Estimating Square Roots

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!!*

Perfect SquaresPerfect Squares: the product of a number being

multiplied by itself. For example: 4 x 4 or 42 = 16What are the Perfect Squares of the following

numbers? 1×1 = 12= 1 2×2 = 22 = 4 3×3 = 4×4 = 5×5 = 6×6 = 7×7 = 8×8 = 9×9 = 10×10 = 11×11 = 12×12 =

Square Roots Square Roots: the opposite of a square; undoing a square What are the Square Roots of the following numbers? Remember if a2=b, then √b=a.√1= √49=

√4= √64=

√9= √81=

√16= √100=

√25= √121=

√36= √144=

Estimating Square RootsWhat 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) √89 Ex. 2) √120

Ex. 3) √256 Ex. 4) √412

You Try!!a) √22

b) √13

c) √45

d) √67

SCIENTIFIC NOTATIONA QUICK WAY TO

WRITE REALLY, REALLY BIG

OR REALLY, REALLY SMALL NUMBERS.

Mathematicians are Lazy!!!

They decided that by using powers of 10, they can create short versions of

long numbers.

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 105 is not in proper

scientific notation. Why?

Example 1:137,000,000 can be

rewritten as

1.37 X 108

Example 2: 347,000Using scientific notation,

rewrite the following number.

Example 3: 6.14 x 105

Using standard and scientific notation,

rewrite the following number

Example 4:The U.S. has a total of 1.2916 X 107 acres of land reserved for state parks. Write this in standard form.

Why does a Negative Exponent give us a small

number? 10000 = 10 x 10 x 10 x 10 = 104 1000 = 10 x 10 x 10 = 103

100 = 10 x 10 = 102

10 = 101 1 = 100 Do you see a pattern?

Negative Exponents – Powers of 10

= 10-1

= = 10-2

= = 10-3

= = 10-4

101

1001

2101

10001

3101

100001

4101

Example 5: Write the following in scientific

notationA. 0.00004B. 0.00053C. 0.012

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

notation.

You Try!!1. 902,000,000.2. 9.02 X 108

3. 0.000414. 6.14 X 10-4

Using scientific notation, rewrite the following number

More Practice:1. 4,000

2. 4 X 103

3. 2.48 X 10-3

4. 2,480

5. 6.123 X 106

6. 0.000623

7. 306,000,000

8. 3.06 X 10-8