Scientific notation.notebook
September 23, 2014
Writing and understanding numbers in
scientific notation
The diameter of a coin measures from one end of the coin to the other going through the centre of the coin.
Measure the diameter of each coin in millimetres and convert them to centimetres.
Record your results in your notebook.
1.6cm = 16mm
2cm = 20mm
2.4cm = 24mm
1.7cm = 17mm
2.2cm = 22mm
20mm = 2cm
25mm = 2.5cm
17mm = 1.7cm
24mm = 2.4cm
21mm = 2.1cm
2 x 10
2.5 x 10
1.7 x 10
2.4 x 10
2.1 x 10
2.5cm = 25mm
What does this mnemonic stand for?
MVEMJSUNP
5.791 x 107
57 910 000
1.082 x 108
108 200 000
1.496 x 108
149 600 000
8
227 940 000 2.2794 x 10
8
778 330 000 7.7833 x 10
9
1 429 400 000 1.4294 x 10
9
2 870 990 000 2.87099 x 10
9
4 504 300 000 4.5043 x 10
9
5 913 520 000 5.91352 x 10
Scientific notation.notebook
September 23, 2014
Scientific notation
Mercury is 57
The probability of winning the
910 000 km
away from the sun.
This can also be written as 5.791
1
/14 million
or 0.000 000 071
lottery is about
x 107
This can also be written as 7.1
x 10-8
32 000 000 watched the 1966 world cup.
The radius of a human hair is 0.053mm
Write this in scientific notation
Write this in scientific notation
3.2 x 107
5.3 x 10-2
Scientific notation
a x 10 n
a x 10 n
∨
1≤ a 10
Write these in
scientific notation
950 =
0.487 =
64800 =
integer
(positive or negative)
Write these as
ordinary numbers
3.5x 102 =
4.67x 10-3 =
7.6x 103 =
7420 =
8.65x 10-4 =
0.016 =
1.05 x 10-1 =
Calculating with scientific notation
1) Write 367 in scientific notation
2) Write 25000 in scientific notation
3) Write 0.06 in scientific notation
4) Write 0.00376 in scientific notation
5) Write 4 x 102 as an ordinary number
6) Write 6.21 x 105 as an ordinary number
7) Write 3 x 10-1 as an ordinary number
8) Write 5.32 x 10-9 as an ordinary number
Scientific notation.notebook
September 23, 2014
Write in scientific notation
Change these numbers into scientific notation
Write as ordinary numbers
Calculations with scientific notation
1) -2 + -3 =
2) -4 - 5 =
3) - 3 - - 2 =
4) 4.5 x 3 =
5) 6.1 x 4 =
6) 4.5 ÷ 9 =
7) 1.8 ÷ 6 =
8) 20.5 ÷ 5 =
Scientific notation.notebook
September 23, 2014
write the following in scientific notation
d) 25.6 x 105
d) 0.36 x 10-1
e) 160 x 10-2
e) 0.014 x 10-3
Calculations with scientific notation
Which number is smaller?
3.46 x 107 or 9.8 x 106
Calculations with scientific notation
Which number is smaller?
