# Measurement Units

Units of measurement are models established to measure different quantities such as length, capacity, mass, time and volume.

The International System of Units (SI) defines the standard unit of each quantity. Based on the decimal metric system, SI arose from the need to standardize the units that are used in most countries.

## Length Measures

There are several length measures, such as yard, inch and foot.

In SI the default unit of length is meter (m). Currently it is defined as the length of the distance light travels in a vacuum over a time interval of 1 / 299,792,458 of a second.

The multiples and submultiples of the meter are: kilometer (km), hectometer (hm), decimeter (dam), decimeter (dm), centimeter (cm) and millimeter (mm).

## Capacity Measures

The most widely used unit of measure is the liter (l). Also used are the gallon, the barrel, the bedroom, among others.

The multiples and submultiples of the liter are: kiloliter (kl), hectoliter (hl), decaliter (dal), deciliter (dl), centiliter (cl), milliliter (ml).

## Mass Measures

In the International System of Units the mass measurement is the kilogram (kg). A platinum and iridium cylinder is used as the universal kilogram standard.

The units of mass are: kilogram (kg), hectogram (hg), decagram (dag), gram (g), decigram (dg), centigram (cg) and milligram (mg).

Examples of mass measurements are at sign, pound, ounce and ton. Being 1 ton equivalent to 1000 kg.

## Volume Measurements

In SI the unit of volume is the cubic meter (m 3 ). The multiples and submultiples of m 3 are: cubic kilometer (km 3 ), cubic hectometer (hm 3 ), cubic decimeter (dam 3 ), cubic decimeter (dm 3 ), cubic centimeter (cm 3 ) and cubic millimeter (mm 3 ) .

We can turn a measure of capacity into volume because liquids take the form of the container that contains them. For this we use the following relation:

1 l = 1 dm 3

## Measurement conversion table

The same method can be used to calculate multiple quantities.

First, let's draw a table and place in its center the base units of measure that we want to convert, for example:

• Capacity: liter (l)
• Length: meter (m)
• Mass: gram (g)
• Volume: cubic meter (m 3 )

Everything on the right side of the base measure is called submultiple. The prefixes deci, centi and mili correspond respectively to the tenth, hundredth and thousandth part of the fundamental unit.

On the left side are the multiples. The prefixes deca, hecto and kilo correspond respectively to ten, one hundred and one thousand times the fundamental unit.

Multiples Base Measure Submultiples
kilo (k) hecto (h) decade) deci (d) centi (c) milli (m)
kiloliter (kl) hectoliter (hl) decaliter (dal) liter (l) deciliter (dl) centiliter (cl) milliliter (ml)
kilometer (km) hectometer (hm) decameter (dam) meter (m) decimeter (dm) centimeter (cm) millimeter (ml)
kilogram (kg) hectogram (hg) decagram (dag) gram (g) decigram (dg) centigram (cg) milligram (mg)
cubic kilometer (km 3 ) cubic hectometer (hm 3 ) cubic diameter (dam 3 ) cubic meter (m 3 ) cubic decimeter (dm 3 ) cubic centimeter (cm 3 ) cubic millimeter (mm 3 )

Examples

1) How many milliliters corresponds to 35 liters?

To make the requested transformation, let's write the number in the table of capacity measurements. Remembering that the measure can be written as 35.0 liters. The comma and the figure that is before it must be in the house of the given unit of measure, which in this case is the liter.

kl hl dal l dl cl ml
3 5, 0

Then we complete the other boxes with zeros until we get to the requested unit. The comma will always be behind the digits in the requested unit box, which in this case is ml.

kl hl dal l dl cl ml
3 5th 0 0 0,

Thus 35 liters corresponds to 35000 ml.

2) Turn 700 grams into kilograms.

Remembering that we can write 700.0 g. We put the comma and 0 before it in the given unit, in this case g and the other digits in the previous boxes.

 kg hg dag g dg cg mg 7th 0 0, 0

Then we complete with zeros until we get to the requested unit, which in this case is the kilogram. The comma then passes behind the figure that is in the kilogram house.

 kg hg dag g dg cg mg 0, 7th 0 0

So 700 g corresponds to 0.7 kg.

3) How many cubic meters has a 4500 cubic centimeter parallelepiped?

In volume transformations (m 3 ), we will proceed in the same way as the previous examples. However, we must put 3 digits in each box.

We write the measurement as 4500.0 cm 3.

 km 3 hm 3 dam 3 m 3 dm 3 cm 3 mm 3 4 500, 0

Now we complete with 3 digits each house until you get the requested unit.

 km 3 hm 3 dam 3 m 3 dm 3 cm 3 mm 3 000, 004 500

We found that 4500 cm 3 corresponds to 0.0045 m 3 .

The base unit of time measurement in SI is the second (s). Currently the second is defined as the duration of 9,192,631,770 vibrations of radiation emitted by the electronic transition between the hyperfine levels of the cesium atom ground state 133.

The multiples of the second are the minute, the hour and the day. These measurements are not decimal, so the following ratios are used:

1 minute (min) = 60 seconds
1 hour = 3 600 seconds
60 minutes (min) = 1 hour (h)
24 hours (h) = 1 day (d)

The submultiples of the second are:

Tenth of a second = 0.1 s or 1/10 s
Hundredth of a second = 0.01 s or 1/100 s
Millisecond = 0.001 s or 1/1000 s

There is a unit of measurement used in astronomy to indicate huge distances.