1. Estimating Square Roots

2. Warm – Up!! Good Morning!! As you walk in, please pick up your calculator! Please pick up a Unit 4 booklet from the podium and then write your name in pen. * GLUE, TAPE, OR HOLE PUNCH your booklet so that you do not loose it!!*

3. Perfect Squares Perfect Squares: the product of a number being multiplied by itself. For example: 4 x 4 or 4 2 = 16 What are the Perfect Squares of the following numbers? 1×1 = 1 2 = 1 2×2 = 2 2 = 43×3 = 4×4 = 5×5 = 6×6 = 7×7 =8×8 = 9×9 = 10×10 =11×11 = 12×12 =

4. Square Roots Square Roots: the opposite of a square; undoing a square What are the Square Roots of the following numbers? Remember if a 2 =b, then √b=a. √1=√49= √4= √64= √9=√81= √16=√100= √25=√121= √36=√144=

5. Estimating Square Roots What if the number is NOT A PERFECT SQUARE? (No Calculators!) We can use the Square Roots that we know to Estimate ones that we Know! Ex. 1) √89Ex. 2) √120 Ex. 3) √256Ex. 4) √412

6. You Try!!  √22  √13  √45  √67

7. SCIENTIFIC NOTATION A QUICK WAY TO WRITE REALLY, REALLY BIG OR REALLY, REALLY SMALL NUMBERS.

8. Mathematicians are Lazy!!! They decided that by using powers of 10, they can create short versions of long numbers.

9. Rules for Scientific Notation To be in proper scientific notation the number must be written with  a number between 1 and 10  and multiplied by a power of 10 Ex.: 23 X 10 5 is not in proper scientific notation. Why?

10. Example 1: 137,000,000 can be rewritten as 1.37 X 10 8

11. Example 2: 347,000 Using scientific notation, rewrite the following number.

12. Example 3: 6.14 x 10 5 Using standard and scientific notation, rewrite the following number

13. Example 4:The U.S. has a total of 1.2916 X 10 7 acres of land reserved for state parks. Write this in standard form.

14. Why does a Negative Exponent give us a small number? 10000 = 10 x 10 x 10 x 10 = 10 4 1000 = 10 x 10 x 10 = 10 3 100 = 10 x 10 = 10 2 10 = 10 1 1 = 10 0 Do you see a pattern?

15. Negative Exponents – Powers of 10 = 10 -1 = = 10 -2 = = 10 -3 = = 10 -4

16. Example 5: Write the following in scientific notation A. 0.00004 B. 0.00053 C. 0.012

17. Example 6: A ribosome, another part of a cell, is about 0.000000003 of a meter in diameter. Write the length in scientific notation.

18. You Try!! 1. 902,000,000. 2. 9.02 X 10 8 3. 0.00041 4. 6.14 X 10 -4 Using scientific notation, rewrite the following number

19. More Practice: 1. 4,000 2. 4 X 10 3 3. 2.48 X 10 -3 4. 2,480 5. 6.123 X 10 6 6. 0.000623 7. 306,000,000 8. 3.06 X 10 -8