Home » Math Theory » Measurements and Time » Conversion of Measuring Length

# Conversion of Measuring Length

## Introduction

The process of associating numbers with physical quantities and phenomena is what we call a system of measurement. We need to measure a lot of things in our real life such as the weight of a bag, the capacity of a jar, length of a table. etc. The word “measurement” is derived from the Greek word “metron,” which means a limited proportion. There are two different systems of measurement in place that are commonly in use. The popular among them is the metric system.

Metric system – It is the international decimal system of weights and measures, based on the metre for length and the kilogram for mass that was adopted in France in 1795 and is now used officially in almost all countries.

US Standard Units – The United States customary units form a system of measurement units commonly used in the United States and U.S. territories since being formalized in 1832. Although U.S. customary units have been defined in terms of metric units since the 19th century, the United States is one of only three countries, the others being Myanmar and Liberia that, as of 2022, have not officially adopted the metric system as the primary means of weights and measures. US Standard Volume is a part of the US standard units. Let us learn more about it.

## Definition of Length

Length is defined as the measurement or extent of something from end to end. In other words, it is the term used for identifying the size of an object or distance from one point to Length is a measure of how long an object is or the distance between two points. The length of an object is its extended dimension, that is, its longest side.

## Definition of Conversion of Measuring Length

Conversion of one unit to another unit of measurement for the same quantity using multiplication/division by conversion factors is known as unit conversion. Therefore, conversion of measuring length means converting the units of length from one form to another, say centimetres to metres, metres to kilometres etc.

## Conversion of Length Chart

The different units of length conversion charts and their equivalents are as below –

• 1 kilometre ( km ) = 10 Hectometres ( hm ) = 1000 m
• 1 Hectometre ( hm ) = 10 Decametres ( dcm ) = 100 m
• 1 Decametre ( dcm ) = 10 Metres (m)
• 1 Metre ( m ) = 10 Decimetres ( dm ) = 100 cm = 1000 mm
• 1 Decimetre ( dm ) = 10 Centimetres ( cm )
• 1 decimetre = 0.1 metre
• 1 Centimetre ( cm ) = 10 Millimetres ( mm )
• 1 centimetre = 0.01 metre
• 1 millimetre = 0.001 metre

The above conversions can be summarised in the form of a table as –

This chart can further be extended as –

## Length Conversion Table of Common Length Units

The length conversion table of common length units is mentioned in the below table –

## Conversion of Larger unit to Smaller Unit

To convert a larger unit into a smaller unit we multiply the units by 10, 100, 1000 or other multiples of 10 depending upon the units being converted into.

Converting kilometre into metre

Let us understand it through an example.

Example

Suppose we wish to convert 4 km into metres

Solution

We are required to convert 4 km into metres. Now from the conversion table, we know that 1 km = 1000 m. This means that in order to convert every km into metres we need to multiply it by 1000. Therefore,

4 km = 4 x 1000 m = 4000 m

#### Converting metres into centimetres

Let us understand it through an example.

Example

Suppose we wish to convert 4 k 280 m into centimetres

Solution

We are required to convert 4 km 280 cm into centimetres. Now from the conversion table, we know that 1 m = 100 cm. This means that in order to convert every m into centimetre we need to multiply it by 100. Therefore,

4 km 280 m = ( 4 x 1000 + 280 ) m = ( 4000 + 280 ) m = 4280 m = 4280 x  100 = 428000 cm

### Converting larger decimal units into smaller units

Let us first recall how multiplication is performed in decimal numbers. It is important to understand that when multiplying by 10, the value of each digit increases 10 times and therefore moves one place to the immediate left. Multiplying by 100 increases the digits’ values by 100 times moving them two places to the left and multiplying by 1000 increases their value 1000 times and moves them three places to the left. Let us consider an example. Suppose we wish to multiply 7 by 10. We know that 7 x 10 = 70. Similarly 7 x 100 = 700 and 7 x 1000 = 7000

To convert a larger decimal unit into a smaller unit we multiply the units by 10, 100, 1000 or other multiples of 10 depending upon the units being converted into.

Let us understand it through an example.

Example

Suppose we wish to convert 1.5 km into metres

Solution

We are required to convert 1.5 km into metres. Now from the conversion table, we know that 1 km = 1000 m. This means that in order to convert every km into metres we need to multiply it by 1000. Therefore,

1.5 km = 1.5 x 1000 m = 1500 m

## Conversion of Smaller unit to Larger Unit

To convert a smaller unit into a larger unit we divide the units by 10, 100, 1000 or other multiples of 10 depending upon the units being converted into.

