Scientific Notation

An ordinary quarter contains about 97,700,000,000,000,000,000,000 atoms. The average size of an atom is about 0.00000003 centimeters across.

The length of these numbers in standard notation makes them awkward to work with.

Scientific notation is a shorthand way of writing such numbers.

Why do we need scientific notation?

Vocabulary

Word Definition

scientific notation A form of writing very large & very small numbers. Written as:• Decimal number greater than or

equal to 1 and less than 10.• Multiplied by power of 10.

Ex: 1800 = 1.8 x 103

Translating Standard Notation to Scientific Notation

0.00709

7.09

7.09 10

To Scientific Notation:1) Move decimal point to right of first

non-zero digit.2) Set up scientific notation.3) Exponent = # places you moved

decimal point.*If very small #, use – exponent.*If very large #, use + exponent.

Write 0.00709 in scientific notation.

So 0.00709 written in scientific notation is 7.09 10–3.

Translating Standard Notation to Scientific Notation

Think: The number is very large so make exponent positive.

14,500,000 Think: The decimal needs to move 7 places to get a number between 1 and 10.1.45

1.45 10 Set up scientific notation.

Check 1.45 107 = 1.45 10,000,000 = 14,500,000

Write 14,500,000 in scientific notation.

So 14,500,000 written in scientific notation is 1.45 107.

Think: The number is very small so make exponent negative.

0.000811 Think: The decimal needs to move 4 places to get a number between 1 and 10.8.11

8.11 10 Set up scientific notation.

Check 8.11 10 = 8.11 0.0001 = 0.000811–4

Write 0.000811 in scientific notation.

So 0.000811 written in scientific notation is 8.11 10–4.

Translating Standard Notation to Scientific Notation

Translating Standard Notation to Scientific Notation

Think: The number is very large so make exponent positive.

225,000 Think: The decimal needs to move 5 places to get a number between 1 and 10.2.25

2.25 10 Set up scientific notation.

Check 2.25 105 = 2.25 100,000 = 225,000

Write 225,000 in scientific notation.

So 225,000 written in scientific notation is 2.25 105.

135,000

1.35 100,000

Think: Move the decimal right 5 places because I am multiplying by a power of 10 and there are 5 zeroes represented by the exponent.

1.35 105

1.35 10 5

10 = 100,000 Note: There are 5 zeroes,

which are represented by the exponent.

5

Translating Scientific Notation to Standard Notation

Write the number in standard notation.

0.0027

To Standard Notation:1.) Write the decimal.2.) Move the decimal point the number of places given by exponent.- Exp. = very small #s (< 1)+ Exp.= very large #s

2.7 10–3

2.7 10–3 10 = –3 11000

Write the number in standard notation.

Translating Scientific Notation to Standard Notation

Positive exponents make the decimal larger because you are multiplying by powers of 10 (move to right).

Negative exponents make the decimal smaller because you are dividing by powers of 10 (move to left).

REMEMBER: A negative exponent is the same as dividing by that number with a

positive exponent.

Ex: 10-3 = 3

1

10A number less than 1 will have a negative exponent when written in scientific notation.

Helpful Hint

2.01 104

20,100Think: Move the decimal right 4 places as positive exponent = very large #.

2.01 104

Translating Scientific Notation to Standard Notation

Write the number in standard notation.

0.000019Think: Move the decimal left 5 places as negative exponent = very small # .

1.9 10 –5

1.9 10–5

Write the number in standard notation.

Translating Scientific Notation to Standard Notation

Lesson Quiz

Write each number in standard notation.

1. 1.72 104

2. 6.9 10–3

4. 57,000,000

17,200

0.0069

3. 0.0053 5.3 10–3

5.7 107

Write each number in scientific notation.

5. Order the numbers from least to greatest. T 2 10–4, 9 10–5, 7 10–5

7 10–5, 9 10–5, 2 10–4