3.46 x 107 or 9.8 x 106
9800000
34600000
2.56 x 108 or 3.1 x 108
2.56 x 108 or 3.1 x 108
310000000
256000000
Explain why 4.2 x 10-5 is smaller than 3 x 10-4
Explain why 4.2 x 10-5 is smaller than 3 x 10-4
0.0003
0.000042
reviewing negative numbers
1) 6 - 7
2) -4 - 8
3) -3 + 5
4) -6 + 2
5) -5 - - 1
6) -7 + -2
7) 5 - - 1
8) 8 + - 3
Calculations with scientific notation
9.2 x 2
x
18.4 x 107
1.84 x 108
105 x 102
Scientific notation.notebook
September 23, 2014
5.1 x 4
2.4 x 6
105 x 102
x
x
104 x 10-6
20.4 x 10-2
14.4 x 107
2.04 x 10-1
1.44 x 108
22.5 x 106
2.25 x 107
1)
2)
Calculations with scientific notation
Write in scientific notation
1)
2)
3)
4)
5)
6)
17.5 x 106
1.75 x 107
3)
33 x 10-5
3.3 x 10-4
1)
450
8792
0.15
0.045
64 x 103
0.015 x 10 -5
4 x 106
9 x 1012
9 x 1012
2)
-
6 x 10-1
2.4 x 1013
4 x 107
3)
42 x 1014
4.2 x 1015
5
43.12 x 101
4.312 x 102
6
23.5 x 10-6
2.35 x 10-5
Scientific notation.notebook
102 ÷ 106
x
2.5 ÷ 5
September 23, 2014
x
4.2 ÷ 7
0.5 x 10-4
0.6 x 104
5 x 10-5
2÷5
108 ÷ 104
6 x 103
4
x
-2
10 ÷ 10
1)
0.4 x 10-3
4 x 10-4
2)
0.5 x 10-4
5 x 10-5
3)
0.6 x 10-4
6 x 10-5
0.4 x 106
4 x 105
Scientific Notation - exam questions
write in scientific notation
write in scientific notation
1﴿ a 52 = b 88 =
c 73 = d 625 =
e 389 = f 781 =
g 3147 = h 45671 =
a 250 h 0.076 b 0.345 i 0.000 76
2﴿ a 0.4 =
b 0.05 = c 0.007 = d 0.123 = e 0.007 65 = f 0.9804 = g 0.0098 = h 0.000 0078 =
c 46 700
d 3 400 000 000
e 20 780 000 000 f 0.000 5678
g 2460 j 0.999 k 234.56 l 98.7654
m 0.0006 n 0.005 67 o 56.0045
Scientific notation.notebook
September 23, 2014
Calculations with standard form
scientific notation
A What is wrong with these answers?
1﴿ a 52 = b 88 =
c 625 =
d 3147 = e 45671 =
8 x 1012
2﴿ a 0.4 =
b 0.05 = c 0.007 = d 0.007 65 = e 0.000 0078 =
6 x 10-2
16 x 1012
2.7 x 1012
B
D
Answer these questions
1)
C
What is wrong with these answers?
1)
2 x 10
2)
4 x 1010
3)
12 x 103
4)
4 x 10-4
solve and write your answer in standard form
8.1 x 109
2)
9.9 x 10-4
0.2 x 103
2 x 102
3)
4)
4.5 x 107
Scientific notation.notebook
September 23, 2014
match up the calculation to it's answer in standard form
solve and write your answer in standard form
a
b
c
d
8.1 x 109
e
f
g
h
9.9 x 10-4
i
j
k
l
m
n
o
p
Answers
3
0.2 x 10
2 x 102
4.5 x 107
match up the calculation to it's answer in standard form
a
b
c
d
e
f
g
h
i
j
k
l
m
n
o
p
answers
g&f
d&h
1)______________
5)______________
p&j
i&e
2)______________
6)______________
c&n
l&a
3)______________
7)______________
o&m
b&k
4)______________
8)______________
Question 3
A typical adult has about 20 000 000 000 000 red corpuscles. Each red corpuscle weighs about 0.000 000 000 1 gram. Write both of these numbers in standard form and work out the total mass of red corpuscles in a typical adult.
Question 4
Evaluate E M
when E = 1.5 × 103 and M = 3 × 10­2, giving your answer in standard form.
1)______________ 5)______________
2)______________ 6)______________
3)______________ 7)______________
4)______________ 8)______________
Question 1
A pixel on a computer screen is 2 × 10–2 cm long by 7 × 10–3 cm wide.
What is the area of the pixel?
Question 2
The star Betelgeuse is 1.8 × 1015 miles from Earth. Light travels at 1.86 × 105 miles per second.
How many seconds does it take light to travel from Betelgeuse to Earth?
Give your answer in standard form.
Question 5
Work out the value of
giving your answer in standard form, correct to two significant figures.
Question 6
Many people withdraw money from their banks by using hole­in­the­wall machines. Each day there are eight million withdrawals from 32 000 machines. What is the average number of withdrawals
per machine?
Scientific notation.notebook
September 23, 2014
Your calculator can write numbers in standard form also.
Question 7
123 000 000 000 How do you write this in standard form?
26
The mass of Saturn is 5.686 × 10 tonnes. The mass of the Earth is 6.04 × 1021 tonnes. How many times heavier is Saturn than the Earth? Give your answer in standard form to a suitable degree of accuracy.
type this into a calculator
your calculator will show
negative powers
0.00000123
write this in standard form
on a calculator you need to type
The star Betelgeuse is 1.8 × 1015 miles from Earth. Light travels at 1.86 × 105 miles per second.
5.79 x 107
How many seconds does it take light to travel from Betelgeuse to Earth?
Give your answer in standard form.
What do you notice?
= 1.8 × 1015 ÷ 1.86 × 105
= (1.8 ÷ 1.86) x (1015 ÷ 105) seconds
= 0.967 741 ... × 1010 seconds
= 9.67741.. × 109 seconds
scientific notation
Starter
1) Write 100 as a power of 10
2) Write 1 000 000 as a power of 10
3) Write 0.01 as a fraction
4) Write 0.001 as a fraction
5) Solve 1.24 x 100
6) Solve 27 x 0.1
7) Write 1/10 in index form
8) Write 1/1000 in index form
and
7.1 x 10-8
are written in standard form
Standard form is written as:
a number between 1 and 10 x a power of 10
(1-10) x 10n
Work out the following. Give your answers in scientific notation.
2×104 × 5.4×103
7.2×10­3 × 4×102
Scientific notation.notebook
scientific notation on a calculator
Sometimes calculators display small and large numbers in this way:
scientific notation
Are these written in scientific
notation?
n
a x 10
September 23, 2014
Write down:
i) what these calculator displays mean
ii) what they are as ordinary numbers
Write in scientific notation
123 000 000 000 =
2.3 x 104
15.452 x 103
0.568 x 102
How would you write it in a calculator?
1.23 EXP 11
INV =
1.2487 x 10-2
1) 52 = 5.2 x 10
2) 73 = 7.3 x 10
3) 625 = 6.25 x 102
4) 389 = 3.89 x 102
5) 3147 = 3.147 x 103
Write in scientific notation
0.00000123 =
How would you write it in a calculator?
6) 42.4 = 4.24 x 10
7) 48715.4 = 4.87154 x 104
8) 14154.5 = 1.41545 x 104
1.23 EXP +/- 6
Scientific notation.notebook
September 23, 2014
-1
0.4 = 4 x 10
2) 0.05 = 5 x 10-2
3) 0.007 = 7 x 10-3
4) 0.123 = 1.23 x 10-1
5) 0.00765 = 7.65 x 10-3
-1
6) 0.9804 = 9.804 x 10
7) 0.0098 = 9.8 x 10-3
-6
8) 0.0000078 = 7.8 x 10
1)
The star Betelgeuse is 1.8 x 1015 miles from
Earth.
Light travels at 1.86 x 105 miles per second.
How many seconds does it take light to
travel from Betelgeuse to Earth?
Give your answer in standard form
D
ST
A pixel on a computer screen is 2 x 10-2 cm
long by 7 x 10-3 cm wide.
What is the area of the pixel?
(2 x 10-2) x (7 x 10-3) =
(2 x 7) x (10-2 x 10-3) =
14 x 10-5 cm2
= 1.4 x 10-4 cm2
Time = Distance
Speed
1.8 x 1015
1.86 x 105
= 1.8 x 10(15-5)
1.86
= 0.967741935 x 1010
= 9.7 x 109 seconds