58 Basic Engineering Mathematics
Hence, 42 × 10
5
= 4.2 × 10
6
in engineering
notation
= 4.2 M in prefix form.
(b) Enter 47 ÷ 10 10 =
47
10 000 000 000
into the calculator. Press =
Now press ENG and the answer is 4.7 × 10
−9 .
From the table of prefixes on page 55, 10 −9
corresponds to nano.
Hence, 47 ÷10 10 F = 4.7 × 10 −9 F in engineering notation
= 4.7 nF in prefix form.
Problem 8. Rewrite (a) 0.056 mA in μA
(b) 16 700 kHz as MHz
(a) Enter 0.056 ÷ 1000 into the calculator (since milli
means ÷1000). Press =
Now press ENG and the answer is 56 × 10 −6 .
From the table of prefixes on page 55, 10 −6
corresponds to micro.
Hence, 0.056 mA =
0.056
1000
A = 56 × 10 −6 A
= 56 μA.
(b) Enter 16 700 × 1000 into the calculator (since kilo
means ×1000). Press =
Now press ENG and the answer is 16.7 × 10 6 .
From the table of prefixes on page 55, 10 6 corresponds to mega.
Hence, 16 700 kHz = 16 700 × 1000 Hz
= 16.7 × 10
6 Hz
= 16.7 MHz
Problem 9. Rewrite (a) 63 × 10 4 V in kV
(b) 3100 pF in nF
(a) Enter 63 × 10 4 into the calculator. Press =
Now press ENG and the answer is 630 × 10 3 .
From the table of prefixes on page 55, 10 3 corresponds to kilo.
Hence, 63 × 10 4 V = 630 × 10 3 V = 630 kV.
(b) Enter 3100 × 10
−12 into the calculator. Press =
Now press ENG and the answer is 3.1 × 10 −9 .
From the table of prefixes on page 55, 10 −9
corresponds to nano.
Hence, 3100 pF = 31 × 10 −12 F = 3.1 × 10 −9 F
= 3.1 nF
Problem 10. Rewrite (a) 14 700 mm in metres
(b) 276 cm in metres (c) 3.375 kg in grams
(a) 1 m = 1000 mm, hence
1 mm =
1
1000
=
1
10 3 = 10 −3 m.
Hence, 14 700 mm = 14 700 × 10 −3 m = 14.7 m.
(b) 1 m = 100 cm, hence 1 cm =
1
100
=
1
10 2 = 10 −2 m.
Hence, 276 cm = 276 × 10
−2 m = 2.76 m.
(c) 1 kg = 1000 g = 10 3 g
Hence, 3.375 kg = 3.375 × 10 3 g = 3375 g.
Now try the following Practice Exercise
Practice Exercise 34 Engineering notation
(answers on page 343)
In problems 1 to 12, express in engineering notation in prefix form.
1. 60 000 Pa
2. 0.00015 W
3. 5 × 10 7 V
4. 5.5 × 10 −8 F
5. 100 000 W
6. 0.00054 A
7. 15 × 10 5
8. 225 × 10 −4 V
9. 35 000 000 000 Hz
10. 1.5 × 10 −11 F
11. 0.000017 A
12. 46 200
Hence, 42 × 10
5
= 4.2 × 10
6
in engineering
notation
= 4.2 M in prefix form.
(b) Enter 47 ÷ 10 10 =
47
10 000 000 000
into the calculator. Press =
Now press ENG and the answer is 4.7 × 10
−9 .
From the table of prefixes on page 55, 10 −9
corresponds to nano.
Hence, 47 ÷10 10 F = 4.7 × 10 −9 F in engineering notation
= 4.7 nF in prefix form.
Problem 8. Rewrite (a) 0.056 mA in μA
(b) 16 700 kHz as MHz
(a) Enter 0.056 ÷ 1000 into the calculator (since milli
means ÷1000). Press =
Now press ENG and the answer is 56 × 10 −6 .
From the table of prefixes on page 55, 10 −6
corresponds to micro.
Hence, 0.056 mA =
0.056
1000
A = 56 × 10 −6 A
= 56 μA.
(b) Enter 16 700 × 1000 into the calculator (since kilo
means ×1000). Press =
Now press ENG and the answer is 16.7 × 10 6 .
From the table of prefixes on page 55, 10 6 corresponds to mega.
Hence, 16 700 kHz = 16 700 × 1000 Hz
= 16.7 × 10
6 Hz
= 16.7 MHz
Problem 9. Rewrite (a) 63 × 10 4 V in kV
(b) 3100 pF in nF
(a) Enter 63 × 10 4 into the calculator. Press =
Now press ENG and the answer is 630 × 10 3 .
From the table of prefixes on page 55, 10 3 corresponds to kilo.
Hence, 63 × 10 4 V = 630 × 10 3 V = 630 kV.
(b) Enter 3100 × 10
−12 into the calculator. Press =
Now press ENG and the answer is 3.1 × 10 −9 .
From the table of prefixes on page 55, 10 −9
corresponds to nano.
Hence, 3100 pF = 31 × 10 −12 F = 3.1 × 10 −9 F
= 3.1 nF
Problem 10. Rewrite (a) 14 700 mm in metres
(b) 276 cm in metres (c) 3.375 kg in grams
(a) 1 m = 1000 mm, hence
1 mm =
1
1000
=
1
10 3 = 10 −3 m.
Hence, 14 700 mm = 14 700 × 10 −3 m = 14.7 m.
(b) 1 m = 100 cm, hence 1 cm =
1
100
=
1
10 2 = 10 −2 m.
Hence, 276 cm = 276 × 10
−2 m = 2.76 m.
(c) 1 kg = 1000 g = 10 3 g
Hence, 3.375 kg = 3.375 × 10 3 g = 3375 g.
Now try the following Practice Exercise
Practice Exercise 34 Engineering notation
(answers on page 343)
In problems 1 to 12, express in engineering notation in prefix form.
1. 60 000 Pa
2. 0.00015 W
3. 5 × 10 7 V
4. 5.5 × 10 −8 F
5. 100 000 W
6. 0.00054 A
7. 15 × 10 5
8. 225 × 10 −4 V
9. 35 000 000 000 Hz
10. 1.5 × 10 −11 F
11. 0.000017 A
12. 46 200