Scientific Notation

Meaning of Scientific Notation 102 100 2 103 1000 3 104 10000 4 105 100000 5 Try to express 10 000 000 000 000 000 as a power of 10. 1016

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

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.

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 0.002 005 -1.4  104

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

Follow-up question Without using a calculator, find the values of the following expressions, and express your answers in scientific notation. (a) 300 000 000 － 5 000 000 Solution (a) 300 000 000 － 5 000 000 = 3  108 － 5  106 = 3  108 － 0.05  108 = 2.95  108

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

Follow-up question Given that the speed of sound is 340.29 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.)