the units of measurement we measure different things or aspects. We will come across them every time we want to quantify something. For example, with measures such as meters and kilometers we can measure length. With measures such as gram, kilogram and ton we can measure weight.

For us the most important measurements are those of the following items:

Length measurements (With units such as the following: centimeter, meter, kilometer).

Measures of weight (With units such as gram, kilogram)

Measures of time (with units such as second, minute, hour)

Monetary measures (with units of the type cent, peso, cent, dollar)

Area measures (With units of the type square centimeter, square meter)

Volume measures (With units of type cubic centimeter, cubic meter, liter)

Practice Units of Measurement

Examples with solutions for Units of Measurement

Exercise #1

Convert dollars to cents:

0.18 $ =? cents

Video Solution

Step-by-Step Solution

In order to answer this question, one must understand that one dollar is equivalent to 100 cents.

Therefore, one dollar is 0.01 cents.

0.18 dollars, therefore, is 18 cents.

You can also achieve this if we multiply by 100.

0.18*100=18

Answer

18 18

Exercise #2

Convert 6112cm3 61\frac{1}{2}cm^3 into cubic decimeter.

Video Solution

Step-by-Step Solution

Let's solve the problem through a series of steps for ease of understanding:

  • Step 1: Identify the volume in cubic centimeters.
    The given volume is 6112cm3 61\frac{1}{2} \, \text{cm}^3 .
  • Step 2: Convert the mixed number to an improper fraction.
    The mixed number 6112 61\frac{1}{2} can be rewritten as 61+12 61 + \frac{1}{2} which equals 1222+12=1232 \frac{122}{2} + \frac{1}{2} = \frac{123}{2} . This is equivalent to 61.5 cubic centimeters.
  • Step 3: Convert cubic centimeters to cubic decimeters.
    Using the fact that 1dm3=1000cm3 1 \, \text{dm}^3 = 1000 \, \text{cm}^3 , we divide the given volume by 1000 to convert from cubic centimeters to cubic decimeters.
    1232÷1000=1232000=61.51000 \frac{123}{2} \div 1000 = \frac{123}{2000} = \frac{61.5}{1000}

Therefore, the volume in cubic decimeters is 61.51000dm3 \frac{61.5}{1000} \, \text{dm}^3 .

Upon examining the available choices, choice 1: 61.51000dm3 \frac{61.5}{1000 \, \text{dm}^3} is the correct answer.

The solution to the problem is 61.51000dm3 \frac{61.5}{1000 \, \text{dm}^3} .

Answer

61.51000dm3 \frac{61.5}{1000dm^3}

Exercise #3

Solve the following problem:

8km2=?m2 8km^2=?m^2

Video Solution

Step-by-Step Solution

Remember that one kilometer equals 1000 meters.

Therefore 8 kilometers equals 8*1000 meters.

The answer is 8000 meters.

Answer

8000m2 8000m^2

Exercise #4

What is 100 m³ written as cm³?

Video Solution

Step-by-Step Solution

To convert 100 m³ to cm³, follow these steps:

  • Step 1: Understand the relationship between meters and centimeters. We know that 1 meter equals 100 centimeters.
  • Step 2: Determine the volume in cubic centimeters for 1 cubic meter. Since 1 m = 100 cm, we have 1 m3=(100cm)31 \text{ m}^3 = (100 \, \text{cm})^3.
  • Step 3: Calculate (100cm)3(100 \, \text{cm})^3. This results in 100×100×100=1,000,000100 \times 100 \times 100 = 1,000,000 cm³.
  • Step 4: Since we need to convert 100 m³, multiply the result for 1 m³ by 100. Thus, 100 m3=100×1,000,000cm3=100,000,000cm3100 \text{ m}^3 = 100 \times 1,000,000 \, \text{cm}^3 = 100,000,000 \, \text{cm}^3.

Therefore, 100 m³ is equivalent to 100,000,000cm3100,000,000 \, \text{cm}^3.

From the given choices, the correct choice is choice 3, which is 100,000,000cm3100,000,000 \, \text{cm}^3.

Answer

100,000,000cm3 100,000,000cm^3

Exercise #5

15min=?hr 15min=?hr

Video Solution

Step-by-Step Solution

To convert 15 minutes to hours, we will use the conversion factor that 1 hour equals 60 minutes. Our task is to determine how many hours 15 minutes represents.

