UNIT 1: NUMBER SENSE

N.S. 1.1- SCIENTIFIC NOTATION

Per 3, 5- 8/22/11 Per 2, 4, 6- 8/23/11

Scientific Notation

 Scientific Notation is a quick way to express very large or very small numbers.

 Scientific Notation will look like this:

A number

×

10 y

You will need to…

 1. Turn a number into scientific notation  2. Turn a number in scientific notation into a number in standard form.

Turning a number into Scientific Notation

Example: 34,500,000,000 Step 1: Identify the first non-zero number that you see.

In this case, it will be 3.

 Step 2: Place a decimal point after that first non zero number, and the list all the other numbers behind the decimal.



In this case, our start will be 3.45

Figuring out the exponent

 Step 3: Look at the original number

34,500,000,000

 We placed a decimal after the 3. From the end of the number, count how many spaces we moved the decimal.

 We moved the decimal 10 spaces from the end of the number so our exponent will be 10.

 Step 4: Putting it all together.

Answer: 3.45 x 10

10

Example 2:

 Scientific Notation is also used to express very small numbers.



0.0000567

 Step 1: Identify the first non-zero number that you see. 0.0000567  In this case, it is 5.

 Step 2: Place a decimal point after that first non zero number, and the list all the other numbers behind the decimal.



=5.67

 Step 3: Look at the original number 0.0000567  We placed a decimal after the 5. Now count the amount of spaces we moved the decimal.

 Since we moved the original decimal to the right, our exponent will be negative.  We moved the decimal 5 spaces to the right so our exponent will be -5.

 Step 4: Putting it all together.

Answer: 5.67 x 10

-5

Whiteboard CFU

 Express the following in scientific notation:

87,650,000,000

Answer:



8.675 x 10 10

Whiteboard CFU

 Express the following in scientific notation: 0.000643

Answer:



6.43 x 10 -4

Independent Practice NS 1.1

1. 0.033 2. 909 3. 49,700 4. 5.32 5. 0.333 6. 6.33 7. 0.0572 8. 0.0087 9. 9.77 10. 0.00046 11. 0.00116 12. 7.96 13. 0.081 14. 21 15. 0.705 16. 75.2          17. 4,740 18. 6,460 19. 0.000375 20. 315 21. 89.9 22. 1.26 23. 9.81 24. 0.0149 25. 0.031