Decimal Measurements - Examples, Exercises and Solutions

To solve this problem, we'll focus on converting the measurements to the same unit:

• Step 1: Convert $0.3$ cm to millimeters. Since $1$ cm \equals $10$ mm, we have:
• $0.3 \, \text{cm} = 0.3 \times 10 \, \text{mm} = 3 \, \text{mm}$.
• Step 2: Compare the converted measurement ($3$ mm) with the given $3$ mm.

We find that both measurements are equal.

Therefore, $0.3$ cm is exactly equal to $3$ mm.

Conclusion: Hence, the correct choice is $=$, indicating both values are equal.

To solve this problem, we'll proceed with the following steps:

• Step 1: Convert 0.6 meters into centimeters.
• Step 2: Use the conversion factor: $1$ meter = $100$ centimeters.
• Step 3: Perform the conversion and compare the results.

Let's work through these steps:

Step 1: The problem gives us 0.6 meters. We need to convert this to centimeters.
Step 2: Using the conversion formula, $1$ meter equals $100$ centimeters.
Step 3: To convert 0.6 meters to centimeters, multiply by the conversion factor:

$0.6 \, \text{meters} \times 100 \, \text{cm/meter} = 60 \, \text{cm}$

Now, we compare 60 cm (from the conversion) with 600 cm:

Since $60 \, \text{cm} < 600 \, \text{cm}$, we conclude:

$0.6 \, \text{mts} < 600 \, \text{cm}$

Thus, the correct answer to the problem is:

$<$

To solve this problem, we need to compare 4 meters with 200 centimeters. We can simplify this comparison by converting 4 meters into centimeters. This involves the following steps:

• Step 1: Convert meters to centimeters using the conversion factor: 1 meter = 100 centimeters.
• Step 2: Calculate the number of centimeters in 4 meters.
      $4 \text{ meters} = 4 \times 100 \text{ centimeters} = 400 \text{ centimeters}$
• Step 3: Compare the values:
      400 centimeters versus 200 centimeters.

By comparing 400 centimeters to 200 centimeters, it is clear that 400 centimeters is greater than 200 centimeters. Hence, 4 meters is greater than 200 centimeters.

Therefore, the solution to the problem is $>$.

To solve the problem of determining which is larger between 50 cm and 5 m, we need to compare the two measurements in the same units. We'll convert 5 meters into centimeters for a direct comparison.

• Step 1: Convert 5 meters into centimeters. Since 1 meter equals 100 centimeters, we multiply 5 meters by 100 to find its equivalent in centimeters:
• 5 m $\times$ 100 cm/m = 500 cm

Step 2: Compare the two values in centimeters:

• 50 cm and 500 cm

Clearly, 50 cm is less than 500 cm.

Therefore, the correct inequality is $50 \, \text{cm} < 5 \, \text{m}$.

This corresponds to choice $<$ which is choice number 2.

To solve this problem, let's follow our planned steps:

• Step 1: Convert the measurement of 3 meters into centimeters.
• Step 2: Compare the two measurements.

Now, we'll go through each step in detail:

Step 1: Convert 3 meters to centimeters. Using the conversion factor: 1 meter $= 100$ centimeters.

Thus, $3$ meters $= 3 \times 100$ centimeters $= 300$ centimeters.

Step 2: Compare the values: 300 centimeters (initial given) and 300 centimeters (converted from 3 meters).

Since both measurements are equal (300 cm), we conclude they are the same size.

Therefore, the correct comparison is $=$.

To solve this problem, we need to compare two distances: 40 meters and 0.04 kilometers.

Let's follow these steps to reach the solution:

• Step 1: Convert 0.04 kilometers to meters.
• Step 2: Compare the converted distance with 40 meters.

Now, we'll work each step in detail:

Step 1: Convert 0.04 kilometers to meters.

The conversion factor is $1 \text{ km} = 1000 \text{ meters}$.

Thus, $0.04 \text{ km} \times 1000 = 40 \text{ meters}$.

Step 2: Compare the two distances:

We have both distances as 40 meters now. Therefore, 40 meters is equal to 40 meters.

The solution is that the two distances are equal, so the comparison operator is:

$=$

To solve this problem, let's convert both measurements to the same unit for a direct comparison:

• Step 1: Convert 5.34 cm to millimeters.
• Step 2: Use the conversion factor $1 \text{ cm} = 10 \text{ mm}$.
• Step 3: Calculate $5.34 \text{ cm} \times 10 = 53.4 \text{ mm}$.

Now, compare this result with 53 mm:

$\text{5.34 cm} = 53.4 \text{ mm}$> $\text{53 mm}$.

Therefore, 5.34 cm is greater than 53 mm, and the correct symbol to use is $\gt$.

Thus, the solution to the problem is $\gt$.

To determine which measurement is larger, we need to convert the units so they are comparable.

Step 1: Convert kilometers to meters
We know that 1 kilometer is equivalent to 1000 meters. Hence, to convert 0.1 kilometers to meters, we perform the following calculation:
$0.1 \text{ km} \times 1000 \text{ meters/km} = 100 \text{ meters}$

Step 2: Compare the measurements
We are now comparing 5 meters with 100 meters, as both are in the same unit of measurement.

