Home / United States / Math Classes / Formulas / Metric Units of Length Conversion Formulas

All objects have different shapes and sizes defined by their length, width, height, and so on. To quantify these properties precisely, a metric system is used. Here we will focus on metric units used to measure length and their equivalent measures. ...Read MoreRead Less

The formulas for the length conversion is given below:

- 1 kilometer = (1×1000) meters
- 1 meter = (1×100) centimeters
- 1 centimeter = (1×10) millimeters

We will discuss these in detail in the next section.

Let us take an example; if someone asks you the distance between your home and school, you might say that the distance between your home and school is 12 kilometers. Notice how the unit we use is kilometers: That is because larger distances are measured in kilometers.

Similarly, if we have to tell someone the length of a running track we will say that the running track is 100 meters long.

What is the length of the file you see below? Well, we can see that it is 30 centimeters long.

How long is the key? We will say that it is 60 millimeters or 6 centimeters long.

From the examples above, we can see that the smaller lengths are measured in units like meter, centimeter and millimeter.

Here, we can say that 1 mm = 10 cm.

Also, 1 cm = 100 m and 1 km = 1000 m.

To convert a larger unit to a smaller unit, we need to multiply the numerical factor. Therefore,

1 kilometer = (1 × 1000) meters

1 meter = (1 × 100) centimeters

1 centimeter = (1 × 10) millimeters

Conversely, to convert a smaller unit to a larger unit we need to divide the numerical factor. Therefore,

1 millimeter \(= \frac{1}{10} \) centimeter

1 centimeter \(= \frac{1}{100} \) meter

1 meter \(= \frac{1}{1000} \) kilometer

**Example 1: Find the equivalent length: 15 cm = ___ mm**

**Solution:**

We know that 1 cm is equivalent to 10 mm

So, 1 cm = 10 mm

15 cm = (15 × 10) mm

15 cm = 150 mm [Multiply]

**Example 2: Find the equivalent length: 5 km = ___ cm**

**Solution:**

We know that 1 km is equivalent to 1000 m and 1 m is equivalent to 100 cm. So first convert km into m and then m into cm.

Now, 1 km = 1000 m

5 km = (5 \(\times \) 1000) m

5 km = 5000 m [Multiply]

Also, 1 m = 100 cm

5000 m = (5000 \(\times \) 100) cm

5000 m = 500000 cm [Multiply]

Therefore, 5 km is equivalent to 5,00,000 cm.

Therefore, 15 cm is equivalent to 150 mm.

**Example 3: Convert 10000 mm to m.**

**Solution:**

We know that 1 mm is equivalent to \(\frac{1}{10}\) cm and 1 cm is equivalent to \(\frac{1}{10}\) m. So first convert mm into cm and then cm into m.

Now, 1 mm \(=~\frac{1}{10}\) cm

10000 mm \(=~\left ( 1000\times\frac{1}{10} \right )\) cm

10000 mm \(=~\left ( \frac{1000}{10} \right )\) cm

10000 mm \(=~1000\) cm [Divide]

Also, 1 cm \(=~\frac{1}{100}\)

1000 cm \(=~\left ( \frac{1000}{100} \right )\) m

1000 cm \(=~10\) [Divide]

Therefore, 10000 mm is equivalent to 10 m.

**Example 4: The pages of a file are 300 mm long and the file cover is 0.35 m long. Will the pages fit into the file?**

**Solution:**

Length of pages = 300 mm

Length of file = 0.35 m

First express the length of the pages and the file in the same unit, that is, cm and then compare the lengths.

We know that 1 mm \(=~\frac{1}{10}\) cm.

Length of pages = 300 mm

\(=~\left ( 300\times\frac{1}{10} \right )\) cm

\(=~\frac{300}{10}\) cm

Length of pages = 30 cm. [Divide]

We know that 1 m is equivalent to 100 cm.

Length of file = 0.35 m

= (0.35 \(\times\) 100) cm [Since, 1 m = 100cm]

= \(\left ( \frac{35}{100}\times100 \right )\) cm

Length of file = 35 cm [Simplify]

Comparing the length of the pages and the length of the file;

35 cm > 30 cm

As the length of the file is greater than the length of pages we can say that pages will fit into the file.

**Example 5: During swimming class John swam 5 laps of the pool and each lap was 100 meters long. Did he cover a distance of 1 km?**

**Solution:**

Total distance covered by John = Number of laps \(\times\) Distance of one lap

= (5 \(\times\) 100) [Substitute the values]

Total distance covered by John = 500 m [Multiply]

Now to check whether he has covered a distance of 1 km or not, we will convert km into m and then compare the distances.

We know that 1 km is equivalent to 1000 m but John only covered 500 m.

500 m < 1000 m

Therefore, John did not cover the 1 km distance.

Frequently Asked Questions

The metric system is the system of measurement that uses units like meter, liter, and grams to measure the length, capacity, weight, and mass of objects.

The units of measurement in the metric system are called metric units or SI units (International System of Units). The units include meter, kilogram, gram, and so on.

We learnt that larger distances are measured in kilometers. So, the distance between 2 towns must be measured in kilometers.

We also learnt that smaller distances or lengths are measured in centimeters and millimeters. So, the length of a pencil is measured in centimeters or millimeters.

To convert a smaller unit to a larger unit, we need to divide the unit by a suitable numerical value.