Standard form is a way of writing very large or very small numbers as a product of a number between 1 and 9 and a power of 10. Numbers written in standard form can only use base 10. To write a number in standard form, it is expressed as a x 10n, where a is between 1 and 9 and n is the power of 10.

1. Standard Form
Standard form is commonly used for numbers that are very large
or very small although any number can easily be written in this
form.
Numbers in standard form can only be expressed in base 10.
A number is in standard form if it is written as:
a x 10n where a is between 1 and 9
Write the following examples out in full:
2.5 x 103 4.62 x 105 5.389 x 107
1 x 107 8.563 x 1012 9.562 x 1034
1.4 x 10-8 8.89 x 10-5 1.1 x 100

2. Writing very large/small numbers in standard form.
6 7 5 4 0 0 0 0 0 0 0 0 0 0 0 0 0 0
Write the number below in standard form
6.754 x 1017
4 3 7 1 0 0 0 0 0 0 0 0 0 0 0
Write the number below in standard form
4.371 x 1014

3. Writing very large/small numbers in standard form.
0 . 0 0 0 0 0 0 0 0 0 0 0 0 0 0 4 2 6
Write the number below in standard form
4.26 x 10-15
0 . 0 0 0 0 0 0 0 0 0 0 5 8 3
Write the number below in standard form
5.83 x 10-11

4. Rules for Counting Significant Figures
1. All non-zero digits are significant.
Example:123.7 has 4 significant figures
2. All zeros between non-zero digits are significant
Example:1207 has 4 sig. figs., 120.007 has 6 sig. figs.
3. All zeros at the left of the number are NOT significant.
Example: 0.00032 has 2 sig. figs, 0.03 has 1 sig. fig.
4. When zeros are at the right of the number:
a) If there is no decimal, the zeros are NOT significant.
Example: 300 has 1 sig. fig., 25400 has 3 sig. figs.
b) If there is a decimal, the zeros ARE significant.
Example: 60.0 has 3 sig. figs., 0.00045300 has 5 sig. figs.
(the 4 zeros at the left of the number do not count, but the 2
zeros at the right of the number do count).

5. Standard Deviation
The standard deviation is a measure of the spread of scores
within a set of data:
A low standard deviation means that most of the numbers are
very close to the average.
A high standard deviation means that the numbers are spread
out.

6. Standard Deviation