• 5 meters
• 100 meters

Since 5 meters $<$ 100 meters, the comparison shows that the measurement of 5 meters is smaller than 0.1 kilometers.

Thus, the correct answer is: $<$.

To determine which measurement is larger, we'll convert the measurement in centimeters to millimeters to make a direct comparison:

• Step 1: Convert 5 centimeters to millimeters.

Using the conversion ratio, 1 cm = 10 mm, we find:

$5 \, \text{cm} \times 10 \, \frac{\text{mm}}{\text{cm}} = 50 \, \text{mm}$

• Step 2: Compare the two measurements.

Now we compare 40 mm and 50 mm:

$40 \, \text{mm}$ is less than $50 \, \text{mm}$.

Therefore, 40 mm is less than 5 cm when both are expressed in millimeters.

So the correct answer is:

<

To solve this problem, we will compare the sizes of 45.6 mm and 2.3 cm in the same units:

• Convert 2.3 cm to millimeters using the conversion factor: $1 \text{ cm} = 10 \text{ mm}$.

Let's calculate the conversion:

$2.3 \text{ cm} \times 10 \frac{\text{mm}}{\text{cm}} = 23 \text{ mm}$

Now, we have two measurements to compare:

• 45.6 mm
• 23 mm

Since 45.6 mm is greater than 23 mm, we have:

$45.6 \text{ mm} > 2.3 \text{ cm}$

Therefore, the solution to the problem is > .

Let's solve the problem step-by-step:

Darrel walks a distance of $1000$ meters every day as part of his exercise.

Darrel also runs a distance of $1$ kilometer daily. To find this distance in meters, we use the conversion factor:
$1\, \text{kilometer} = 1000\, \text{meters}$

Thus, Darrel runs $1000$ meters.

To find the total distance Darrel covers each day, add the distance he walks to the distance he runs:

Total distance = Walking distance + Running distance

Total distance = $1000 + 1000$

Total distance = $2000$ meters

Therefore, Darrel covers a total of $2000$ meters each day.

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

• Step 1: Convert the total length of the wall Nigel builds from kilometers to meters.
• Step 2: Calculate the average number of meters built each day.

Now, let's work through each step:

Step 1: Nigel builds a wall that is 5 kilometers long. Since $1 \text{ km} = 1000 \text{ m}$, we convert kilometers to meters:

$5 \text{ km} = 5 \times 1000 \text{ m} = 5000 \text{ m}$

Step 2: Since the wall is built over 2 days, we divide the total length in meters by the number of days to find the average:

$\text{Average meters per day} = \frac{5000 \text{ m}}{2 \text{ days}} = 2500 \text{ m/day}$

Therefore, on average, Nigel builds 2500 meters of the wall each day.

Thus, the correct answer is choice $\boxed{3}$ with 2500 m per day.

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

• Step 1: Convert the distance traveled to the grandfather's house from meters to kilometers.
• Step 2: Add the converted distance to the distance traveled from the grandfather's house to the workplace.
• Step 3: Present the total distance in kilometers.

Now, let's work through each step:

Step 1: Miguel travels 300 meters to his grandfather's house. Since 1 kilometer equals 1000 meters, we convert 300 meters to kilometers as follows:

$300 \text{ meters} = \frac{300}{1000} \text{ kilometers} = 0.3 \text{ kilometers}$

Step 2: Miguel then travels 5 kilometers from his grandfather's house to his workplace. To find the total distance traveled, we add these two distances:

$0.3 \text{ kilometers} + 5 \text{ kilometers} = 5.3 \text{ kilometers}$

Step 3: Therefore, the total distance Miguel travels from his house to his workplace each day is $5.3 \text{ kilometers}$.

To calculate the total distance Miguel travels from his house to work each day, we need to consider both segments of his journey:

• First, the distance from his house to his grandfather's house is directly given as 300 meters.
• Next, the distance from his grandfather's house to his workplace is given as 5 kilometers.

We need to convert the 5 kilometers into meters because we want the entire distance in meters. Recall that $1 \text{ kilometer} = 1000 \text{ meters}$.

So, converting 5 kilometers to meters, we have:

$5 \text{ km} = 5 \times 1000 \text{ meters} = 5000 \text{ meters}$

Now, we add the two segments of his journey:

• Distance from the house to grandfather's house: 300 meters
• Distance from grandfather's house to workplace: 5000 meters

The total distance from his house to work is:

$300 \text{ meters} + 5000 \text{ meters} = 5300 \text{ meters}$

Therefore, Miguel travels a total of 5300 meters each day from his house to his workplace.

Given the choices, the correct answer is choice : $5300$.

Let's proceed with the solution:

Step 1: Convert running distance from kilometers to meters.
Since $1 \text{ km} = 1000 \text{ meters}$, the running distance is $1 \times 1000 = 1000$ meters.

Step 2: Add the walking distance and running distance to find the total distance.
Total distance = Walking distance + Running distance.

Walking distance: $1000$ meters.
Running distance: $1000$ meters.

Therefore, the total distance traveled each day is:

$1000 \text{ meters} + 1000 \text{ meters} = 2000 \text{ meters}$.

Thus, Darrel travels $2000$ meters each day.

Please note, the original question presents these as integer values, and there might be a mismatch due to a contextual issue. However, based solely on the given data, the computed total is $2000$ meters.