Units of Measurement - Examples, Exercises and Solutions

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

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 $\frac{61.5}{1000 \, \text{dm}^3}$.

Remember that one kilometer equals 1000 meters.

Therefore 8 kilometers equals 8*1000 meters.

The answer is 8000 meters.

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 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: $\text{hours} = \frac{\text{minutes}}{60} = \frac{15}{60}$
• Step 4: Simplify the fraction $\frac{15}{60}$ by dividing the numerator and the denominator by their greatest common divisor, which is 15.
• Step 5: Simplify $\frac{15}{60}$ to $\frac{1}{4}$.

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

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

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 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: $1 \text{ dm} = 10 \text{ cm}$.
• Step 3: Perform the conversion by dividing the number of centimeters by 10. Thus, the calculation is $12 \div 10 = 1.2$.

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

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

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

• Step 1: Recognize that the conversion factor is $1$ kilometer = $1000$ meters.
• Step 2: Multiply $\frac{1}{5}$ kilometers by $1000$ to find the equivalent in meters.

Let's carry out the calculation:

$\frac{1}{5} \text{ km} = \frac{1}{5} \times 1000 \text{ m}$ $= \frac{1000}{5} \text{ m}$ $= 200 \text{ meters}$

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

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: $50$.

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 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, 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 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 $1 \text{ kg} = 1000 \text{ g}$.
• Step 3: Perform the necessary multiplication.

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

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

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 $1 \, \text{m} = 100 \, \text{cm}$. To convert 5000 centimeters to meters, we divide by 100:
$5000 \, \text{cm} \div 100 = 50 \, \text{m}$

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

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