Scientificnotation

SCIENTIFIC NOTATION

Why use the Scientific Notation?Scientific Notation

Is a way to express very small or very large numbers that is often used in “scientific” calculations where the analysis must be very precise.

Rules to Scientific NotationScientific Notation

Two Parts:

Coefficient – must be a number from 1 to 9

Exponent – a power of 10 (Tells you how many times to use that number in multiplication)

2.5 x

Easier than writing 2,500,000

Coefficient Exponent

Rules to Scientific NotationScientific Notation

Two Parts:

Coefficient – must be a number from 1 to 9Exponent – a power of 10 (Tells you how many times to use that number in multiplication)

2.5 x

Easier than writing 2,500,000

Coefficient Exponent

Between 1 and 0 multiplied by a power of 10

Rules to Scientific NotationScientific Notation

Two Parts:

Coefficient – must be a number from 1 to 9Exponent – a power of 10 (Tells you how many times to use that number in multiplication)

2.5 x

Easier than writing 2,500,000

Coefficient

Exponent Count the number of decimal places the decimal point has “moved” from the original number. This will be the exponent on the 10.

25000001 2 3

(Use zeros to fill in places.)4 5 6

Rules to Scientific NotationScientific Notation

Two Parts:

Coefficient – must be a number from 1 to 9Exponent – a power of 10 (Tells you how many times to use that number in multiplication)

2.5 x Easier than writing 2,500,000

Coefficient Exponent

Which are in Scientific Notation?

2.5 x 3.9

3.0 x 12 x

0.5 x must be a number from 1 to 9

missing power of ten

must be a number between 1 to 9. Not over 9

YES NO

1 x

Changing Scientific Notation to Standard Form

Scientific Notation

Move the decimal point to the LEFT for negative exponent 10.

(Use zeros to fill in places.)

3.1 x

Count the number of decimal places the decimal point has “moved” from the original number. This will be the exponent on the 10.

0.031= 0.031

12

Place the decimal point so that there is one non-zero digit to the left of the decimal point.

Changing Scientific Notation to Standard Form

Scientific Notation

Simply move the decimal point to the RIGHT for positive exponent 10.

Move the decimal point to the LEFT for negative exponent 10.

(Use zeros to fill in places.)

2.5 x 3.1 x

250

= 250

Count the number of decimal places the decimal point has “moved” from the original number. This will be the exponent on the 10.

0.031= 0.031

12 1 2

Place the decimal point so that there is one non-zero digit to the left of the decimal point.

Changing Scientific Notation to Standard Form

Scientific Notation

Move the decimal point to the LEFT for negative exponent 10.

(Use zeros to fill in places.)

1.2 x

0.0012= 0.0012

23 1

Changing Scientific Notation to Standard Form

Scientific Notation

Move the decimal point to the LEFT for negative exponent 10.

(Use zeros to fill in places.)

1.2 x

0.0012= 0.0012

23 1

1 x

0.01= 0.01

2 1

Changing Scientific Notation to Standard Form

Scientific Notation

Simply move the decimal point to the RIGHT for positive exponent 10.

Move the decimal point to the LEFT for negative exponent 10.

(Use zeros to fill in places.)

9.88 x 1.2 x

9,880

= 9,880

0.0012= 0.0012

23 1 21

1 x

0.01= 0.01

2 1

3

Changing Scientific Notation to Standard Form

Scientific Notation

Simply move the decimal point to the RIGHT for positive exponent 10.

Move the decimal point to the LEFT for negative exponent 10.

(Use zeros to fill in places.)

9.88 x 1.2 x

9,880

= 9,880

0.0012= 0.0012

23 1 21

1 x

0.01= 0.01

2 1

3

8 x = 8

Changing Standard Form to Scientific Notation

Scientific Notation

Multiplying a number by a positive power of 10 will make the number greater; multiplying by a negative power of 10 will make the number less.

Move the decimal point to the right of the first nonzero digit.

4,530

4.530

Find the number by moving the decimal point that is between 1 to 9.

Changing Standard Form to Scientific Notation

Scientific Notation

Multiplying a number by a positive power of 10 will make the number greater; multiplying by a negative power of 10 will make the number less.

Move the decimal point to the right of the first nonzero digit.

4,530

4.530

Find the number by moving the decimal point that is between 1 to 9.

4.530

Count the number of places you moved the decimal point.

3 2 1

Write a positive expnent which is equal to the number of places you moved the decimal point to the left.

Changing Standard Form to Scientific Notation

Scientific Notation

Multiplying a number by a positive power of 10 will make the number greater; multiplying by a negative power of 10 will make the number less.

Move the decimal point to the right of the first nonzero digit.

4,530

4.530

Find the number by moving the decimal point that is between 1 to 9.

4.530

Count the number of places you moved the decimal point.

3 2 1

The number of places in Step 2 is the absolute value of the exponent on 10.

4.530 x

Write a positive exponent which is equal to the number of places you moved the decimal point to the left.

Changing Standard Form to Scientific Notation

Scientific Notation

Multiplying a number by a positive power of 10 will make the number greater; multiplying by a negative power of 10 will make the number less.

Move the decimal point to the right of the first nonzero digit.

0.00291

Find the number by moving the decimal point that is between 1 to 9.

002.91

Changing Standard Form to Scientific Notation

Scientific Notation

Multiplying a number by a positive power of 10 will make the number greater; multiplying by a negative power of 10 will make the number less.

Move the decimal point to the right of the first nonzero digit.

0.00291

Find the number by moving the decimal point that is between 1 to 9.

002.91

Count the number of places you moved the decimal point.

321

002.91

Write a negative exponent which is equal to the number of places you moved the decimal point to the right.

Changing Standard Form to Scientific Notation

Scientific Notation

Multiplying a number by a positive power of 10 will make the number greater; multiplying by a negative power of 10 will make the number less.

Move the decimal point to the right of the first nonzero digit.

0.00291

Find the number by moving the decimal point that is between 1 to 9.

002.91

Count the number of places you moved the decimal point.

321

The number of places in Step 2 is the absolute value of the exponent on 10.

2.91 x 002.91

Write a negative exponent which is equal to the number of places you moved the decimal point to the right.

6.5 x 10

ANSWER:

6,500,000

Scientific Notation

6

1. Simply move the decimal point to the RIGHT for positive exponent 10.

65000001 2 3 4 5 6

(Use zeros to fill in places.)

6.5 x 10

ANSWER:

65

Scientific Notation

1

1. Simply move the decimal point to the RIGHT for positive exponent 10.

651

(Use zeros to fill in places.)

6.5 x 10

ANSWER:

65

Scientific Notation

1

1. Simply move the decimal point to the RIGHT for positive exponent 10.

651

(Use zeros to fill in places.)

6.5 x 10

ANSWER:

0.65

Scientific Notation

-1

1. Simply move the decimal point to the LEFT for negative exponent 10.

651

(Use zeros to fill in places.)

SUMMARYScientific Notation

Changing Scientific Notation to Standard FormSimply move the decimal point to the RIGHT for positive exponent 10.

Move the decimal point to the LEFT for negative exponent 10.

(Use zeros to fill in places.)

2.5 x 3.1 x = 250= 0.031

Changing Standard Form to Scientific Notation

= =