#### Converting grams into kilograms

Example

Suppose we wish to convert 3 m into kilometres

Solution

We are required to convert 3 m into kilometres. Now from the conversion table, we know that 1 m = 1 / 1000 km. This means that in order to convert every m into kilometre we need to divide it by 1000. Therefore,

3 m = 3 / 1000 km = 0.003 km

#### Converting centimetres into metres

Example

Suppose we wish to convert 5732 cm into metres

Solution

We are required to convert 5732 cm into metres. Now from the conversion table, we know that 1 cm = 1 / 100 m. This means that in order to convert every cm into metre we need to divide it by 100. Therefore,

5732 cm = 5732 / 100 m = 57.32 m

### Converting smaller decimal units into larger units

Let us first recall how division is performed in decimal numbers. Dividing whole numbers and decimal numbers by powers of 10 has the opposite effect of multiplying. The value of the digits decreases as opposed to increasing and the digits move to the right as opposed to the left on a place value chart. Let us, for example, take the number 745 and divide it by 10. We will have 745 ÷ 10 = 74.5. Similarly, 745 ÷ 100 = 7.45 and 745 ÷ 1000 = 0.745

To convert a smaller decimal unit into a larger unit we divide the units by 10, 100, 1000 or other multiples of 10 depending upon the units being converted into.

Let us understand it through an example.

Example

Suppose we wish to convert 3.8 m into kilometres

Solution

We are required to convert 3.8 m into kilometres. Now from the conversion table, we know that 1 m = 1 / 1000 km. This means that in order to convert every metre into kilometres we need to divide it by 1000. Therefore,

3.8 m = 3.8 / 1000 km = 0.0038 km

The above conversions can be summarised as –

## Solved Examples

Example 1 Maria purchased 24 m 25 cm rope and Nancy purchased 17 m 15 cm rope. What is the total length of ropes both of them purchased in centimetres?

Solution We have been given that Maria purchased 24 m 25 cm rope and Nancy purchased 17 m 15 cm rope. We need to find the total length of rope purchased by them in centimetres. Let us first summarise the information available to us. We have,

Length of rope purchased by Maria = 24 m 25 cm

Length of rope purchased by Nancy = 17 m 15 cm

Since we need to find the total length in centimetres, let us first convert the above information into centimetres. We know that 1 m = 100 cm. We will thus have,

Length of rope purchased by Maria = 24 m 25 cm = ( 24 x 100 + 25 ) = ( 2400 + 25 ) = 2425 cm . . . . . . . . . . . . . . . . . . . . .  . . . . . . . . . . ( 1 )

Length of rope purchased by Nancy = 17 m 15 cm = ( 17 x 100 + 15 ) cm = ( 1700 + 15 ) cm = 1715 cm . . . . . . . . . . . . . . . . . . . . .  . . . . . . . . . . ( 2 )

Now, in order to find the total length of the rope purchased, we will have to add the values obtained in equation ( 1 ) and equation ( 2 ). Thus,

Total length of rope purchased by Maria and Nancy = ( 2425 + 1715 ) cm = 4140 cm

Hence, Maria and Nancy purchased rope of length 4140 cm

Example 2 Sam bought 9 m 75 cm of cloth. He used 2 m 30 cm from it. How much cloth is left in centimetres?

Solution We have been given that Sam bought 9 m 75 cm of cloth. He used 2 m 30 cm from it. We need to find the length of the cloth left in centimetres.

Let us first summarise the information available to us. We have,

Length of cloth purchased by Sam = 9 m 75 cm

Length of cloth used by Sam = 2 m 30 cm

Since we need to find the total length in centimetres, let us first convert the above information into centimetres. We know that 1 m = 100 cm. We will thus have,

Length of cloth purchased by Sam = 9 m 75 cm = ( 9 x 100 + 75 ) cm = ( 900 + 75 ) cm = 975 cm . . . . . . . . . . . . . . . . . . . . .  . . . . . . . . . . ( 1 )

Length of cloth used by Sam = 2 m 30 cm = ( 2 x 100 + 30 ) cm = ( 200 + 30 ) cm = 230 cm . . . . . . . . . . . . . . . . . . . . .  . . . . . . . . . . ( 2 )

Now, in order to find the length of the cloth left with Sam, we will have to subtract the length of the cloth used from the total length of cloth. This means we will have to subtract the value obtained in equation ( 2 ) from the value obtained in equation ( 1 ). Thus,

Length of cloth left with Sam = ( 975 – 230 ) cm = 745 cm

Hence, the length of the cloth left with Sam is 745 cm.

Example 3 Convert 3.450 m into km and m

Solution We need to convert 3.450 m into km and m

Now, we know that 1 km = 1000 m

Therefore, by dividing 3.450 by 1000 we will get 3 as the quotient and 450 as the remainder.

Hence, 3.450 km = 3 km 450 m

## Key Facts and Summary

1. Length is defined as the measurement or extent of something from end to end.
2. 1 kilometre ( km ) = 10 Hectometres ( hm ) = 1000 m
3. 1 Hectometre ( hm ) = 10 Decametres ( dcm ) = 100 m
4. 1 Decametre ( dcm ) = 10 Metres (m)
5. 1 Metre ( m ) = 10 Decimetres ( dm ) = 100 cm = 1000 mm
6. 1 Decimetre ( dm ) = 10 Centimetres ( cm )
7. 1 decimetre = 0.1 metre
8. 1 Centimetre ( cm ) = 10 Millimetres ( mm )
9. 1 centimetre = 0.01 metre
10. 1 millimetre = 0.001 metre
11. To convert a larger unit into a smaller unit we multiply the units by 10, 100, 1000 or other multiples of 10 depending upon the units being converted into.
12. To convert a smaller unit into a larger unit we divide the units by 10, 100, 1000 or other multiples of 10 depending upon the units being converted into.