Length Units: Arrange the numbers in Ascending Order

To order the given lengths from smallest to largest, we first convert all measurements to a common unit, such as centimeters:

• $2$ cm is already in centimeters.
• $0.4$ dm: Using the conversion $1$ dm = $10$ cm, $0.4$ dm = $0.4 \times 10 = 4$ cm.
• $30$ mm: Using the conversion $1$ mm = $0.1$ cm, $30$ mm = $30 \times 0.1 = 3$ cm.
• $0.01$ m: Using the conversion $1$ m = $100$ cm, $0.01$ m = $0.01 \times 100 = 1$ cm.

Now, we can arrange the lengths in ascending order by their converted measurements:

• $0.01$ m = $1$ cm
• $2$ cm = $2$ cm
• $30$ mm = $3$ cm
• $0.4$ dm = $4$ cm

Therefore, the correct order from smallest to largest is:

$0.01$ m
$2$ cm
$30$ mm
$0.4$ dm

To compare the measurements, convert all units to meters:

• $45$ mm = $0.045$ m.

• $0.3$ dm = $0.03$ m.

• $5$ cm = $0.05$ m.

• The smallest is $0.007$ m itself.

Order from smallest to largest:

$0.007$ m
$0.03$ m
$0.045$ m
$0.05$ m

To order the given lengths from smallest to largest, we need to convert each measurement into meters:

• $35 \text{ mm}$: Convert using $35 \text{ mm} \times 0.001 = 0.035 \text{ m}$.
• $15 \text{ cm}$: Convert using $15 \text{ cm} \times 0.01 = 0.15 \text{ m}$.
• $0.05 \text{ dm}$: Convert using $0.05 \text{ dm} \times 0.1 = 0.005 \text{ m}$.
• $0.2 \text{ m}$ is already in meters.

After conversion, we have:

• $0.035 \text{ m}$ from 35 mm
• $0.15 \text{ m}$ from 15 cm
• $0.005 \text{ m}$ from 0.05 dm
• $0.2 \text{ m}$.

Next, arrange these values from smallest to largest:

• $0.005 \text{ m}$ from $0.05 \text{ dm}$
• $0.035 \text{ m}$ from $35 \text{ mm}$
• $0.15 \text{ m}$ from $15 \text{ cm}$
• $0.2 \text{ m}$ from $0.2 \text{ m}$.

The ordering from smallest to largest is $0.05 \text{ dm}$, $35 \text{ mm}$, $15 \text{ cm}$, $0.2 \text{ m}$.

Therefore, the correct order is choice 1:

$0.05$ dm
$35$ mm
$15$ cm
$0.2$ m

To solve this problem, we'll convert each measurement to millimeters and order them accordingly.

Step-by-step solution:

• Convert each measurement to millimeters:
• $60$ mm is already in millimeters.
• $8$ cm: Since $1$ cm equals $10$ mm, $8$ cm is $8 \times 10 = 80$ mm.
• $0.1$ m: Since $1$ m equals $1000$ mm, $0.1$ m is $0.1 \times 1000 = 100$ mm.
• $0.09$ dm: Since $1$ dm equals $100$ mm and $0.09$ dm equals $0.09 \times 100 = 9$ mm.
• List the lengths in millimeters: $9$ mm (from $0.09$ dm), $60$ mm, $80$ mm (from $8$ cm), $100$ mm (from $0.1$ m).
• Order the original measurements from smallest to largest:
• $0.09$ dm
• $60$ mm
• $8$ cm
• $0.1$ m

Therefore, the solution to the problem is:

$0.09$ dm
$60$ mm
$8$ cm
$0.1$ m

To solve this problem, we'll convert all the lengths to meters so that they can be directly compared:

• Convert $0.06$ m to meters.
  Since it's already in meters, it remains $0.06$ m.

• Convert $9$ cm to meters.
  Since $1$ cm equals $0.01$ m, $9$ cm equals $9 \times 0.01 = 0.09$ m.

• Convert $70$ mm to meters.
  Since $1$ mm equals $0.001$ m, $70$ mm equals $70 \times 0.001 = 0.07$ m.

• Convert $0.08$ dm to meters.
  Since $1$ dm equals $0.1$ m, $0.08$ dm equals $0.08 \times 0.1 = 0.008$ m.

Now, we can list them in ascending order of meters:

1. $0.08$ dm = $0.008$ m
2. $0.06$ m
3. $70$ mm = $0.07$ m
4. $9$ cm = $0.09$ m

Therefore, ordered from smallest to largest, the measurements are:

$0.08$ dm
$0.06$ m
$70$ mm
$9$ cm

To solve this problem, we'll convert each given length to centimeters:

• The length $11$ cm is already in centimeters.
• The length $0.1$ dm; knowing $1$ dm = $10$ cm, gives $0.1 \times 10 = 1$ cm.
• The length $90$ mm; knowing $1$ cm = $10$ mm, gives $90 / 10 = 9$ cm.
• The length $0.011$ m; knowing $1$ m = $100$ cm, gives $0.011 \times 100 = 1.1$ cm.

Now, we list the lengths in centimeters:

1. $0.1$ dm = $1$ cm
2. $0.011$ m = $1.1$ cm
3. $90$ mm = $9$ cm
4. $11$ cm = $11$ cm

The correct order from smallest to largest is:

1. $0.1$ dm
2. $0.011$ m
3. $90$ mm
4. $11$ cm

Therefore, the order from smallest to largest is: $0.1$ dm, $0.011$ m, $90$ mm, $11$ cm.

