# Standard Unit

Over the years in so many companies, organisations and businesses, there has always been a call to determine performance. In order to achieve this, several metrics have been developed such as calculating the performance of workers and such measurements tend to be in units.

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Hereafter, you will be learning standard units, types of standard units and examples of their application.

## What is standard unit in maths?

Standard unit is a simple and single unit of measurement generally used for a quantity. For example, centimetres, seconds, kilograms, centigrade, etc.

A unit of measurement is just 1 unit of a particular quantity. For example, 1 centimetre, 1 kilogram, 1 second, etc.

Standard units are also simple units which are used in combination with other standard units to derive compound units.

### Non-standard units

Non-standard units are things, everyday objects, used to give an impression of the measure of another thing or object by comparing their measurements to one another.

These units of measurement tell us how long/short or light/heavy substances are but without precision. They are introduced in the early years' foundation school for children because at such young ages it would be complex for them to understand the use of scale.

Examples of non-standard units are:

• using a pencil to measure the length of a sofa by the number of pencils that fit in its length;

• using a cup to measure the capacity of a jar by how many cups it can contain;

• measuring the distance between two objects on the floor using the feet, and counting how many feet apart they are.

Although they cannot give an accurate measurement of a quantity, they provide a visual impression on what the value of the measurement is. For example, instead of saying a gallon is 10 litres, a child would better understand it to be measured as 20 cups.

### Compound units

Unlike standard units,

Compound units are derived from a combination of two or more standard units.

For example, kilometre per hour (kph) is a unit used in measuring speed or velocity as is derived by combining two standard units such as kilometre and hour. More examples of compound units are Newton, ms-2, Pascal, joules, etc.

## What are the types of standard units

There are two basic types of standard units which are the imperial units and the metric units.

### Imperial units

Imperial units take their origin from the UK, Great Britain more precisely.

According to the 1824 and 1878 Weights and Measures Act, formal terms of units were used in measurement and generalised in their application over other units of measurement.

Some imperial units are pints, feet, inches, ounce, grain, mile, acre, etc.

This system of unit measurement is also found in Libya and Myanmar.

### Metric units

Metric units are standard units used in most parts of the world and are often regarded as International System of Units (SI units). This system of measurement relies on a decimal system due to the representation of its units in indices of 10. For example, kilograms, metres, litres, etc.

## What is the standard unit of length?

The standard unit used in measuring length is metre which has the symbol 'm'. However, some other metre-derived units are used since they can be expressed in powers or roots 10 when compared to metre. The table below shows the relationship between metre-derived units and meters.

 Metre-derived units Value in metres (m) Value in metres (m) in index form 1 Kilometre (km) 1000 103 1 Decimetre (dm) 0.1 10-1 1 Centimetre (cm) 0.01 10-2 1 Millimetre (mm) 0.001 10-3 1 Micrometre or micron (μm) 0.000001 10-6

However, there are other units used to measure length such as feet (ft), inches (in), nautical miles, mile, yard, rod, fathom, etc.

The table below shows the conversion of other units (metric units) to meters.

 Imperial unit Metric unit in meters (m) 1 inch 2.54 × 10–2 1 foot 3.048 × 10–1 1 yard 9.144 × 10–1 1 mile 1.609 × 103

## Other standard units of measurement

There are standard units of measurement and their respective conversions. These tables below would serve as a guide when measuring other standard quantities as well as their conversion.

### Standard units of area

Though we are much conversant with the measurement of are in square centimetres, metres or kilometres, there are are some other units which are used in measuring areas. The table below shows their conversion.

 Unit Conversion in squared metre (m2) 1 acre 102 m2 1 hectare 104 m2

Note that area is also measured in square feet, inches, miles and yard. To achieve this, you just have to make conversion knowing the measurement of 1m to the respective unit.

### Standard units of volume

Similarly, we are more inclined to measure volume in cubic centimetres, metres or kilometres. There are other units with which volume can be measured in. The table below shows their conversion.

 Unit Conversion to cubic metre (m3) 1 litre 10-3 1 gallon ≅3.7854 × 10–3 1 barrel ≅1.5899 × 10–1 1 pint ≅4.7318 × 10–4

### Standard units of mass

Measurement of mass in most cases is in grams and kilograms, however, there are several other units used in measuring mass, See the table below for their conversion.

 Unit Conversion to kilograms (kg) 1 gram (g) 10–3 1 ounce (oz) 2.835 × 10–2 1 pound (lb) 4.536 × 10–1 1 ton (t) 9.072 × 102 1 atomic mass unit (a.m.u.) 1.661 × 10–27

The atomic mass unit (a.m.u.) is used in determining masses of subatomic particles, it is a standard unit but not an SI unit.

### Time

The units used in measuring time are quite numerous, however, we will show a few on the table.

 Units Conversion to nearest unit of time 1 minute 60 seconds (s) 1 hour 60 minutes 1 day 24 hours 1 week 7 days 1 fortnight 2 weeks 1 month 4 weeks 1 year 12 months 1 quarantine 40 days 1 year 365 days (common)366 days (leap)354.37 days (lunar)

## What formula is used in calculating standard units?

There is no formula used in calculating standard units, rather standard units may be affected when formulas are applied depending on the operations involved.

