PDF Scientific Notation

[Pages:28]Scientific Notation

Section 7-1 Part 2

Goals

Goal ? To write numbers in

scientific notation and standard form. ? To compare and order numbers using scientific notation.

Vocabulary

? Scientific Notation

Powers of 10

The table shows relationships between several powers of 10.

? Each time you divide by 10, the exponent in the power decreases by 1 and the decimal point in the value moves one place to the left.

? Each time you multiply by 10, the exponent in the power increases by 1 and the decimal point in the value moves one place to the right.

Powers of 10

? You can find the product of a number and a power of 10 by moving the decimal point of the number.

? If the exponent is positive, move the decimal point to the right.

? If the exponent is negative, move the decimal point to the left.

? You may need to write zeros to the right or left of the number in order to move the decimal point.

Example: Multiplying by

Powers of 10

Multiply.

A. 14 x 104

14.0 0 0 0

Since the exponent is a positive 4, move the decimal point 4 places to the right.

140,000

B. 3.6 x 10-5

0 0 0 0 3.6

0.000036

Since the exponent is a negative 5, move the decimal point 5 places to the left.

Your Turn:

Multiply.

A. 2.5 x 105

2.5 0 0 0 0

250,000

B. 10.2 x 10-3

0 10.2

0.0102

Since the exponent is a positive 5, move the decimal point 5 places to the right.

Since the exponent is a negative 3, move the decimal point 3 places to the left.

Definition

? Scientific Notation - is a way to express numbers that are very large or very small.

? Powers of 10 are used when writing numbers in scientific notation.

? Numbers written in scientific notation are expressed as 2 factors.

? One factor is a number greater than or equal to 1. ? The other factor is a power of 10.

? Example:

? 1.43 1012 ? 5.8 10-9

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