Conversion of Units of Length: In Mathematics, we consider different units of measurements for better understanding. The length of a chair is measured in inches, whereas the length of a playground is measured in yards. We cannot measure the size of a finger in miles. 

The conversion of units is needed to solve several mathematical problems. For example, suppose the length of a rectangle is given in metres and the breadth in centimetres. We are asked to determine the perimeter of the rectangle. In that case, we need to convert the units to make them uniform.  In this article, we will learn about the conversions of units of length. 

Conversion of Units of Length: Overview

In our day-to-day life, we measure many small things by standard and non-standard units of measurement of length. But how can we measure the distance? Chennai \({\rm{100}}\,{\rm{km,}}\) Trichy \({\rm{170}}\,{\rm{km,}}\) Madurai \({\rm{310}}\,{\rm{km,}}\) the metric units are used to measure the length and distance.

The measurement of length is classified into two categories, non-standard units and standard units.

The non-standard units of measurement of length were used in ancient times when the standard units of measurement of length were not introduced. The images shown below represent the non-standard units of measurements.

Some of the standard units of measuring length are ruler, measuring tape, metric stick etc. Using these instruments, we can measure the length in millimetre, centimetre, decimetre, metre, decametre, hectometre, and kilometres. The millimetre is the smaller unit of measurement of length, the metre is the base unit, and the kilometre is the larger unit of measure of length.

Conversion of Smaller Metric Unit into a Larger Metric Unit

To convert a smaller unit of length into a larger unit of length, divide by \(10\) for every step in the following conversion chain from right to left.

The same conversion chain is used for the conversion of the smaller units of mass and capacity into their respective larger units. The only difference is that the metre gets replaced by a \({\rm{gram}}\) or \({\rm{litre}}{\rm{.}}\)

If a smaller unit is given as a decimal number, then dividing that unit by \(10, 100\) and \(1000\) results in shifting the decimal point to the left by one, two, and three places.

For example: \(33.05\;{\rm{cm}} = \frac{{33.05}}{{10}}{\rm{dm}} = 3.305\,{\rm{dm}}\)

Conversion of a Millimetre to Centimetre

To convert a millimetre to a centimetre, divide by \(10.\)

For example: Convert \(59\;{\rm{mm}}\) to \({\rm{cm}}{\rm{.}}\)

To convert \(59\;{\rm{mm}}\) to \({\rm{cm}}\) we will divide by \(10.\)

Therefore, \(59\;{\rm{mm}} = \frac{{59}}{{10}}\;{\rm{cm}} = 5.9\;{\rm{cm}}\)

Conversion of a Centimetre to Decimetre

To convert a centimetre to a decimetre, divide by \(10.\)

For example: Convert \(834\;{\rm{cm}}\) to \({\rm{dm}}{\rm{.}}\)

To convert \(834\;{\rm{cm}}\) to \({\rm{dm,}}\) we will divide by \(10.\)

Therefore, \({\rm{834\;cm = }}\frac{{{\rm{834}}}}{{{\rm{10}}}}{\rm{dm = 83}}{\rm{.4}}\,{\rm{dm}}\)

Conversion of a Decimetre to Metre

To convert a decimetre to a metre, divide by \(10.\)

For example: Convert \(83\;{\rm{dm}}\) to \({\rm{m}}{\rm{.}}\)

To convert \(83\;{\rm{dm}}\) to \({\rm{m}}\) we will divide by \(10.\)

Therefore, \({\rm{83}}\,{\rm{dm = }}\frac{{{\rm{83}}}}{{{\rm{10}}}}{\rm{dm = 8}}{\rm{.3}}\,{\rm{dm}}\)

Conversion of a Metre to Hectometre

To convert a decametre to a hectometre, divide by \(10.\)

For example: Convert \(16\;{\rm{dam}}\) to \({\rm{hm}}{\rm{.}}\)

To convert \(16\;{\rm{dam}}\) to \({\rm{hm}}\) we will divide by \(10.\)

Therefore, \({\rm{16}}\,{\rm{dam = }}\frac{{{\rm{16}}}}{{{\rm{10}}}}{\rm{hm = 16}}\,{\rm{hm}}\)

Conversion of a Hectometre to Kilometre

To convert a hectometre to a kilometre, divide by \(10.\) Let us understand this with the help of an example.

For example: Convert \(86\;{\rm{hm}}\) to \({\rm{km}}{\rm{.}}\)

To convert \(86\;{\rm{hm}}\) to \({\rm{km}}\) we will divide by \(10\)

Therefore, \({\rm{86}}\,{\rm{hm = }}\frac{{{\rm{86}}}}{{{\rm{10}}}}{\rm{hm = 8}}{\rm{.6}}\,{\rm{km}}\)

Conversion of Larger Metric Unit into a Smaller Metric Unit

To convert a larger metric unit of length into a smaller unit of length, multiply by \(10\) for every step in the following conversion chain from left to right.

