Unit 5 - Scientific Notation

Summary of knowledge:

The goals for this investigation are to remember all what we learned in this unit and help our classmates and us to study for the final exam. Students should understand the difference between scientific notation and standard notation and how to work them.



Key Vocabulary:
Exponent: A number, letter, or any quantity written on the right hand of and and above another quantity and the denoting how many times the latter is repeated as a factor to produce the power indicated.

Scientific Notation: A short way to write very large or very small numbers. A number written in scientific notation is expressed in this form: A number greater than or equal to one but less than 10x10 raised to an exponent.

Standard Notation: The most common form of written numbers. For example 254 is the standard notation for 2 hundreds, 5 tens, and 4 ones.



Task Analysis:

Scientific notation to standard notation:

1.- Rewrite the number that is multiplied by ten.
2.- If the exponent next to the ten is positive, move that number of times from the decimal to the right, and if it is negative from from decimal to the left.

Examples:


10^8=100,000,000

3.6 x 10^11 = 360,000,000,000

7 x 10^3 = 7,000

7.56 x 10^-7 = .000000756

4.5 x 10^-2 = .045

6 x 10^-5 = .00006

Standard notation to scientific notation:
1.- Put a decimal point after the first number of the number sentence.
2.- From there count now how many spaces there are till the end of the number.
3.- The you eliminate the zeros at the end and you write the number times ten and then you put the number of spaces counted as the exponent.

Examples:

10,000,000= 1 x 10^7

7,534,000= 7.534 x 10^6

8,007,000= 8.007 x 10^6

.0005768= 5.768 x 10^-4

.057 = 5.7 x 10^-2

.0008 = 8 x 10^-4

Example problem and solution:

Scientific Notation » create exams

This video shows what is scientific notation, and how to manage small and big numbers.
It will explain to you why this works, and show you a task analysis.
It includes examples and clear explanations.


Useful links:
This is a website that explains what is scientific notation.
This is a scientific notation problem generator. Create your own problems and solve them!
This website gives your exercises and explanations