In many situations, we are faced with the need to convert units, which are established models to measure different quantities.
The International System of Units (SI) determined the units to measure 7 fundamental quantities and from them the other quantities can be represented.
Next, you'll learn how to convert the units of measurements for length, mass, time, area, volume, temperature, and velocity.
Conversion of units of length
The fundamental unit of the SI for the magnitude of length is the subway, which corresponds to the distance traveled by light in a vacuum in 1/299 792 458 of a second.
To represent large distances we use multiples of the meter and for small lengths there are submultiples, as shown in the table below.
Remember that these are not the only units, but the most used.
For example, if I want to know how much 19 cm represents in meters, I do the following conversion.
19 cm = 19 x 0.01 m = 0.19 m
You can also write in scientific notation, as 0.01 m is the same thing as 10-2 m. The exponent (-2) means that we must “walk” with the decimal point 2 places to the left.
19 cm = 19 x 10-2 m = 0.19 m
Another way to convert units of length is using the table below.
Note that if you want to convert meter (m) to millimeter (mm) you need to multiply by 10 three times.
Example:
4 m → mm
4 x 10 x 10 x 10 = 4 x 1000 = 4000 mm
To convert meter (m) into kilometer (km), it is necessary to divide the measure by 10 three times.
Example:
6000 m → km
6000: 10: 10: 10 = 6000: 1000 = 6 km
know more about length measurements.
Conversion of mass units
The fundamental unit of the SI for the quantity mass is the kilogram, established in terms of Planck's constant, whose value is 6.62607015 x 10-34 J.s.
The units used to describe the mass quantities are: kilogram (kg), hectogram (hg), decagram (dag), gram (g), decigram (dg), centigram (cg) and milligram (mg).
The multiples and submultiples of the standard mass measurement system are decimal, that is, conversions are made by multiplying or dividing by 10, as shown in the table below.
Examples:
450 mg → g
450: 10: 10: 10 = 450: 1000 = 0.450 g
20 kg → dag
20 x 10 x 10 = 20 x 100 = 2000 dag
In addition to the units seen, there are also those used to indicate large quantities, such as the ton (1 ton = 1000 kg) and the arroba (1 arroba = 15 kg).
know more about mass measurements.
Conversion of time units
The fundamental unit of the SI for the greatness of time is the second, which corresponds to the duration of 9 192 631 770 periods of radiation in the transition between two hyperfine levels of the ground state cesium-133 atom.
As we know, 1 hour equals 60 minutes and each minute contains 60 seconds. So 1 hour contains 3600 seconds.
See in the table below how to make the conversions.
So if we have the time expressed in hours and we want to change it to minutes we should multiply it by 60. If we want to transform time expressed in seconds to minutes, we divide by 60.
Examples:
2 h → min
2 x 60 = 120 min
180 s → min
180: 60 = 3 min
Check the table below for other ways to express time.
know more about time measures.
Conversion of Area Units
The SI unit for large area is the square meter (m2). This unit presents as multiple square kilometers (km2), square hectometer (hm2) and square dekameter (dam2). The submultiples are square decimeters (dm2), square centimeter (cm2), square millimeter (mm2).
See in the table below how to convert between units.
Examples:
5 m2 → cm2
5 x 100 x 100 = 5 x 10000 = 50 000 cm2
10000 dam2 → km2
10000: 100: 100 = 10000: 10000 = 1 km2
Also read about area and perimeter.
Conversion of volume units
The SI unit for the volume quantity is the cubic meter (m3). This unit presents as multiple cubic kilometers (km3), cubic hectometer (hm3), cubic decameter (dam3). The submultiples are cubic decimeter (dm3), cubic centimeter (cm3) and cubic millimeter (mm3).
Volume units are converted by multiplying and dividing by 1000, as shown in the table below.
Examples:
4 dm3 → mm3
4 x 1000 x 1000 = 4 x 1 000 000 = 4 000 000 mm3
10,000,000 m3 → km3
10 000 000: 1000: 1000: 1000 = 10 000 000: 1 000 000 000 = 0.01 km3
Another unit widely used for volume measurements is the liter, which is equivalent to a cubic decimeter.
1 L = 1 dm3
To perform conversions using the liter as the base unit, see the table below.
know more about volume measurements.
Conversion of temperature units
In SI, the unit for measuring the temperature quantity is the Kelvin. The thermometer is the instrument used to measure temperature and the thermometric scales used are: degrees Celsius (º C), degrees Fahrenheit (º F) and Kelvin. The three scales are listed as follows:
Example: 20°C conversion to Fahrenheit scale
To make calculations easier, instead of using fractional relationships, you can use the following formulas.
know more about thermometric scales.
