# Powers of 10

The International Bureau of Weights and Measures has adopted a series of prefix names and symbols for decimal multiples and submultiples of SI units. They are expressed as powers of 10 and range from 1030 to 10-30.

### Badge of BIPM

The badge of the International Bureau of Weights and Measures (BIPM) represents an allegory of science holding the new metre standard with its decimal divisions. The badge carries the inscription in Greek ‘metro kro’ or ‘use the measure’.

**Rights:**Image reproduced with permission of the BIPM, which retains full internationally protected copyright (© BIPM)

The advantages of basing the multiples and submultiples on the decimal system are:

there are no fractions – decimals only

there are no long rows of zeros – prefixes replace them

they are unique, unambiguous letter symbols

they eliminate the confusion of old number names – is a billion a thousand million (USA) or a million million (Europe)?

## SI prefixes

Larger and smaller quantities are expressed by using appropriate prefixes with the base unit. For example, the base unit of length is the metre. For small lengths, the millimetre (10-3 m) may be the appropriate quantity, whereas for large distances, the kilometre (103 m) may be more appropriate.

These prefixes multiply base units for larger measurements

These prefixes are decimal fractions that multiply base units for smaller measurements

Prefix

Symbol

Multiple

Prefix

Symbol

Submultiple

quetta

2

1030

deci

d

10-1

ronna

R

1027

centi

c

10-2

yotta

Y

1024

milli

m

10-3

zetta

Z

1021

micro

μ

10-6

exa

E

1018

nano

n

10-9

peta

P

1015

pico

p

10-12

tera

T

1012

femto

f

10-15

giga

G

109

atto

a

10-18

mega

M

106

zepto

z

10-21

kilo

k

103

yocto

y

10-24

hecto

h

102

ronto

r

10-27

deka

da

101

quecto

q

10-30

100 = 1

The first letter of the SI abbreviation represents the prefix and the second letter represents the base unit.

In the You, Me and UV resources, information is given about the UV index. One unit on the UV index is roughly equivalent to 25 millijoules of UV energy falling per second on a 1 square metre area. In abbreviated form, this amount of energy is written as 25 mJ.

In the Nanoscience resources, it is reported that fingernails grow at about 1 nanometre per second. In abbreviated form, this length is written as 1 nm.

The Space revealed resources deal with extremely large distances. For example, in the article Distances in space, it states: When the Space Shuttle goes into space, it orbits about 700 km above the surface of the Earth. The ‘km’ means kilometre, which is 103 m. The distance from the Earth to Mars is 78 million kilometres, which is 78 x 106 km, and this in turn is 78 x 109 m. Using the prefix for 109 from the table above, this becomes 78 Gm, which is pronounced as ‘seventy-eight gigametres’.

## Prefix names

To many people, the choice of prefix names seems strange. For example, where does ‘kilo’ come from?

Prefix names have been mostly chosen from Greek words (positive powers of 10) or Latin words (negative powers of 10), although recent extensions of the range of powers of 10 has resulted in the use of words from other languages. ‘Kilo’ comes from the Greek word for 1000 (103), and ‘milli’ comes from the Latin word for one thousandth (10-3).

## Regular prefixes

Most of the prefixes in the table above are multiples of a thousand. These are referred to as regular prefixes and may be used with any SI unit.

Using metre as an example:

Multiples of the metre

Submultiples of the metre

1000 m = 1 km = 103 m (kilometre)

0.001 m = 1 mm =10-3 m (millimetre)

1000 km = 1 Mm =106 m (megametre)

0.001 mm = 1 μm =10-6 m (micrometre)

1000 Mm = 1 Gm =109 m (gigametre)

0.001 μm = 1 nm =10-9 m (nanometre)

Prefixes are easier to write and pronounce than powers of 10. The following example shows the same quantity written in different ways. Which is easiest?

The average daily energy requirement of an active 14-year-old boy is:

13 MJ (pronounced as ‘13 megajoules’)

13 x 106 J

1.3 x 107 J

13,000,000 joules

## Nature of Science

A large number of scientific terms have their origins in Latin words. The reason for this is that Latin was used in scholarly writing well into the 19th century. For example, Sir Isaac Newton’s major works, such as *Principia*, were all written in Latin. Today, although the popularity of the language has fallen away, Latin roots continue to serve as a major source for the derivation of new terms in the sciences.

## Related content

Explore the science ideas and concept of size further with these articles:

## Activity ideas

Measuring foot pressure provides practice using SI units, derived units and prefixes. Precision and accuracy provides various datasets for students to judge precision and accuracy in scientific settings. How long is it? is a collection of length measurements found within the Science Learning Hub. Lengths range from the very small to the very big, helping students develop an understanding of the decimal system as applied to length measurement.

## Useful links

In this interactive view the Milky Way at 10 million light years from the Earth. Then move through space towards the Earth in successive orders of magnitude.

Explore cell size and scale in this interactive from the Univerty of Utah.

Visit the The International Bureau of Weights and Measures (BIPM) website. In 2022 new metric prefixes to express the world's largest and smallest measurements, were added to the International System of Units (SI).

**Published:**17 August 2011