The same conversion chain is used for the conversion of the larger units of mass and capacity into their respective smaller units. The only difference is that metre gets replaced by \({\rm{gram}}\) or \({\rm{litre}}{\rm{.}}\)

If a larger unit is given as a decimal number, then multiplying that unit by \(10,100\) and \(1000\) results in shifting the decimal point to the right by one, two, and three places.

For example: \(4.36\;{\rm{m}} = 4.36 \times 10\,{\rm{dm}} = 43.6\,{\rm{dm}}\)

Conversion of a Kilometre to Hectometre

To convert a kilometre to a hectometre, multiply by \(10.\)

For example: Convert \({\rm{26}}\,{\rm{km}}\) to \({\rm{hm}}{\rm{.}}\)

To convert \({\rm{26}}\,{\rm{km}}\) to \({\rm{hm}}\) we will multiply by \(10.\)

Therefore, \(26\;{\rm{km}} = 26 \times 10\,{\rm{hm}} = 260\,{\rm{hm}}\)

Conversion of a Hectometre to Decametre

To convert a hectometre to decametre, multiply by \(10.\)

For example: Convert \(1.64\,{\rm{hm}}\) to \({\rm{dam}}{\rm{.}}\)

To convert \(1.64\,{\rm{hm}}\) to \({\rm{dam}}\) we will multiply by \(10.\)

Therefore, \(1.64\,{\rm{hm}} = 1.64 \times 10\,{\rm{dam}} = 16.4\,{\rm{dam}}\)

Conversion of a Decametre to Metre

To convert a decametre to a metre, multiply by \(10.\)

For example: Convert \(88.9435\,{\rm{dam}}\) to \({\rm{m}}{\rm{.}}\)

To convert \(88.9435\,{\rm{dam}}\) to \({\rm{m}}\) we will multiply by \(10.\)

Therefore, \({\rm{8}}\,{\rm{dam = 8 \times 10\;m = 80\;m}}\)

Conversion of a Metre to Decimetre

To convert a meter to a decimetre, multiply by \(10.\) Let us understand this with the help of an example.

For example: Convert \(38.2\,{\rm{m}}\) to \({\rm{dm}}{\rm{.}}\)

To convert \(38.2\,{\rm{m}}\) to \({\rm{dm}}\) we will multiply by \(10.\)

Therefore, \(38.2\;{\rm{m}} = 38.2 \times 10\,{\rm{dm}} = 382\,{\rm{dm}}\)

Conversion of a Decimetre to Centimetre

To convert decimetre to a centimetre, multiply by \(10.\)

For example: Convert \(8.34\,{\rm{dm}}\) to \({\rm{cm}}{\rm{.}}\)

To convert \(8.34\,{\rm{dm}}\) to \({\rm{cm}}{\rm{,}}\) we will multiply by \(10.\)

Therefore, \(8.34\,{\rm{dm}} = 8.34 \times 10\;{\rm{cm}} = 83.4\;{\rm{cm}}\)

Conversion of a Centimetre to Millimetre

To convert a centimetre to a millimetre, multiply by \(10.\)

For example: Convert \(95\,{\rm{cm}}\) to \({\rm{mm}}{\rm{.}}\)

To convert \(95\,{\rm{cm}}\) to \({\rm{mm}}\) we will multiply by \(10.\)

Therefore, \(95\;{\rm{cm}} = 95 \times 10\;{\rm{mm}} = 950\;{\rm{mm}}\)

Metric Ladder

By using the metric ladder, we will understand the conversion of units better. If we go down, then for each step, we need to multiply by \(10.\) And if we go up, then for each step, we need to divide by \(10.\)

Relationship between Smaller and Larger Units

The relationship between the smaller and larger units are given below:

1. \({\rm{10\;mm = 1\;cm = }}\frac{{\rm{1}}}{{{\rm{10}}}}{\rm{dm}}\)
2. \({\rm{10\;cm = 1\;dm = }}\frac{{\rm{1}}}{{{\rm{10}}}}{\rm{m}}\)
3. \({\rm{10\;hm = 1\;km = }}\frac{{\rm{1}}}{{{\rm{10}}}}{\rm{dam}}\)
4. \({\rm{10\;m = 1\;dam = }}\frac{{\rm{1}}}{{{\rm{10}}}}{\rm{hm}}\)
5. \({\rm{10\;dam = 1\;hm = }}\frac{{\rm{1}}}{{{\rm{10}}}}{\rm{km}}\)
6. \({\rm{10\;hm = 1\;km}}\)

