Scientific and standard notation, conversion

What is Scientific Notation A number expressed in scientific notation is expressed as a decimal number between 1 and 10 multiplied by a power of 10 (eg, 7000 = 7 x 103 or 0.0000019 = 1.9 x 10 -6)

It’s a shorthand way of writing very large or very small numbers used in science and math and anywhere we have to work with very large or very small numbers.

Why do we use it?

Scientific and standard notation, conversion

Scientific Notation: expressing a number in the form c x 10n , where 1 < c < 10.

Examples: Are the following numbers written in scientific notation?

a. 42 x 106 b. 9.3 x 103

No, 42 is Yesgreater than 10

Examples: Write in scientific notation:

a. 236,000 b. 0.04325

c. 0.000725

Move the decimal left or right so that c is between 1 and 10. Count the # of places you moved.

4.325 x 10–2

7.25 x 10-4

2.36 x 105

Example: Write in decimal notation: a. 2.45 x 10–3

b. 1.38 x 108

To change from scientific notation back to decimal notation, move the decimal n of places, where n is the power of 10.

0.00245

138,000,000

Scientific Notation Cornel Notes

Changing from Standard Notation to Scientific NotationEx. 6800

Scientific Notation Cornel Notes

Changing from Standard Notation to Scientific NotationEx. 6800

6800

1. Move decimal to get a number between 1 & 10 and count places moved.

123

Scientific Notation Cornel Notes

Changing from Standard Notation to Scientific NotationEx. 6800

6800

1. Move decimal to get a number between 1 & 10 and count places moved.

2. Answer is a number between 1 & 10 times the power of ten ( places moved).

68 x 103

123

Changing from Standard Notation to Scientific NotationEx. 6800

6800

1. Move decimal to get a single digit # and count places moved

2. Answer is a single digit number times the power of ten of places moved.

68 x 103

If the decimal is moved left the power is positive.

If the decimal is moved right the power is negative.

123

Try This

Changing from Standard Notation to Scientific NotationEx. 720,000

Try This

Changing from Standard Notation to Scientific NotationEx. 720,000

1. Move decimal to get a single digit # and count places moved.

720000

12345

Try This

Changing from Standard Notation to Scientific NotationEx. 720,000

1. Move decimal to get a single digit # and count places moved.

72000072 x 105

12345

2. Answer is a number between 1 & 10 times the power of ten (# of places moved.

Scientific Notation Cornel Notes

Changing from Scientific Notation to Standard NotationEx. 4.5 x 10-3

Changing from Scientific Notation to Standard NotationEx. 4.5 x 10-3

1. Move decimal the same number of places as the exponent of 10.

(Right if Pos. Left if Neg.)

00045

123

Try This

Changing from Scientific Notation to Standard NotationEx. 8.9 x 105

Try This

Changing from Scientific Notation to Standard NotationEx. 8.9 x 105

1. Move decimal the same number of places as the exponent of 10.

(Right if Pos. Left if Neg.)

890000

1 2 3 4 5

Addition and subtractionScientific Notation

1. Make exponents of 10 the same2. Add 0.2 + 3 and keep the 103 intact

The key to adding or subtracting numbers in Scientific Notation is to make sure the exponents are the same.

2.0 x 102 + 3.0 x 103

.2 x 103 + 3.0 x 103

= .2+3 x 103

= 3.2 x 103

2.0 x 107 - 6.3 x 105

2.0 x 107 -.063 x 107

= 2.0-.063 x 107

= 1.937 x 107

1. Make exponents of 10 the same2. Subtract 2.0 - .063 and keep the 107 intact

Changing from StandardNotation to Scientific NotationEx. 6800

6800 1. Move decimal to geta single digit # andcount places moved

2. Answer is a singledigit number timesthe power of ten ofplaces moved.

68 x 103

If the decimal is moved left the power is positive.

If the decimal is moved right the power is negative.

123

What is Scientific NotationA number expressed in scientific notation isexpressed as a decimal number between 1 and 10multiplied by a power of 10 (eg, 7000 = 7 x 103 or0.0000019 = 1.9 x 10 -6)

It’s a shorthand way of writing very large or verysmall numbers used in science and math andanywhere we have to work with very large or verysmall numbers.

Why do we use it?

Changing from ScientificNotation to Standard NotationEx. 4.5 x 10-3

1. Move decimal the samenumber of places as theexponent of 10.(Right if Pos. Left if Neg.)

00045123

Multiply two numbersin Scientific Notation(3 x 104)(7 x 10–5)

1. Put #’s in ( )’s Putbase 10’s in ( )’s

2. Multiply numbers3. Add exponents of 10.4. Move decimal to put

Answer in ScientificNotation

= (3 x 7)(104 x 10–5)

= 21 x 10-1

= 2.1 x 100

or 2.1

6.20 x 10–5

8.0 x 103DIVIDE USING SCIENTIFIC

NOTATION

= 0.775 x 10-8

= 7.75 x 10–9

1. Divide the #’s &Divide the powers of ten(subtract the exponents)

2. Put Answer in ScientificNotation

6.20

8.0

10-5

103

9.54x107 miles

1.86x107 milesper second

Addition and subtractionScientific Notation

1. Make exponents of 10 the same2. Add 0.2 + 3 and keep the 103 intact

The key to adding or subtracting numbersin Scientific Notation is to make sure theexponents are the same.

2.0 x 102 + 3.0 x 103

.2 x 103 + 3.0 x 103

= .2+3 x 103

= 3.2 x 103

2.0 x 107 - 6.3 x 105

2.0 x 107 -.063 x 107

= 2.0-.063 x 107

= 1.937 x 107

1. Make exponents of 10 the same2. Subtract 2.0 - .063 and keep the 107 intact

Scientific Notation Makes These Numbers Easy