  • Step 1: Start with the given number of minutes, which is 15 minutes.
  • Step 2: Use the conversion formula, which states that the number of hours is equal to the number of minutes divided by 60. This is because there are 60 minutes in one hour.
  • Step 3: Apply the formula: hours=minutes60=1560 \text{hours} = \frac{\text{minutes}}{60} = \frac{15}{60}
  • Step 4: Simplify the fraction 1560\frac{15}{60} by dividing the numerator and the denominator by their greatest common divisor, which is 15.
  • Step 5: Simplify 1560\frac{15}{60} to 14\frac{1}{4}.

Therefore, 15 minutes is equivalent to 14\frac{1}{4} hours.

The correct answer is 14 \frac{1}{4} .

Answer

14 \frac{1}{4}

Exercise #6

What is 18 liters written in milliliters?

Video Solution

Step-by-Step Solution

To convert 18 liters to milliliters, we will follow these steps:

  • Identify the conversion factor from liters to milliliters.
  • Multiply the given number of liters by this conversion factor.

Step 1: The conversion factor is 1 liter=1000 milliliters 1 \text{ liter} = 1000 \text{ milliliters} .

Step 2: Multiply 18 liters by 1000 to convert it to milliliters:

18×1000=18000 18 \times 1000 = 18000 milliliters.

Thus, 18 liters is equal to 18,000 18,000 milliliters.

Therefore, the correct answer is choice 3:18,000 ml\text{choice 3}: 18,000 \text{ ml} . The answer, when compared to the choices, confirms that choice 3 is indeed the correct one.

Answer

18,000ml 18,000ml

Exercise #7

12cm=?dm 12cm=?dm

Video Solution

Step-by-Step Solution

To convert centimeters to decimeters, we'll follow these steps:

  • Step 1: Identify the given information, which is that we have 12 centimeters to convert.
  • Step 2: Recall the conversion relationship: 1 dm=10 cm1 \text{ dm} = 10 \text{ cm}.
  • Step 3: Perform the conversion by dividing the number of centimeters by 10. Thus, the calculation is 12÷10=1.212 \div 10 = 1.2.

Performing the calculation, we find 12 cm=1.2 dm12 \text{ cm} = 1.2 \text{ dm}.

Therefore, the solution to the problem is 1.2 dm1.2 \text{ dm}.

Answer

1.2 1.2

Exercise #8

Convert 6.8dm3 6.8dm^3 into milliliters.

Video Solution

Step-by-Step Solution

To convert 6.8dm36.8dm^3 into milliliters, we'll follow these steps:

  • Step 1: Identify the given volume in cubic decimeters, which is 6.8dm36.8dm^3.
  • Step 2: Use the conversion factor that 1dm3=1000ml1dm^3 = 1000ml.
  • Step 3: Multiply the given volume by the conversion factor to convert cubic decimeters to milliliters.

Now, let's perform the conversion:
Given: 6.8dm36.8dm^3

Using the conversion factor, we calculate:
6.8dm3×1000ml/dm3=6800ml6.8dm^3 \times 1000ml/dm^3 = 6800ml

Therefore, the volume of 6.8dm36.8dm^3 is equivalent to 6800ml6800ml.

Answer

6800ml 6800ml

Exercise #9

15km=?m \frac{1}{5}km=?m

Video Solution

Step-by-Step Solution

To convert 15\frac{1}{5} kilometers to meters, we follow these steps:

  • Step 1: Recognize that the conversion factor is 11 kilometer = 10001000 meters.
  • Step 2: Multiply 15\frac{1}{5} kilometers by 10001000 to find the equivalent in meters.

Let's carry out the calculation:

15 km=15×1000 m \frac{1}{5} \text{ km} = \frac{1}{5} \times 1000 \text{ m} =10005 m = \frac{1000}{5} \text{ m} =200 meters = 200 \text{ meters}

Therefore, the equivalent of 15\frac{1}{5} kilometers in meters is 200\boxed{200}.

Answer

200 200

Exercise #10

0.5m=?cm 0.5m=?cm

Video Solution

Step-by-Step Solution

To solve the problem of converting 0.5 meters to centimeters, we proceed with the following steps:

  • Step 1: Understand the conversion factor. We know that 1 meter is equivalent to 100 centimeters.
  • Step 2: Apply the conversion factor to the given length in meters. Multiply the given length in meters by 100 to convert it to centimeters.

Now, let's apply these steps to solve the problem:
0.5 meters × 100 centimeters per meter = 50 centimeters.

Thus, 0.5 meters is equivalent to 50 centimeters.

Therefore, the correct answer choice is Choice 3: 50 50 .

Answer

50 50

Exercise #11

143535 milliliters are? liters

Video Solution

Step-by-Step Solution

To solve the problem of converting 143535 milliliters to liters, follow these steps:

  • The given quantity is 143535 milliliters (ml).
  • Use the conversion factor: 1 liter=1000 milliliters 1 \text{ liter} = 1000 \text{ milliliters} .
  • Convert milliliters to liters by dividing the milliliters by 1000.