If an operation involves only addition and subtraction, then the standard unit for such quantity is unchanged, e.g., when finding the perimeter of a shape. However, when operations involve multiplication or division such standard unit would either change to a higher power unit (as in area and volume) or the unit may be lost (as in ratio).

Imisi, Nonso, Kohe and Ireti are 33, 35, 6, and 4 years respectively. What is the sum of their ages?

Solution

The total of their ages is

$33+35+6+4=78$

Hence the sum of their ages is 78 years.

Observe that the units did not change as a result of the addition operation.

Find the area of a rectangular lawn 5m by 2m.

Solution

The area of a rectangle is

$Area=length×breadth$

Hence, the area of the rectangular lawn is calculated as

$Area=5m×2m\phantom{\rule{0ex}{0ex}}\phantom{\rule{0ex}{0ex}}=10{m}^{2}$

Notice the change in units from m to m2 because the operation involved multiplication. Although, in an earlier section the unit of area was tabulated.

Find the ratio between the masses of rock A, 60kg, and rock B, 50kg.

Solution

The ratio of mass A to B is

$A:B=60kg:50kg\phantom{\rule{0ex}{0ex}}\phantom{\rule{0ex}{0ex}}=\frac{60kg}{50kg}\phantom{\rule{0ex}{0ex}}\phantom{\rule{0ex}{0ex}}=\frac{6\overline{)0}\overline{)kg}}{5\overline{)0}\overline{)kg}}\phantom{\rule{0ex}{0ex}}\phantom{\rule{0ex}{0ex}}=\frac{6}{5}\phantom{\rule{0ex}{0ex}}\phantom{\rule{0ex}{0ex}}=6:5$

Note that the unit is lost at the end because of the division operation that took place.

## Examples of problems with standard units

A better understanding of standard units is surely understood by application in certain tasks.

If Imisi's height is 170 cm, find her height in feet.

Solution

Here, Imisi's height has been given in centimetres which is a metric unit, but we are asked to convert her height to feet which is an imperial unit.

Recall that

$1ft=3.048×{10}^{-1}m\phantom{\rule{0ex}{0ex}}\phantom{\rule{0ex}{0ex}}1m={10}^{2}cm$

We would have to convert 170 cm to m.

$170cm=\frac{170}{100}m\phantom{\rule{0ex}{0ex}}\phantom{\rule{0ex}{0ex}}170cm=1.7m$

Now, we have to convert from m to ft.

$1ft=0.3048m$

Let x be the unknown value of 1.7 m in ft. So,

$1ft=0.3048m\phantom{\rule{0ex}{0ex}}xft=1.7m$

You should express as ratio and equate to become proportion.

$1ft:xft=0.3048m:1.7m\phantom{\rule{0ex}{0ex}}\phantom{\rule{0ex}{0ex}}\frac{1ft}{xft}=\frac{0.3048m}{1.7m}\phantom{\rule{0ex}{0ex}}\phantom{\rule{0ex}{0ex}}\frac{1\overline{)ft}}{x\overline{)ft}}=\frac{0.3048\overline{)m}}{1.7\overline{)m}}\phantom{\rule{0ex}{0ex}}\phantom{\rule{0ex}{0ex}}\frac{1}{x}=\frac{0.3048}{1.7}\phantom{\rule{0ex}{0ex}}\phantom{\rule{0ex}{0ex}}x\left(0.3048\right)=1\left(1.7\right)\phantom{\rule{0ex}{0ex}}\phantom{\rule{0ex}{0ex}}0.3048x=1.7\phantom{\rule{0ex}{0ex}}\phantom{\rule{0ex}{0ex}}\frac{0.3048x}{0.3048}=\frac{1.7}{0.3048}\phantom{\rule{0ex}{0ex}}\phantom{\rule{0ex}{0ex}}x=5.5774\phantom{\rule{0ex}{0ex}}\phantom{\rule{0ex}{0ex}}x\approx 5.6\left(1d.p.\right)$

This means Imisi's height in ft is approximately 5.6 ft.

Classify the following under metric, imperial, compound and non-standard units;

i) liters

ii) ms-1

iii) number of toothpicks

iv) pounds

Solution

i) Litres can be classified under metric units.

ii) ms-1 can be classified as compound units.

iii) the number of toothpicks can be classified as non-standard units.

iv) pounds can be classified under imperial units.

## Standard Unit - Key takeaways

• Standard unit is a simple and single unit of measurement generally used for a quantity. For example, centimetres, seconds, kilograms, centigrade, etc.
• Non-standard units are things used to give an impression of the measure of a quantity.
• compound units are derived from a combination of two or more standard units.
• There are two basic types of standard units which are the imperial units and the metric units.
• There is no formula used in calculating standard units, rather standard units may be affected when formulas are applied depending on the operations involved.
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What is standard unit example?

An example of a standard unit is meters. Others include liters, kilograms, seconds etc.

What are the standard units in maths?

Standard unit is a simple and single unit of measurement generally used for a quantity. For example, centimeters, seconds, kilograms, centigrade etc.

Does standard deviation have units?

Standard deviation has no unit of its own but it takes the unit of the quantity it actually measures.

What is the standard unit of volume?

The standard unit for volume is cubic meters (m3)

What is the formula of standard unit?

There is no formula used in calculating standard units, rather standard units may be affected when formulas are applied depending on the operations involved.

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