In science, we typically represent numbers
in a form called scientific notation.
In scientific notation, numbers have two parts:
the significant figures
and the order of magnitude.
In the following example, the significant figures
are 3.45 and the order of magnitude is +6.
Sometimes, the significant figures are referred to
as the coefficient
and the order of magnitude is referred to as
the exponent.
In this class, I prefer to use the term
"significant figures" and "order of magnitude."
All of the numbers you are used to writing,
such as 10, 28, 415891, are called
numbers in standard notation.

There are multiple ways of writing a number in scientific notation.

Most typically, it is written as significant digits multiplied by a power of ten:
\( 3.45 \cdot 10^{6} \)

However, scientific notation can also be written with a capital "E":
3.45E6

It can be written with a lower case "e".
3.45e6

Lastly, it can be written with a small font size capital "E".
I personally find this notation easiest to read.
3.45E6
Converting Scientific Notation to Standard Notation

Rule 1:

Move the decimal point to the RIGHT if the exponent is POSITIVE.

Move the decimal point to the LEFT if the exponent is NEGATIVE.

Move the decimal point as many spots as the exponent.

Rule 2:
After moving the decimal, add zeroes in any empty spots.
Questions:
Convert each number to standard notation.

\( 3.45 \times 10^4 = \)

\( 4.23 \times 10^7 = \)

\( 9.12 \times 10^2 = \)

\( 4.87 \times 10^5 = \)

\( 8.25 \times 10^6 = \)

\( 2.45 \times 10^0 = \)

\( 2.45 \times 10^1 = \)

\( 3.89 \times 10^0 = \)

\( 4.23 \times 10^{3} = \)

3.28E8

6.78E5

3.85e4

5.28e7

3.42E5

4.23E2

What do we call the digits at the beginning of a scientific notation number?

What do we call the exponent in a scientific notation number?
Answers: