Units of Measurement - Examples, Exercises and Solutions

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

• Step 1: Identify the given information
• Step 2: Apply the appropriate formula
• Step 3: Perform the conversion

Now, let's work through each step:
Step 1: The problem provides us with the volume $16,848 \, \text{dm}^3$.
Step 2: We know that $1 \, \text{dm}^3 = 1 \, \text{l}$. This means that each cubic decimeter is equivalent to one liter.
Step 3: Using this direct equivalence, we can convert $16,848 \, \text{dm}^3$ directly into $16,848 \, \text{l}$.

Therefore, the volume of $16,848 \, \text{dm}^3$ is equivalent to $16,848 \, \text{l}$.

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

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

Now, let's perform the conversion:
Given: $6.8dm^3$

Using the conversion factor, we calculate:
$6.8dm^3 \times 1000ml/dm^3 = 6800ml$

Therefore, the volume of $6.8dm^3$ is equivalent to $6800ml$.

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

• Step 1: Identify the given amount in milliliters which is $3850 \, \text{ml}$.
• Step 2: Use the conversion factor $1 \, \text{dm}^3 = 1000 \, \text{ml}$.
• Step 3: Divide the milliliters by 1000 to convert to cubic decimeters.

Now, let's work through each step:
Step 1: We have $3850 \, \text{ml}$.
Step 2: We need to convert this volume to cubic decimeters using the conversion factor where $1000 \, \text{ml} = 1 \, \text{dm}^3$.
Step 3: Perform the conversion by dividing the milliliters by the conversion factor:

$\frac{3850 \, \text{ml}}{1000 \, \text{ml/dm}^3} = 3.85 \, \text{dm}^3$

Therefore, the solution to the problem is $3.85 \, \text{dm}^3$.

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

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

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

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

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

• Step 1: Identify the conversion factor between liters and milliliters.
• Step 2: Perform the conversion by multiplying the volume in liters by 1000 since $1 \text{ liter} = 1000 \text{ milliliters}$.

Now, let's work through each step:
Step 1: The conversion factor is $1 \text{ liter} = 1000 \text{ milliliters}$.
Step 2: We have $1.6 \text{ liters}$. To convert this into milliliters, multiply $1.6$ by $1000$:

$1.6 \times 1000 = 1600$

Therefore, the solution to the problem is $1600 \text{ ml}$.

The correct choice from the given options is: $1600 \text{ ml}$.

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

• Step 1: Identify the conversion factor.
• Step 2: Apply the conversion factor to the given volume in cubic meters.
• Step 3: Calculate the corresponding volume in liters.

Now, let's work through each step:

Step 1: We know that $1 \, m^3$ is equivalent to $1000 \, l$.

Step 2: We have a volume of $31 \, m^3$. To convert this to liters, we multiply the given volume by the conversion factor:

$31 \, m^3 \times 1000 \, \frac{l}{m^3} = 31000 \, l$.

Step 3: Hence, the volume of $31 \, m^3$ is $31000 \, l$.

Therefore, the solution to the problem is $31000 \, l$.

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

• Step 1: Recognize the equivalence $1 \, \text{cm}^3 = 1 \, \text{ml}$.
• Step 2: Apply the conversion to the given volume.

Now, let's work through the solution:

Step 1: We know that $1 \, \text{cm}^3$ is equal to $1 \, \text{ml}$. This is a standard conversion where every cubic centimeter corresponds exactly to one milliliter.

Step 2: Given the volume of $84 \, \text{cm}^3$, we apply the conversion factor:
$84 \, \text{cm}^3 = 84 \times 1 \, \text{ml} = 84 \, \text{ml}.$

Thus, the volume of $84 \, \text{cm}^3$ is equivalent to $84 \, \text{ml}$.

Therefore, the solution to the problem is $84 \, \text{ml}$.

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

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

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

This calculation shows that 143535 milliliters equals 143.535 liters.

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

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 $1 \text{ m}^3 = (100 \, \text{cm})^3$.
• Step 3: Calculate $(100 \, \text{cm})^3$. This results in $100 \times 100 \times 100 = 1,000,000$ cm³.
• Step 4: Since we need to convert 100 m³, multiply the result for 1 m³ by 100. Thus, $100 \text{ m}^3 = 100 \times 1,000,000 \, \text{cm}^3 = 100,000,000 \, \text{cm}^3$.

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

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

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

• Step 1: Identify the given volume in cubic centimeters. We have $35.3 \, \text{cm}^3$.
• Step 2: Use the conversion factor between cubic centimeters and cubic meters. We know that $1 \, \text{m}^3 = 1,000,000 \, \text{cm}^3$.
• 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:

$\frac{35.3 \, \text{cm}^3}{1,000,000} = \frac{35.3}{1,000,000} \, \text{m}^3$

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

Thus, the correct answer is:

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

From the given choices, the correct choice is:

$\frac{35.3}{1,000,000m^3}$

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 $1 \text{ liter} = 1000 \text{ milliliters}$.

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

$18 \times 1000 = 18000$ milliliters.

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

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

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:

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

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

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

• Step 1: Identify the relationship between meters and centimeters.
• Step 2: Convert from m³ to cm³ using the cubed conversion factor.
• Step 3: Perform the calculation of the volume conversion.

Let's work through each step:
Step 1: We understand that 1 meter is equivalent to 100 centimeters.
Step 2: To convert cubic meters to cubic centimeters, we calculate $(100 \, cm/m)^3$.
Step 3: Perform the calculation $100 \times 100 \times 100 = 1,000,000$.

Therefore, the number of cubic centimeters in a cubic meter is $1,000,000 \, cm^3$.

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

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

• Understand the units conversion relationship.
• Use the conversion factor for area units: $1 \ \text{m}^2 = 10,000 \ \text{cm}^2$.
• Perform the division to obtain the area in square meters.

Now, let's work through each step:

Step 1: We have an area of $291 \ \text{cm}^2$.

Step 2: Use the conversion factor $1 \ \text{m}^2 = 10,000 \ \text{cm}^2$. Therefore, to convert square centimeters to square meters, divide by 10,000.

Step 3: Calculating using the conversion: $291 \ \text{cm}^2 \div 10,000 = 0.0291 \ \text{m}^2$

Therefore, the solution to the problem is $0.0291 \ \text{m}^2$.