Units, prefixes and engineering notation 57
In problems 6 and 7, express the numbers given as
integers or decimal fractions.
6. (a) 1.01 × 10 3 (b) 9.327 × 10 2
(c) 5.41 × 10
4 (d) 7 × 10
0
7. (a) 3.89 × 10 −2 (b) 6.741 × 10 −1
(c) 8 × 10 −3
In problems 8 and 9, evaluate the given expressions, stating the answers in standard form.
8. (a) (4.5 × 10 −2 )(3 × 10 3 )
(b) 2 × (5.5 × 10 4 )
9. (a)
6 × 10 −3
3 × 10 −5
(b)
(2.4 × 10 3 )(3 × 10 −2 )
(4.8 × 10 4 )
10. Write the following statements in standard
form.
(a) The density of aluminium is 2710
kg m
−3 .
(b) Poisson’s ratio for gold is 0.44
(c) The impedance of free space is
376.73 .
(d) The electron rest energy is 0.511 MeV.
(e) Proton charge–mass ratio is 95789700
C kg −1 .
(f ) The normal volume of a perfect gas is
0.02241 m 3 mol −1 .
8.5 Engineering notation
In engineering, standard form is not as important as
engineering notation. Engineering notation is similar
to standard form except that the power of 10 is always
a multiple of 3.
For example, 43 645 = 43.645 × 10
3
in engineering notation
and
0.0534 = 53.4 × 10
−3
in engineering notation
From the list of engineering prefixes on page 55 it is
apparent that all prefixes involve powers of 10 that are
multiples of 3.
For example, a force of 43 645 N can rewritten as
43.645 × 10 3 N and from the list of prefixes can then
be expressed as 43.645 kN.
Thus,
43 645N ≡ 43.645 kN
To help further, on your calculator is an ‘ENG’ button.
Enter the number 43 645 into your calculator and then
press =. Now press the ENG button and the answer is
43.645 × 10 3 . We then have to appreciate that 10 3 is the
prefix ‘kilo’, giving 43 645 N ≡ 43.645 kN.
In another example, let a current be 0.0745 A. Enter
0.0745 into your calculator. Press =. Now press
ENG and the answer is 74.5 × 10 −3 . We then have
to appreciate that 10 −3 is the prefix ‘milli’, giving
0.0745 A ≡ 74.5 mA.
Problem 6. Express the following in engineering
notation and in prefix form:
(a) 300 000 W (b) 0.000068 H
(a) Enter 300 000 into the calculator. Press =
Now press ENG and the answer is 300 × 10
3 .
From the table of prefixes on page 55, 10 3 corresponds to kilo.
Hence, 300 000 W = 300 × 10 3 W in engineering
notation
= 300 kW in prefix form.
(b) Enter 0.000068 into the calculator. Press =
Now press ENG and the answer is 68 × 10 −6 .
From the table of prefixes on page 55, 10 −6
corresponds to micro.
Hence, 0.000068 H = 68 × 10 −6 H in engineering
notation
= 68 μH in prefix form.
Problem 7. Express the following in engineering
notation and in prefix form:
(a) 42 × 10
5
(b) 4.7 × 10
−10 F
(a) Enter 42 × 10 5 into the calculator. Press =
Now press ENG and the answer is 4.2 × 10 6 .
From the table of prefixes on page 55, 10 6 corresponds to mega.
In problems 6 and 7, express the numbers given as
integers or decimal fractions.
6. (a) 1.01 × 10 3 (b) 9.327 × 10 2
(c) 5.41 × 10
4 (d) 7 × 10
0
7. (a) 3.89 × 10 −2 (b) 6.741 × 10 −1
(c) 8 × 10 −3
In problems 8 and 9, evaluate the given expressions, stating the answers in standard form.
8. (a) (4.5 × 10 −2 )(3 × 10 3 )
(b) 2 × (5.5 × 10 4 )
9. (a)
6 × 10 −3
3 × 10 −5
(b)
(2.4 × 10 3 )(3 × 10 −2 )
(4.8 × 10 4 )
10. Write the following statements in standard
form.
(a) The density of aluminium is 2710
kg m
−3 .
(b) Poisson’s ratio for gold is 0.44
(c) The impedance of free space is
376.73 .
(d) The electron rest energy is 0.511 MeV.
(e) Proton charge–mass ratio is 95789700
C kg −1 .
(f ) The normal volume of a perfect gas is
0.02241 m 3 mol −1 .
8.5 Engineering notation
In engineering, standard form is not as important as
engineering notation. Engineering notation is similar
to standard form except that the power of 10 is always
a multiple of 3.
For example, 43 645 = 43.645 × 10
3
in engineering notation
and
0.0534 = 53.4 × 10
−3
in engineering notation
From the list of engineering prefixes on page 55 it is
apparent that all prefixes involve powers of 10 that are
multiples of 3.
For example, a force of 43 645 N can rewritten as
43.645 × 10 3 N and from the list of prefixes can then
be expressed as 43.645 kN.
Thus,
43 645N ≡ 43.645 kN
To help further, on your calculator is an ‘ENG’ button.
Enter the number 43 645 into your calculator and then
press =. Now press the ENG button and the answer is
43.645 × 10 3 . We then have to appreciate that 10 3 is the
prefix ‘kilo’, giving 43 645 N ≡ 43.645 kN.
In another example, let a current be 0.0745 A. Enter
0.0745 into your calculator. Press =. Now press
ENG and the answer is 74.5 × 10 −3 . We then have
to appreciate that 10 −3 is the prefix ‘milli’, giving
0.0745 A ≡ 74.5 mA.
Problem 6. Express the following in engineering
notation and in prefix form:
(a) 300 000 W (b) 0.000068 H
(a) Enter 300 000 into the calculator. Press =
Now press ENG and the answer is 300 × 10
3 .
From the table of prefixes on page 55, 10 3 corresponds to kilo.
Hence, 300 000 W = 300 × 10 3 W in engineering
notation
= 300 kW in prefix form.
(b) Enter 0.000068 into the calculator. Press =
Now press ENG and the answer is 68 × 10 −6 .
From the table of prefixes on page 55, 10 −6
corresponds to micro.
Hence, 0.000068 H = 68 × 10 −6 H in engineering
notation
= 68 μH in prefix form.
Problem 7. Express the following in engineering
notation and in prefix form:
(a) 42 × 10
5
(b) 4.7 × 10
−10 F
(a) Enter 42 × 10 5 into the calculator. Press =
Now press ENG and the answer is 4.2 × 10 6 .
From the table of prefixes on page 55, 10 6 corresponds to mega.