Warm Up Order each set of numbers from least to greatest. 1. 10, 10, 10, 10 2. 8, 8, 8, 8 3. 2, 2, 2, 2 4. 5.2, 5.2, 5.2, 5.2 04 –1 –2 10, 10, 10, 10 40

Warm UpOrder each set of numbers from least to greatest.

1. 10 , 10 , 10 , 10

2. 8 , 8 , 8 , 8

3. 2 , 2 , 2 , 2

4. 5.2 , 5.2 , 5.2 , 5.2

04 –1 –2

10 , 10 , 10 , 10 40–1–2

3 02 –2

8 , 8 , 8 , 8 320–2

13 –4 –6

–22 9 –1

5.2 , 5.2 , 5.2 , 5.2 92–1–2

2 , 2 , 2 , 2 31–4–6

Mathematicians and scientists often work with numbers that are

extremely large and numbers that are extremely small.

It can be challenging (and boring) to write out such

numbers over and over again.

Also, a calculator can only fit about 10 digits on its screen.

For example, suppose that you were studying the planet Pluto.

Pluto is 2,670,000,000 miles away from Earth.

2,670,000,000 is a huge number. Imagine how tedious it would be to write this number multiple times or do calculations with this number.

Mathematicians and scientists use a system called scientific notation to abbreviate numbers like these.

2,670,000,000

2,670,000,000 = 2.67 x 109

Mathematicians and scientists use a system called scientific notation to abbreviate numbers like these.

Scientific notation works by rewriting numbers as the product of

a number times 10 to a certain power.

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The exponent tells about the size of the number.

A positive exponent means a BIG number.

A negative exponent means a small number.

Scientific notation has 3 parts.

ONLY 1 number in front of the

decimal!

Xmultiplication symbol – do not use multiplication dot

a power of 10

101.25

Scientific notation works by rewriting numbers as the product of a number

times 10 to a certain power.

45,000,000 = 4.5 x 107

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45,000,000 = 4.5 x 107

Notice that there is one digit in front of the decimal point.



45,000,000 = 4.5 x 107

The exponent of “7” refers to the number of times that the decimal point “moved.”



45,000,000 = 4.5 x 107




45,000,00 0 =4.5 x 106

one move



45,000,0 00 =4.5 x 105

two moves



45,000, 000 =4.5 x 104

three moves



45,00 0,000 =4.5 x 103

four moves



45,0 00,000 =4.5 x 102

five moves



45, 000,000 =4.5 x 101

six moves



4 5,000,000 =4.5 x 100

seven moves



45,000,000 = 4.5 x 107


Scientific notation can also be used to abbreviate numbers that

are really small.

.0022 is a really small number that can be rewritten using scientific notation.

.0022 = 2.2 x 10-3

.0022 is a really small number that can be rewritten using scientific

notation.

.0022 = 2.2 x 10-3

Notice that there is one digit in front of the decimal point.

The exponent of “-3” refers to the number of times that the decimal point “moved.”


.0022 = 2.2 x 10-3


.0022 = 2.2 x 10-3


0 022 = 2.2 x 10-2

1 move


00 22 = 2.2 x 10-1

2 moves


002 2 = 2.2 x 100

3 moves


.0022 = 2.2 x 10-3

3 moves

to the leftThe exponent is negative because multiplying by .001 will move the decimal to the left 3 times.

Rules to Write in Standard NotationIf the exponent is positive, move the decimal point as

many places to the right as indicated by the exponent.

1.120000

1.12 x 106

. 1,120,000 positive exponent large number

If the exponent is negative, move the decimal point as many places to the left as indicated by the exponent.

4.3 x 10-4 0004.3

.00043

negative exponent small number

.

Example 1 Write in standard notation (decimal form).1. Write problem.

3.0259 x 108

2. Write standard form.

000,590,302

PracticeA. 6.7 x 105

B. 1.38 x 10-4

C. 6.12 x 10-5

D. 5.4 x 104

= 670,000 = .000138 = .0000612 = 54,000

Rules to Write in Scientific NotationMove the decimal point to create a number greater than or

equal to 1 and less than 10. Count the decimal positions to identify the exponent. If the original number is greater than or equal to 1, the exponent is positive. If the original number is between zero and 1, the exponent is negative.

3.25 x 1063,250,000• use a positive exponent original

number is > 1

0.000817 8.17 x 10-

4

use a negative exponent original

number is between 0 and 1

•

•

Example 2 Write in scientific notation.

