Decimal Measurements

🏆Practice decimal measurements

Decimal Measures

To equalize decimal measures, we will proceed according to the following steps:
First step: Identify the larger measure.
Second step: Convert the number with the smaller unit of measure to the larger unit of measure.
Third step: Compare the numbers that now have the same unit of measure

Let's remember the conversion relationship:
11 mm = 1010  cm
100100  cm = 11 meter
11 m = 10001000 mm = 100100 cm

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Test yourself on decimal measurements!

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Which is larger?

0.3 cm ⬜ 3 mm

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Decimal Measurements

In this article, we will learn everything about decimal measurements and we will introduce you to practical methods that will help you convert one measurement to another and even compare them easily. Shall we start?

First, you should know that we will focus on the primary measurements: millimeters, centimeters, and meters or, abbreviating, mm, cm, and m.

The mm measurement unit: is used to measure very small sizes like the length of an ant.
The cm measurement unit: is used to measure slightly larger sizes like the length of a computer or geometric figures.
The meter measurement unit: is used to measure large sizes like the length of a room.

It is important to know the relationship between the different measurements:

11 mm = 1010  cm
100100  cm = 11 meter
11 m = 10001000 mm = 100100 cm

And in practice:
To convert from mm to cm we divide by 1010
To convert from cm to m we divide by 100100
To convert from mm to m we divide by 10001000


What are decimal measurements?

Decimal measurements are measurements that appear in the form of a decimal number.
For example 1.51.5 meters, 143.2143.2 cm, or 6565 mm.
In order for us to compare them, it is crucial that we convert them to the same unit of measurement.

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What will we do?

We will always look for the largest unit of measure among those given to us and convert the others to it.
We will rely on the conversion relationship we noted earlier and thus we will be able to compare the numbers easily.

How is that? Let's see it in an exercise.

Place the appropriate sign = , < ,> 
145.6145.6 cm ______ 1.51.5 meters

Solution:
We will always prefer to convert to the larger unit of measure between the 22 given measurements.
In this exercise, the larger unit of measure is the meter, therefore, we will want to convert 145.6145.6 cm to meters.

How will we do it?
Let's look at the list of relationships between the units, from cm to m 11 meter –> 100100 cm
Therefore, we must divide 145.6145.6 by 100100
*If you don't know how to easily divide decimal numbers by 1010, 100100 or 1,0001,000, you can find everything in the corresponding article and then come back here.
After dividing we obtained 1.4561.456 meters.
Now let's compare the numbers again, having both in the same unit of measure -> meters:

1.4561.456 meters __<___1.51.5
The answer will be (how to compare decimal numbers is explained in the article Decimal Number Comparison)


Do you know what the answer is?

Another exercise

Place the appropriate sign = , < ,> 
2020 cm______ 0.20.2 meters

Solution:
Let's find the largest unit of measure between the 22 given measurements -> meters
Let's convert the given number in centimeters to meters: 2020 cm to meters:
20:100=0.220:100=0.2
Let's write the exercise again:
0.20.2 meters_____ 0.20.2 meters
The answer is ==


Advanced level exercise

Pablo's height is 1.431.43 meter and Daniel's is 177177 cm.
What is the height difference between Pablo and Daniel?

a - 0.340.34 cm
b - 0.340.34 meter
c - 3434 mm

Solution:
We will act according to the steps learned and convert the number with the smaller unit of measure to the larger unit of measure given.
177177 cm are 1.771.77 meter
177:100=1.7177:100=1.7
Now let's calculate the difference between 1.771.77 meter (Daniel's height) and 1.481.48 meter (Pablo's height) and we will get:
1.771.48=0.341.77-1.48=0.34

Attention: the calculation of the difference was made in meters, therefore, the difference is also given in meters and the correct answer is b b –> 0.34 0.34 meter.


Examples and exercises with solutions of decimal measures

Exercise #1

Which is larger?

0.3 cm ⬜ 3 mm

Video Solution

Step-by-Step Solution

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

  • Step 1: Convert 0.30.3 cm to millimeters. Since 11 cm \equals 1010 mm, we have:
  • 0.3cm=0.3×10mm=3mm0.3 \, \text{cm} = 0.3 \times 10 \, \text{mm} = 3 \, \text{mm}.
  • Step 2: Compare the converted measurement (33 mm) with the given 33 mm.

We find that both measurements are equal.

Therefore, 0.30.3 cm is exactly equal to 33 mm.

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

Answer

= =

Exercise #2

Which is larger?

0.6 mts ⬜ 600 cm

Video Solution

Step-by-Step Solution

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: 11 meter = 100100 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, 11 meter equals 100100 centimeters.
Step 3: To convert 0.6 meters to centimeters, multiply by the conversion factor:

0.6meters×100cm/meter=60cm0.6 \, \text{meters} \times 100 \, \text{cm/meter} = 60 \, \text{cm}

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

Since 60cm<600cm60 \, \text{cm} < 600 \, \text{cm}, we conclude:

0.6mts<600cm0.6 \, \text{mts} < 600 \, \text{cm}

Thus, the correct answer to the problem is:

< <

Answer

<

Exercise #3

Which is larger?

4 mts. ⬜ 200 cm

Video Solution

Step-by-Step Solution

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 meters=4×100 centimeters=400 centimeters 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 > > .

Answer

>

Exercise #4

Which is larger?

50 cm ⬜ 5 meters

Video Solution

Step-by-Step Solution

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 50cm<5m 50 \, \text{cm} < 5 \, \text{m} .

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

Answer

<

Exercise #5

Which is larger?

300 cm ⬜ 3 meters

Video Solution

Step-by-Step Solution

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 = 100 centimeters.

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

Answer

= =

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