Download Standard form 11F

Standard form
11F
Scientists use standard form or scientific notation to write very large and very small numbers.
A number in scientific notation takes the form a × 10p where:
a is a decimal number between 1 and 10
p is either a positive or negative integer (whole number).
Example
Solution
1 The distance of the planet Pluto from the
Sun is 5 900 000 000 km. Write this in
standard form.
Shift the decimal point nine places to the left:
5 900 000 000· = 5·9 × 109 km
2 Write 8·45 × 106 as a basic numeral.
Shift the decimal point six places to the right:
8·45 × 106 = 8·450 000 = 8 450 000
3 Write the diameter of an atom, which is
0·000 000 1 millimetres, as a standard
form number.
Shift the decimal point seven places to
the right:
0·000 000 1 = 1·0 × 10–7 mm
4 Write 4·25 × 10–4 as a basic numeral.
Shift the decimal point four places to the left:
4·25 × 10–4 = 00 004·25 = 0·000 425
A TI-89 calculator can be used to work with large numbers in
standard form.
5·9 × 109 = 5 900 000 000
8·45 × 106 = 8 450 000
If a result cannot be displayed in the number of digits specified
in Display Digits of the MODE menu, then standard form is
used in which E represents the power of 10.
1·0 × 10–7 = 0·000 000 1
The results displayed are:
1
1·0 × 10–7 = -------------------------10 000 000
Approximate mode 1·0 × 10–7 = 1·E–7
Exact mode
Exercise 11F
1 Write the following basic numerals in standard form:
a 60 000
b 120 800
c 550
e 490 000
f 750
g 50
d 75 000 000
h 3·5
2 Write the following standard form numbers as basic numerals:
a 2·5 × 103
b 8·05 × 106
c 7·621 × 105
e 4·9 × 108
f 9·5 × 102
g 6·0 × 101
d 8·205 × 106
h 9·5 × 100
3 Write the following basic numerals in standard form:
a 0·006
b 0·001 08
c 0·75
e 0·5
f 0·000 000 6
g 0·000 002 5
d 0·000 625
h 0·000 061
Chapter 11 Exponential and Logarithmic Relations
359
11F
4 Write the following standard form numbers as basic numerals:
a 5·3 × 10–3
b 7·0 × 10–5
c 7·5 × 10–1
e 1·05 × 10–2
f 6·75 × 10–1
g 9·99 × 10–5
d 2·5 × 10–3
h 7·3 × 10–3
5 Write the following as standard form numbers:
a 299 792 500 metres per second, the speed of light
b 15 000 000 000 years ago, the time since the Big Bang
c 228 000 000 kilometres, the approximate distance of Mars from the Sun
d 150 million kilometres, the approximate distance of the Sun from the Earth
e 0·000 000 000 000 000 000 000 000 001 67 kg, the mass of a proton in an atom
f 0·000 000 000 000 000 000 000 000 000 000 911 kg, the mass of an electron
6 Use a calculator to complete the following:
a (2·5 × 107) × (6·25 × 104)
c (3·625 × 10–2) × (2·25 × 103)
e (8·75 × 108) ÷ (2·5 × 105)
g (2·275 × 105) ÷ (3·25 × 10–2)
i
1·903 × 10 –3 × 1·903 × 10 4
----------------------------------------------------------------8·25 × 10 –5
b
d
f
h
(3·75 × 103) × (1·5 × 10–5)
(9·25 × 10–2) × (8·75 × 10–2)
(6·75 × 102) ÷ (2·25 × 104)
(4·53 × 107) ÷ (75·5 × 10–3)
j
6·5 × 10 6 × 1·3 × 10 5
--------------------------------------------------------------( 4·7 × 10 –5 × 6·25 × 10 –3 )
7 The speed of light is 299 792 500 metres per second and the distance of the Earth from the
Sun is 150 million kilometres.
a How many seconds does it take light from the Sun to reach the Earth?
b How many minutes is this?
8 The Moon is 384 000 kilometres from the Earth. How
long does it take reflected light from the Moon to reach
the Earth?
9 Radio signals travel at the speed of light through space.
How long would it take a signal to reach Earth from a
space probe passing:
a Mars (7·8 × 107 km from Earth)?
b Pluto (5·75 × 109 km from Earth)?
10 A light-year is the distance that light will travel in 1 year:
a Find this distance in kilometres.
b What is the distance in light-years of the Earth from
the Sun?
c How many light-years is it from one side of the solar
system to the other?
(Assume that Pluto is at the extreme edge of the
solar system. Pluto is 5·9 × 109 km from the Sun.)
360
Maths Dimensions 10