1. Write problem.

42,000,000

2. Write scientific notation.

710 x 2.4

PracticeA. 0.000052B. 3,107,000C. 970,000,00

0D. 0.0063

= 5.2 x 10-5 = 3.107 x 106 = 9.7 x 108

= 6.3 x 10-3

What do you already know about the sign

of the exponent?

LOL Moment!

Operations with Scientific Notation 36 10 x 410 x 3

Group the whole/decimal numbers together.

4 x 3

Group the powers of 10 together.

36 10 x10

Simplify within each group.

12

Write the whole/decimal number in scientific notation.

10 x 2.1 1

Combine the powers of ten.

9110 x 2.1

3610 x

910 x 12 10 x 9

1010 x 2.1

Perform the indicated operation. Write the result in scientific notation.

53 10 x 210 x 3

2. Group the whole/decimal numbers together.

2 x 3


53 10 x10

3. Simplify within each group.

6

4. Combine the powers of ten.

1. Write problem.5310 x

810 x 6

What do you know about the size of

this number?


64 10 x 610 x 4


6 x 4


64 10 x10


24

4. Write the whole/decimal number in scientific notation.

110 x 4.2


10110 x 4.2


1010 x 24 1010 x

1110 x 4.2


this number?


48 10 x 810 x 1.7


8 x .17


48 10 x10


8.56


110 x 5.68


4110 x 68.5


410 x 8.56 410 x

310 x 68.5


this number?


39 10 x 4.010 x 2.1


0.4 x 2.1


39 10 x10


48.0


110 x 8.4


6110 x 8.4

1. Write problem. 3910 x

610 x 48.0 610 x

510 x 8.4


this number?


24 10 x .8510 x .52


5.8 x .52


24 10 x10


50.14


110 x 45.1


6110 x 45.1


610 x 50.14 610 x

710 x 45.1


this number?

210 x


3

5

10 x 2

10 x 6


2 6


3

5

10

10


3

1. Write problem.

What is left over and

where is it located?


2

6

10 x 8

10 x 5


85


2

6

10

10 x


625.

4. Write the whole/decimal number in scientific notation.5. Combine the powers of ten.

110 x 25.6

1. Write problem.

410 x 410 x

310 x 25.6


6

2

10 x 810 x 5


85


6

2

1010 x


625.


110 x 25.6


4110 x 6.25

1. Write problem.

2

6

1010 x

410 x .625 410 x

310 x 6.25What do you know about the size of

this number?


1. Write problem. 24-10 x 5

2. Use power of product property.

242 10 x5


110 x 2.5

4. Combine the powers of ten. -710 x 2.5

810 x 25 810 x


this number?

4) Write the missing exponent.

1) 3 x 10?

2) 6.8 x 10?

3) 3.5 x 10?

4) 2.45 x 10?

= 30,000

= 680,000

= .0035

= .0000245

1) 3 x 104

2) 6.8 x 10?

3) 3.5 x 10?

4) 2.45 x 10?

= 30,000

= 680,000

= .0035

= .0000245


1) 3 x 104

2) 6.8 x 105

3) 3.5 x 10?

4) 2.45 x 10?

= 30,000

= 680,000

= .0035

= .0000245


1) 3 x 104

2) 6.8 x 105

3) 3.5 x 10-3

4) 2.45 x 10?

= 30,000

= 680,000

= .0035

= .0000245


1) 3 x 104

2) 6.8 x 105

3) 3.5 x 10-3

4) 2.45 x 10-5

= 30,000

= 680,000

= .0035

= .0000245


5) Write each number in scientific notation.

1) 357,000

2) 6,250,000

3) .00045

4) .0027


1) 357,000

2) 6,250,000

3) .00045

4) .0027

= 3.57 x 105


1) 357,000

2) 6,250,000

3) .00045

4) .0027

= 3.57 x 105

= 6.25 x 106


1) 357,000

2) 6,250,000

3) .00045

4) .0027

= 3.57 x 105

= 6.25 x 106

= 4.5 x 10-4


1) 357,000

2) 6,250,000

3) .00045

4) .0027

= 3.57 x 105

= 6.25 x 106

= 4.5 x 10-4

= 2.7 x 10-3

Documents

Warm Up Order each set of numbers from least to greatest. 1. 10, 10, 10, 10 2. 8, 8, 8, 8 3. 2, 2, 2, 2 4. 5.2, 5.2, 5.2, 5.2 04 –1 –2 10, 10, 10, 10 40