Introduction to Electric Circuits

6 Units and dimensions

1.4 MULTIPLES AND SUBMULTIPLES OF UNITS

There is an enormous range of magnitudes in the quantities encountered in
electrical and electronic engineering. For example, electric potential can be
lower than 0.000 001 V or higher than 100 000 V. By the use of multiples and
submultiples we can avoid having to write so many zeros. Table 1.2 shows their
names and abbreviations.

Table 1.2
Multiple Abbreviation Value Submultiple Abbreviation Value
exa E 10 TM milli m 10 -3
peta P 1015 micro tx 10 -6
tera T 1012 nano n 10 -9
giga G 10 9 pico p 10 -12
mega M 10 6 femto f 10 -15
kilo k 10 3 atto a 10 -18

These are the preferred multiples and submultiples and you will see that the

powers are in steps of 3. However, because of their convenience there are some

others in common use. For example, deci (d), which is 10 -~, is used in decibel

(dB); and centi (c), which is 10 -2, is used in centimetre (cm). Capital letters are

used for the abbreviations of multiples and lower case letters are used for the

abbreviations of submultiples. The exception is kilo for which the abbreviation

is the lower case k, not the capital K.

Example 1.7

Express 10 seconds in (1) milliseconds, (2) microseconds.

Solution

1 To convert from units to multiples or submultiples of units it is necessary to

divide by the multiple or submultiple. To find the number of milliseconds in

1 second we simply divide by the submultiple 10 -3. Thus 1 second -

1/10 -3 - 10 3 milliseconds. In 10 seconds there are therefore

10 • 10 3= 10 4 ms.

2 To find the number of microseconds in 10 seconds we divide by the

submultiple 10 -6. Thus in 10 s there are 10/10 .-6 - 10 7 l~S.

Example 1.8

Express 1 metre in (1) kilometres, (2) centimetres.

Solution

1 To find the number of kilometres in 1 metre we divide by the multiple 10 3.

Thus in 1 m there are 1/10 3 -- 10 -3 km.