Conversion of Units (Mathematical Conversions) - Tables & Examples (2024)

In Mathematics, it is required to convert the units while solving many problems. To carry out the required calculations, mathematical conversions are needed. For example, to find the area of a triangle, if a base is given in cm, and height is given in meter, and you are asked to find the area of a triangle in cm, it is necessary to convert the height in meters into centimetres. Therefore, it is required to know the conversion of units to convert a unit into the required unit.

What is Conversion of Units?

The use of a unit depends on the situation, such as the area of a room is expressed in meters, but the length of a pencil is expressed in centimetres and its thickness in mm.

Thus, we need to convert one unit to another. Before understanding the concept of conversion of units, we need to understand the relationship between units.

Length and Mass conversion

Mensuration is an ancient concept. Every physical quantity, like length, mass, time, temperature etc., have a specific unit. By definition, a unit is a magnitude of a physical quantity.

There are two systems of units:

Conversion of Units (Mathematical Conversions) - Tables & Examples (1)

  1. SI units (International System of Units)
  2. Metric system

For example, the SI unit of length is a metre (m), while metric units are kilometre (km), meter (m), decimetre (dm), centimetre (cm) and millimetre (mm).

SI unit of mass is Kilograms (kg).

Importance of Mathematical Conversions

In order to have accuracy and avoid confusion in measurement, we need to convert one unit to another. For instance, we do not measure the length of a pencil in kilometres. In such a case, one has to convert kilometre (km) to centimetre (cm). Generally, the conversion of one unit to another unit of the same quantity is performed using multiplicative conversion factors. Let’s see how to convert a different unit of length and mass.

Table for Length Conversion

The conversion of units related to length can be represented as:

Conversion of Units (Mathematical Conversions) - Tables & Examples (2)

The length conversion is given in the figure above. The relation between the adjacent unit varies by the multiple of 10 (moving left to the right) and vice-versa (i.e. moving right to the left).

The table for conversion of length is:

Unit conversion for Length
1 millimeter0.001 meter
1 centimeter0.01 meter
1 decimeter0.1 meter
1 decameter10 meters
1 hectometer100 meters
1 kilometer1000 meters
1 inch2.54 × 10−2 meters
1 foot0.3048 meters
1 mile1.609344 km
Example: Convert 2 mm to dam.

Solution: Given 2 mm length.

From the length conversion table, we see dam is 4th position left to mm.

Thus, dividing the given length by 104.

⇒ 2 mm = 2/104 dam

⇒ 2 mm = 0.0002 dam

Table for Mass Conversion

The conversion of mass or weight can be done as shown in the below figure.

Conversion of Units (Mathematical Conversions) - Tables & Examples (3)

The below table helps to understand the convection of units for mass.

Unit conversion for Mass
1 milligram0.001 gram
1 centigram0.01 gram
1 decigram0.1 gram
1 decagram10 gram
1 hectogram100 gram
1 kilogram1000 grams

Unit Conversion Table

Let’s have a look at some basic unit conversion of mass and length.

Units of LengthUnits of Mass
1 km = 10 hm

= 100 dam

= 1000 m

1 kg = 10 hg

= 100 dag

= 1000 g

1m = 10 dm

= 100 cm

= 1000 mm

1 g = 10 dg

= 100 cg

= 1000 mg

1 dm = 10 cm

= 100 mm

1 dg = 10 cg

= 100 mg

1 cm = 10 mm1 cg = 10 mg

From the table above, we have seen values of units of length are not the same, i.e. 1 km ≠ 1m. When 1 km is equal to 1000 m, we need 1000 meters to make up one kilometre. This makes a kilometre a bigger unit than a meter. This is same for 1 kg = 1000g. Conversion of units can be done in a few steps.

In mathematics, we also come across time-related problems, for example, simple and compound interest, speed and distance, work, etc.

The below table shows the conversion of units for time.

Conversion of Units for Time
1 minute60 seconds
1 hour60 minutes (or) 3600 seconds
1 day24 hours
1 week7 days
1 year365 days

In geometry, we deal with many problems of finding the area and perimeter of shapes. In such cases, one may need to convert the units of measure of area. The below table helps in such types of conversions.

Conversion of Units for Area
1 sq. inch6.4516 x 10-4 square meter
1 sq. foot9.2903 x 10-2 square meter
1 acre4.0468 x 103 square meter
1 hectare1 x 104 square meter
1 sq. mile2.5888 x 106 square meter

Points to remember:

  • To convert bigger units to a smaller unit multiply.
  • To convert a smaller unit to a bigger unit divide.

Conversion of Units Solved Examples

Example 1: Convert 2 cm to km.

