1. Scientific Notation

2. Meaning of Scientific Notation
102
100 2
103
1000 3
104
10000 4
105
100000 5
Try to express as a power of 10.
1016

3. What is the advantage in expressing numbers as a power of 10?
In many aspects, we often encounter extremely large and small numbers…
… we can express them as powers of 10 to make them easier for reading and writing.
For example:
1. The volume of Jupiter
2. The mass of a water molecule

4. When we write numbers in the form like or , they are said to be written in scientific notation.
A positive number x is in scientific notation if it is written as , where and n is an integer.

5. Follow-up question 7.7  105 54 000 1.8  10-5 0.002 005 -1.4  104
Complete the following table.
7.7  105
54 000
1.8  10-5
-1.4  104

6. Applications of Scientific Notation
For expressions involving extremely large and/or small numbers, expressing them in scientific notation may help in calculation.
For example,

7. Follow-up question
Without using a calculator, find the values of the following expressions, and express your answers in scientific notation.
(a) －
Solution
(a) －
= 3  108 － 5  106
= 3  108 － 0.05  108
= 2.95  108

8. If there are 30 days in a month, how many seconds are there in a month
If there are 30 days in a month, how many seconds are there in a month? Round off your answer correct to 2 significant figures, and express it in scientific notation.
Solution
The number of seconds in a month

9. Follow-up question
Given that the speed of sound is m/s, and the speed of light is times that of sound. Express the speed of light in scientific notation.
(Give your answer correct to 3 significant figures.)
Solution
The speed of light
(cor. to 3 sig. fig.)