Download Scientific Notation (Standard Form)

Scientific Notation (Standard Form)
The distance from the Earth to the Sun is 152,000,000 km. The
nearest star to our Sun is 3800000000000000km (4 Light Years)
away - Alpha Centauri. The mass of an atom is approximately
0.00000000000000000000000042 kg !! There must be an easier
way of writing these!
Indices are a really useful tool for writing very large and very small
numbers in a simple way. (Remember Mathematicians are lazy!! They like to find simple, efficient ways of solving problems)
Multiplying or dividing by 10 or multiples of ten is easy, all you have
to do is move the decimal point.
Eg:
2.45 x 10 = 24.5
3.78 x 100 = 378
58.5 ÷ 10 = 5.85
Try the following:
1. 67.25 X 10 =
3. 78.9 ÷ 10 =
2. 0.875 x 100 =
4. 34 x 10000 =
Now remember from the worksheet you have just done that:
10 = 101
100 = 102
1000 = 103 etc
Scientific Notation (Standard Form) is ‘standard’ because it is
written the same way every time. This is a number with only one
digit before the decimal point (but not zero) multiplied by a power
of 10.
Eg: 3.75 x 103 is the same as 3.75 x 1000 = 3750, so can you
see the short cut?
4.657 X 105 = 4.657 x ______
= _________
SO, 7.3 x 10-2 = ________
Write a rule for converting a number in scientific form to a basic
number.
__________________________________________________
__________________________________________________
Try the puzzle sheet ‘Who is the Famous Fellow’
Now what if we want to convert a number to scientific form (it is
just the opposite of what you have been doing!
Eg: 349 = 3.49 X 102
Try the following:
24000 = 2.4 X 10_
6730000 = ____ X 10_
0.034 = 3.4 X 10_
Write each of the following using scientific notation:
a 315
b 4300
c 6700 000 000 000
d 4.5
e 90 000 000 000 000 000
f 23
g 67 800
h 0.0122
i 0.007 89
j 0.234 56
k 0.000 78
l 0.000 005
m 61.78