Comparing with the options provided, the correct choice is option 2.

To solve this problem, we need to convert each measurement to meters and then order them:

• Convert 50 mm to meters:
  Since 1 meter = 1000 millimeters, we have:
  $\frac{50 \text{ mm}}{1000} = 0.05$ meters
• Convert 0.2 dm to meters:
  Since 1 meter = 10 decimeters, we have:
  $\frac{0.2 \text{ dm}}{10} = 0.02$ meters
• Convert 4 cm to meters:
  Since 1 meter = 100 centimeters, we have:
  $\frac{4 \text{ cm}}{100} = 0.04$ meters
• Convert 0.005 m to meters:
  It is already given in meters:
  $0.005$ meters

Now, let's compare the values in meters:
- 0.005 meters
- 0.02 meters (from 0.2 dm)
- 0.04 meters (from 4 cm)
- 0.05 meters (from 50 mm)

Order them from smallest to largest:
1. $0.005$ meters
2. $0.02$ meters
3. $0.04$ meters
4. $0.05$ meters

Therefore, the order from smallest to largest in their original units is:
1. $0.005$ m
2. $0.2$ dm
3. $4$ cm
4. $50$ mm

Therefore, the correct ordering is choice 4 which matches:
$0.005$ m, $0.2$ dm, $4$ cm, $50$ mm.

To solve this problem, we will convert each measurement to millimeters so that we can easily compare their sizes:

• Convert $0.09 \, \text{dm}$ to mm: $0.09 \, \text{dm} = 0.09 \times 100 \, \text{mm} = 9 \, \text{mm}$
• Convert $6 \, \text{cm}$ to mm: $6 \, \text{cm} = 6 \times 10 \, \text{mm} = 60 \, \text{mm}$
• Convert $0.04 \, \text{m}$ to mm: $0.04 \, \text{m} = 0.04 \times 1000 \, \text{mm} = 40 \, \text{mm}$

Now, compare the lengths in millimeters:

• $9 \, \text{mm}$ (originally $0.09 \, \text{dm}$)
• $30 \, \text{mm}$ (originally $30 \, \text{mm}$)
• $40 \, \text{mm}$ (originally $0.04 \, \text{m}$)
• $60 \, \text{mm}$ (originally $6 \, \text{cm}$)

The order from smallest to largest is:

$0.09 \, \text{dm}$, $30 \, \text{mm}$, $0.04 \, \text{m}$, $6 \, \text{cm}$

To solve this problem, we need to convert all the given lengths to a common unit of measurement, here we'll use meters.

First, let's convert each measurement to meters:

• $0.03$ m is already in meters.
• $5$ cm: Since $1 \text{ cm} = 0.01 \text{ m}$, then $5 \text{ cm} = 5 \times 0.01 \text{ m} = 0.05 \text{ m}$.
• $25$ mm: Since $1 \text{ mm} = 0.001 \text{ m}$, then $25 \text{ mm} = 25 \times 0.001 \text{ m} = 0.025 \text{ m}$.
• $0.001$ dm: Since $1 \text{ dm} = 0.1 \text{ m}$, then $0.001 \text{ dm} = 0.001 \times 0.1 \text{ m} = 0.0001 \text{ m}$.

Next, we compare the values we have in meters:

• $0.0001$ m (from $0.001$ dm)
• $0.025$ m (from $25$ mm)
• $0.03$ m
• $0.05$ m (from $5$ cm)

Thus, ordering from smallest to largest is: $0.001$ dm, $25$ mm, $0.03$ m, $5$ cm.

Therefore, the correct order from smallest to largest is:

$0.001$ dm
$25$ mm
$0.03$ m
$5$ cm

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

• Step 1: Convert each length to meters for a fair comparison.
• Step 2: Order the lengths from smallest to largest.

Now, let's work through each step:

Step 1: Convert all measurements to meters.

• $0.04 \, \text{m}$ is already in meters.
• $8 \, \text{cm} = \frac{8}{100} \, \text{m} = 0.08 \, \text{m}$.
• $50 \, \text{mm} = \frac{50}{1000} \, \text{m} = 0.05 \, \text{m}$.
• $0.2 \, \text{dm} = \frac{0.2}{10} \, \text{m} = 0.02 \, \text{m}$.

Step 2: Order the lengths from smallest to largest based on the meter conversions:

• $0.02 \, \text{m}$ (which is $0.2 \, \text{dm}$)
• $0.04 \, \text{m}$
• $0.05 \, \text{m}$ (which is $50 \, \text{mm}$)
• $0.08 \, \text{m}$ (which is $8 \, \text{cm}$)

Therefore, the order from smallest to largest is:

$0.2 \, \text{dm} < 0.04 \, \text{m} < 50 \, \text{mm} < 8 \, \text{cm}$.

Let's begin by converting each measurement to millimeters:

• $55$ mm is already in millimeters, so it stays at $55$ mm.
• $0.5$ cm = $0.5 \times 10$ mm = $5$ mm.
• $0.007$ m = $0.007 \times 1000$ mm = $7$ mm.
• $0.09$ dm = $0.09 \times 100$ mm = $9$ mm.

Now, comparing these converted lengths in millimeters:

• The smallest value is $5$ mm which corresponds to $0.5$ cm.
• The next smallest is $7$ mm which corresponds to $0.007$ m.
• The third is $9$ mm which corresponds to $0.09$ dm.
• The largest is $55$ mm which corresponds directly to $55$ mm.

Therefore, in ascending order, the lengths are:

$0.5$ cm
$0.007$ m
$0.09$ dm
$55$ mm