Numbers and Scientific Notation
Numbers and Digits
‘c’ is a letter.
‘cat’ is a word with three letters.
‘3’ is a digit.
‘467’ is a number with three digits. {‘Digit’ also means ‘finger’; it means
a single number because people used to count on their fingers!}
Scientific Notation
When we write large or small numbers in science we write them as a small number
multiplied by a power of ten.
That is, we don’t write 56 000 000, we write 5.6 x 107.
Powers of ten
101 =
107 =
102 =
108 =
103 =
109 =
104 =
1010 =
105 =
1011 =
106 =
1012 =
Negative Powers of ten
If the power of ten is negative, it means you must divide by that number, not multiply.
For example:
10–2 = 1 ÷ 102 = 1/100 = 0.01
10–1 =
10–2 =
10–3 =
10–4 =
10–5 =
10–6 =
Remember 10 0 = 1.
Write these numbers in full:
3 x 101 =
1 x 105 =
2 x 103 =
0 x 102 =
4 x 104 =
7 x 100 =
6 x 102 =
3 x 1012 =
8 x 107 =
5 x 104 =
page 1
Scientific notation and Indices
Complete this table and write the words for the numbers:
Ordinary number
{words}
forty five million
Ordinary
number
45 000 000
Scientific
notation
Scientific notation
{words}
four point five times ten to the
power of seven O R four point 5
by 10 to the seventh
4.5 x 107
623 000
310 000 000
0.03
0.000 07
0.000 000 093
3 x 102
3.4 x 102
6.23 x 107
4.5 x 10-4
3.219 45 x 108
6.023 x 10-12
Why do we use these numbers?
In Science and Maths there are some common numbers which are difficult to write or
say in any other way.
For example:
a proton’s mass is 1.772 4 x 10-27 kilograms
speed of light is 3 x 108 metres per second
Avogadro’s number is 6.025 x 1026
A very big number is a googol which is 10100
100
A bigger number is a googolplex which is 10googol ! That is 1010 .
Scientific notation and Indices
page 2