Let's perform the calculation:
143535 ml÷1000=143.535 liters 143535 \text{ ml} \div 1000 = 143.535 \text{ liters}

This calculation shows that 143535 milliliters equals 143.535 liters.

Therefore, the solution to the problem is 143.535l 143.535l .

Answer

143.535l 143.535l

Exercise #12

How many milliliters are in a liter?

Video Solution

Step-by-Step Solution

To solve this conversion problem, follow these steps:

  • Step 1: Recognize the standard conversion in the metric system where 1 liter is equivalent to 1,000 milliliters.
  • Step 2: Apply this knowledge directly to the problem.

Let's work through the steps:

Step 1: Using the metric conversion, we know that 1 liter equals 1,000 milliliters. The metric system is based on powers of ten, which makes conversions straightforward. Here, 1 liter is defined as 1,000 milliliters because 'milli' signifies one-thousandth (1/1,000), making 1 liter = 1,000 * 1 ml.

Step 2: Therefore, applying the conversion to 1 liter yields:

1 liter=1,000 milliliters 1 \text{ liter} = 1,000 \text{ milliliters}

Therefore, the solution to the problem is 1,000ml 1,000ml .

Answer

1,000ml 1,000ml

Exercise #13

35.3 cm³ are? m³

Video Solution

Step-by-Step Solution

To solve this problem, let's follow the necessary conversion steps:

  • Step 1: Identify the given volume in cubic centimeters. We have 35.3cm3 35.3 \, \text{cm}^3 .
  • Step 2: Use the conversion factor between cubic centimeters and cubic meters. We know that 1m3=1,000,000cm3 1 \, \text{m}^3 = 1,000,000 \, \text{cm}^3 .
  • Step 3: Convert the given volume from cubic centimeters to cubic meters. To do this, divide the volume in cubic centimeters by 1,000,000:

35.3cm31,000,000=35.31,000,000m3\frac{35.3 \, \text{cm}^3}{1,000,000} = \frac{35.3}{1,000,000} \, \text{m}^3

Therefore, the equivalent volume in cubic meters is 35.31,000,000m3\frac{35.3}{1,000,000} \, \text{m}^3.

Thus, the correct answer is:

35.31,000,000m3\frac{35.3}{1,000,000} \, \text{m}^3

From the given choices, the correct choice is:

35.31,000,000m3 \frac{35.3}{1,000,000m^3}

Answer

35.31,000,000m3 \frac{35.3}{1,000,000m^3}

Exercise #14

7kg=?gr 7kg=?gr

Video Solution

Step-by-Step Solution

To solve this problem of converting kilograms to grams, we will follow these steps:

  • Step 1: Identify the given weight in kilograms.
  • Step 2: Use the conversion factor 1 kg=1000 g 1 \text{ kg} = 1000 \text{ g} .
  • Step 3: Perform the necessary multiplication.

Let's go through these steps in detail:
Step 1: We have been given a weight of 7 7 kilograms.
Step 2: Recall that 1 kilogram=1000 grams 1 \text{ kilogram} = 1000 \text{ grams} .
Step 3: Multiply the number of kilograms by the conversion factor: 7 kg×1000 g/kg=7000 g 7 \text{ kg} \times 1000 \text{ g/kg} = 7000 \text{ g} This calculation confirms that 7 7 kilograms is equivalent to 7000 7000 grams.

Therefore, the solution to the problem is 7000 grams 7000 \text{ grams} .

Answer

7000 7000

Exercise #15

5000cm=?km 5000cm=?km

Video Solution

Step-by-Step Solution

To solve this problem, we'll follow these steps:

  • Step 1: Convert centimeters to meters.
  • Step 2: Convert meters to kilometers.

Let us work through each step in detail:

Step 1: Convert centimeters to meters.
We know that 1m=100cm 1 \, \text{m} = 100 \, \text{cm} . To convert 5000 centimeters to meters, we divide by 100:
5000cm÷100=50m 5000 \, \text{cm} \div 100 = 50 \, \text{m}

Step 2: Convert meters to kilometers.
We know that 1km=1000m 1 \, \text{km} = 1000 \, \text{m} . To convert 50 meters to kilometers, we divide by 1000:
50m÷1000=0.05km 50 \, \text{m} \div 1000 = 0.05 \, \text{km}

Therefore, the distance of 5000 centimeters is equivalent to 0.05km 0.05 \, \text{km} .

Answer

0.05 0.05