Conversion of speed units
The velocity magnitude presents as a unit in the SI meters per second (m/s). However, it is also common to use kilometers per hour (km/h).
As 1 km corresponds to 1000 m and 1 h is equivalent to 3600 s, to convert m/s into km/h it is multiplied by 3.6 and to transform km/h into m/s the value is divided by 3.6 .
Examples:
10 m/s → km/h
10 x 3.6 = 36 km/h
36 km/h → m/s
36: 10 = 3.6 m/s
Also read about average speed.
International System of Units
O International System of Units presents a base of 7 quantities with their respective fundamental units so that from them the other quantities are defined.
The fundamental units of the SI are:
| fundamental magnitude | base unit | unit symbol |
|---|---|---|
| Pasta | kilogram | kg |
| Time | second | s |
| Length | subway | m |
| Electric current | ampere | THE |
| Light intensity | candela | CD |
| amount of substance | mol | mol |
| thermodynamic temperature | kelvin | K |
prefix table
To represent very large or very small quantities, prefixes are used before units. The prefixes correspond to powers of 10 that multiply the measurements.
Examples:
2 nanometers = 2 nm = 2 x 10-9 m = 0.000000002 m
2 kilometers = 2 km = 2 x 103 m = 2000 m
| multiples | submultiples | ||||
|---|---|---|---|---|---|
| Prefix | Symbol | Factor |
Prefix | Symbol | Factor |
| deca | gives | 101 | I decided | d | 10-1 |
| hecto | H | 102 | centi | ç | 10-2 |
| kilo | k | 103 | milli | m | 10-3 |
| mega | M | 106 | micro | 10-6 | |
| gigantic | G | 109 | nano | no | 10-9 |
| will have | T | 1012 | peak | P | 10-12 |
| peta | P | 1015 | femtus | f | 10-15 |
| eh | AND | 1018 | act | The | 10-18 |
| zetta | Z | 1021 | zepto | z | 10-21 |
| yotta | Y | 1024 | yocto | y | 10-24 |
Unit Conversion Exercises
question 1
A cartographic scale represents a landscape on a map. For this, the reduction of measures is carried out proportionally. For example, on a scale of 1:100,000 it means that 1 cm on the map corresponds to 100,000 cm in the real landscape, which in km is equal to
a) 1 km
b) 0.1 km
c) 10 km
d) 0.01 km
Correct alternative: a) 1 km.
question 2
Soft drinks are drinks based on water and sugar. A 350 ml soda has about 37000 mg of sugar. This amount, in grams, corresponds to:
a) 370 g
b) 0.37 g
c) 37 g
d) 3.7 g
Correct alternative: c) 37 g.
question 3
Usain Bolt is a Jamaican athlete famous for winning sprint events and considered the fastest man in the world. In 2009, the sprinter broke the record by performing the 100-meter race in 9.58 seconds, which would be, in minutes, about
a) 0.14 min
b) 0.12 min
c) 0.16 min
d) 0.17 min
Correct alternative: c) 0.16 min
question 4
The Vatican is the smallest country in the world. Although located within the city of Rome, Italy, the territory known as the seat of the Catholic Church is independent and covers an area of 0.44 km2, that in m2 stands for
a) 4400 m2
b) 44 000 m2
c) 440 m2
d) 440 000 m2
Correct alternative: d) 440 000 m2.
question 5
Although the volume of blood in the human body varies from one person to another for several factors, it is estimated that on average an adult has 5 liters of blood. If we wanted to express this quantity in m3, we would have the volume
a) 0.5 m3
b) 0.005 m3
c) 0.05 m3
d) 5 m3
Correct alternative: b) 0.005 m3.
question 6
The Sun is the closest star to the planet and the center of our Solar System, which provides us with light and heat. The visible surface of the Sun is called the photosphere and it is also the layer with the lowest temperature, around 5800 K, which in ºC corresponds to
a) 5 242.39 °C
b) 5,328.72 °C
c) 5,526.85°C
d) 5 416.20 °C
Alternative: c) 5,526.85°C.
question 7
The peregrine falcon is the fastest animal on the planet, as it can reach a speed of 320 km/h in one flight. If velocity were measured in m/s, this bird would reach approximately
a) 89.6 m/s
b) 94.4 m/s
c) 76.5 m/s
d) 88.9 m/s
Correct alternative: d) 88.9 m/s.
Learn more about units of measure.