Step 1: Draw a line or box as shown below,

kmhmdamm dmcmmm

Step 2: Put 1 at the larger unit to be converted.

Here we want to convert cm to km,

Since km is the larger unit, thus put 1 under the corresponding column (km).

km

1

hmdammdmcmmm

Step 3: Now put 0 till the smaller unit.

Here we want to convert cm to km, put 0 till the corresponding smaller unit.

km

1

hmdammdmcmmm

We see the conversion is from a smaller to a larger unit. Thus, we need to divide the given length by 100000 (i.e. 105).

2cm = 2/105km

⇒2cm = 0.00002 km

Example 2: Convert 5 grams to milligrams.

Solution: We have to convert 5 grams to milligrams.

We know, 1 g = 1000 mg

Thus, 5 g = 5 × 1000 = 5000 mg

To solve more problems on the topic, download BYJU’S – The Learning App and watch interactive videos. Also, take free tests to practice for exams.

Conversion of Units (Mathematical Conversions) - Tables & Examples (2024)

FAQs

What are examples of conversion units? ›

Conversion of Units Measurements
QuantityRelationship
Length1 mile = 1760 yards = 5280 feet = 63,360 inches
TemperatureC/5=F-32/9=K-273/5
Volume (Capacity)1 gallon = 4 quarts = 8 pints = 128 fluid ounces
Weight (Mass)1 ton = 2000 pounds = 32,000 ounces

How to remember conversion of units? ›

You can remember the order of the prefixes by using the following sentence: Good Morning King Henry Died By Drinking Chocolate Milk. Since the multiples and divisions of the base units are all factors of ten, you just need to move the decimal to convert from one to another.

What is a conversion table in math? ›

noun. : a table of equivalents for changing units of measure or weight into other units.

What is the easiest way to convert measurements? ›

Rule 1: When converting from a larger unit to a smaller unit, multiply. Rule 2: When converting from a smaller unit to a larger unit, divide. This basic rule applies to all conversions, no matter the object being measured or the system you're using.

What is the formula for conversion? ›

Conversion Rate = Total number of conversions / Total number of sessions * 100. Conversion Rate = Total number of conversions / Total number of unique visitors * 100.

What is the shortcut to learn the conversion of units? ›

Deci - 10 times smaller. Centi - 100 times smaller. Milli - 1,000 times smaller. A handy trick for remembering the basic metric prefixes is the mnemonic "King Henry Died Until Drinking Chocolate Milk," (or, if you prefer, "King Henry Doesn't Usually Drink Chocolate Milk").

What is the standard formula of unit conversion? ›

There isn't a single universal formula for unit conversion because it depends on the specific units you're converting between. However, the general process involves using conversion factors. Conversion Factors: A conversion factor is a number used to change one set of units to another, by multiplying or dividing.

What is the rule for converting units? ›

Basic Conversion Rule

The basic rule is: If you need to convert from a larger unit to a smaller unit, multiply. If you need to convert from a smaller unit to a larger unit, divide.

What is an example of conversion? ›

The company is undergoing a conversion to a new computer system. They have suggested conversion of the old school into apartments. Conversion to gas heating will continue over the next few years. a conversion from Catholicism to Judaism He is thinking about conversion to Buddhism.

How do you calculate %conversion? ›

Conversion rates are calculated by simply taking the number of conversions and dividing that by the number of total ad interactions that can be tracked to a conversion during the same time period. For example, if you had 50 conversions from 1,000 interactions, your conversion rate would be 5%, since 50 ÷ 1,000 = 5%.

What are conversion examples? ›

Examples of conversion in a Sentence

The company is undergoing a conversion to a new computer system. They have suggested conversion of the old school into apartments. Conversion to gas heating will continue over the next few years. a conversion from Catholicism to Judaism He is thinking about conversion to Buddhism.

What are some common conversions? ›

  • 1 ft = 12 in.
  • 1 yd = 3 ft.
  • 1 mi = 5280 ft. Weight (Mass)
  • 1 lb = 16 oz.
  • 1 tn = 2000 lb. Temperature.
  • 1 c = 8 oz.
  • 1 pt = 16 oz.
  • 1 qt = 32 oz.

Which one is the example of conversion? ›

Conversion is a type of word formation process in which a word is assigned to a new word class or part of speech without any change in form. An example of conversion is an email (noun) changing to a verb; to email.

What is an example of converting units of time? ›

Example.
Step 1: Recall the relation between second and minute1 minute = 60 seconds
Step 2: Smaller to larger unit, divide720 / 60
Step 3: Write the correct unit in the answer12 minutes
Final answer720 seconds = 12 minutes

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