Compute with scientific notation

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Algebra 8.4 Scientific Notation

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Transcript of Compute with scientific notation

Page 1: Compute with scientific notation

Algebra

8.4Scientific Notation

Page 2: Compute with scientific notation

The Form

A number is written in scientific notation when it is in the form

where c is a value 1and<10

andnis aninteger.

nc×10

Page 3: Compute with scientific notation

The Form

7.65 10

where c is a value 1and<10

andnis aninteger.

nc×10

43.12 10

Not Scientific Notation Scientific Notation

331.2 1066.5 10

68042 10 38.042 10

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Large and small values

One purpose of scientific notation is to allow you to write very large numbers and very small numbers easily, without lots of 0’s.

48.4912×10

Small numbers have negative exponents.

84,912

Large numbers have positive exponents.

- 42.65×10.000265

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Scientific Notation Decimal

Move decimal point right for positive exponent.Move decimal point left for negative exponent.

33.128×101. 3128

46.4 ×102. 64,000

- 13.9×103.

- 56.12×104.

.39

.0000612

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Decimal Scientific Notation

Move decimal point right or left to arrange one digit to the left of decimal point.

45.2314 ×101. 52,314

03.2×102. 3.2

3.

4. 602,000,000

Move left 4 places

No need to move

.0000428 Move right 5 places- 54.28×10

Move left 8 places86.02×10

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Exercises

22.834 ×101. 283.4- 61.23×102. .00000123

43.469×103.

- 23.9×104.

34,690

.039

Rewrite in decimal form.

Rewrite in scientific notation.

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Computing with Scientific Notation

Another purpose of scientific notation is to allow you to compute with large and small values easily using the rules of exponents.

Numbers can be multiplied.

4 2

4 2

4+2 6 7

(8×10 )(3×10 )

=(8×3)(10 ×10 )

=24 ×10 =24 ×10 =2.4×10

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Computing with Scientific Notation

Numbers can be divided.

6 6

2 2

6-2 4

4.8×10 4.8 10= ×

2.4 ×10 2.4 10

=2×10 =2×10

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Exercise

Evaluate. Write answer in scientific notation.

4 3(1.4 ×10 )(7.6×10 )

4 3=(1.4 ×7.6)(10 ×10 ) Associative property

710.64 ×10 Simplify

81.064 ×10 Rewrite in SN

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Exercise

Evaluate. Write answer in scientific notation.- 3

- 5

(8×10 )(5×10 )

- 3

- 5

8 10=

5 10Associative property

- 3- (- 5)1.6×10 Subtract exponents

21.6×10 Simplify to SN

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Homework

pg. 63 #’s 1, 2, 4, 6, 8, 9, 10, 11