Main Idea and New Vocabulary

Example 1: Express Numbers in Standard Form

Example 2: Express Numbers in Standard Form

Example 3: Write Numbers in Scientific Notation

Example 4: Write Numbers in Scientific Notation

Example 5: Real-World Example

• Use scientific notation to write large and small numbers.

• scientific notation

Express Numbers in Standard Form

Write 9.62 × 105 in standard form.

9.62 × 105 = 962,000. The decimal point moves 5 places right.

Answer: 962,000

A. 0.0071

B. 0.071

C. 710

D. 7,100

Write 7.1 × 103 in standard form.

Write 2.85 × 10–6 in standard form.

Express Numbers in Standard Form

2.85 × 10–6 = 0.00000285 The decimal point moves 6 places left.

Answer: 0.00000285

A. 0.000509

B. 0.00509

C. 5,090

D. 50,900

Write 5.09 × 10–4 in standard form.

Write Numbers in Scientific Notation

Write 931,500,000 in scientific notation.

931,500,000 = 9.315 × 100,000,000

The decimal point moves 8 places.

Answer: 9.315 × 108

= 9.315 × 108 Since 931,500,000 > 1, the exponent is positive.

A. 1.2 × 10–5

B. 1.2 × 104

C. 12.0 × 104

D. 1.2 × 105

Write 120,000 in scientific notation.

Write 0.00443 in scientific notation.

Write Numbers in Scientific Notation

0.00443 = 4.43 × 0.001 The decimal point moves 3 places.

Answer: 4.443 × 10–3

= 4.43 × 10–3 Since 0 < 0.00443 < 1, the exponent is negative.

A. 9.2 × 10–6

B. 9.2 × 10–5

C. 92.0 × 10–4

D. 9.2 × 105

Write 0.000092 in scientific notation.

VISIBLE LIGHT The following table lists the maximum frequency for the colors of the visible light spectrum. List the colors from greatest to least frequency.

Since all the maximum frequencies have the same power of ten, compare the factors that are less than 10.

7.5 > 6.7 > 6.1 > 5.1 > 3.8 violet blue green orange red

Answer: The colors from greatest to least frequency

are violet, blue, green, orange, and red.

A. Mercury, Venus, Saturn, Earth, Mars

B. Mars, Mercury, Earth, Venus, Saturn

C. Mercury, Mars, Venus, Earth, Saturn

D. Mercury, Mars, Saturn, Venus, Earth

PLANETS The following table lists the masses of five planets. List the planets from least to greatest mass.

4.87 1024Venus

5.69 1026Saturn

3.30 1023Mercury

6.42 1023Mars

5.98 1024Earth

Mass (kg)Planet