Solved Examples on Conversion of Units of Length

Q.1. Convert \(65\;{\rm{cm}}\,6\;{\rm{mm}}\) into millimetre.
Ans: To convert centimetre into millimetre, multiply the given centimetre by \(10.\)
\(65\;{\rm{cm}}\,6\;{\rm{mm}} = (65 \times 10) + 6\;{\rm{mm}}\)
\(=650+6\)
\({\rm{ = 656}}\,{\rm{mm}}\)

Q.2. Convert \(5\;{\rm{m}}\) into centimetres.
Ans: To convert meter into centimetre, multiply the given meters by \(100.\)
\({\rm{5m = (5 \times 100)cm}}\)
\({\rm{ = 500\;cm}}\)

Q.3. Convert \({\rm{900}}\,{\rm{m}}\) into kilometre.
Ans: To convert meters into kilometres, divide the given meters \(1000.\)
\(9000\;{\rm{m}} = 9000 \div 1000\;{\rm{m}}\)
\({\rm{ = 9}}\,{\rm{km}}\)

Q.4. Convert \(7\;{\rm{km}}\,50\;{\rm{m}}\) into metres.
Ans: To convert a kilometre into a metre, multiply the given kilometre by \(1000.\)
\(7\;{\rm{km}}\,50\;{\rm{m}} = (7 \times 1000) + 50\;{\rm{m}}\)
\( = 7000 + 50\;{\rm{m}}\)
\( = 7050\;{\rm{m}}\)

Q.5. Convert \({\rm{7}}\,{\rm{km}}\) into decimetre.
Ans: To convert kilometre into decimetre, multiply the given kilometre by \(10000.\)
\(7\;{\rm{km}} = (7 \times 10000){\rm{dm}}\)
\( = 70000\,{\rm{dm}}\)

Summary

In this article, we have discussed the standard and non-standard units of measuring length. Also, learned about the conversions of smaller metric units of length to larger metric units of length and conversions of larger metric units of length to smaller metric units of length. And we have also discussed the relationship between the smaller and the larger units of length.

We learned that some of the standard units of measuring length are measuring tape, ruler, metric stick etc. By utilising these instruments we can measure the length in centimetre, decimetre, metre, decametre, etc. Furthermore, it is important to note that a conversion factor is a number that is used to change one set of units to another, either by multiplying or by dividing. Unit conversions are important in solving several real-life problems like exchanging money, buying and selling, cooking, baking, etc.

FAQs on Conversion of Units of Length

Q.1. What is the conversion table of length?
Ans: The conversion of the table of length is given below:

Unit Conversion Table

\(1\;{\rm{km}} = 10\,{\rm{hm}} = 100\,{\rm{dam}} = 1000\;{\rm{m}}\)

\(1\;{\rm{m}} = 10\,{\rm{dm}} = 100\;{\rm{cm}} = 1000\;{\rm{mm}}\)

\({\rm{1dm = 10\;cm = 100\;mm}}\)

\(1\;{\rm{cm}} = 10\;{\rm{mm}}\)

Q.2. Explain the conversion of units of length with an example.
Ans: To convert the length from a larger unit (like \({\rm{km}}\)) into a smaller unit (like \({\rm{m}}\)), multiply by the conversion factor.
To convert the length from a smaller unit (like \({\rm{cm}}\)) into a larger unit (like \({\rm{m}}\)), divide by the conversion factor.
For example: To convert \({\rm{120}}\,{\rm{km}}\) into \({\rm{m,}}\) we multiply \(120\) by the conversion factor \(1000.\)
Therefore, \(120\;{\rm{km}} = 120 \times 1000 = 120000\;{\rm{m}}\)

Q.3. Why is unit conversion important?
Ans: Unit conversions are essential in solving many real-life problems, such as exchanging money, purchasing and selling, cooking, baking, etc.

Q.4. How do you convert the unit if a larger unit is given as a decimal?
Ans: If a larger unit is given as a decimal number, then multiplying that unit by \(10,100\) and \(1000\) results in shifting the decimal point to the right by one, two, and three places.
For example: \(4.36\;{\rm{m}} = 4.36 \times 10\,{\rm{dm}} = 43.6\,{\rm{dm}}\)

Q.5. What are the conversion factors?
Ans: A conversion factor is a number that is used to change one set of units to another, either by multiplying or by dividing. An appropriate conversion factor makes calculation quicker and easier. For example, the appropriate conversion value, to convert \({\rm{km}}\) to \({\rm{m,}}\) is \({\rm{1}}\,{\rm{km = 1000}}\,{\rm{m}}{\rm{.}}\)

We hope this detailed article on the conversion of units is helpful to you. If you have any queries, ping us through the comment box below and we will get back to you as soon as possible.