Main Idea and New Vocabulary

Key Concept: Scientific Notation

Example 1: Express Large Numbers in Standard Form

Example 2: Express Small Numbers in Standard Form

Example 3: Express Numbers in Scientific Notation

Example 4: Express Numbers in Scientific Notation

Example 5: Compare Numbers in Scientific Notation

• Express numbers in scientific notation and in standard form.

• scientific notation

Express Large Numbers in Standard Form

Express 3.56 × 105 in standard form.

Answer: 356,000

3.56 × 105 = 3.56 × 100,000 105 = 100,000

= 356,000 Move the decimalpoint 5 places.

A. 0.414

B. 4.14

C. 41.4

D. 414

Express 4.14 102 in standard form.

Express 1.4 × 10

–6 in standard form.

Express Small Numbers in Standard Form

Answer: 0.0000014

1.4 × 10

–6 = 1.4 × 0.000001 10

–6 = 0.000001

= 0.0000014Move the

decimalpoint 6 places.

A. 0.000213

B. 0.00213

C. 0.0213

D. 0.213

Express 2.13 × 10

–4 in standard form.

Express Numbers in Scientific Notation

Express 268,000 in scientific notation.

Answer: 2.68 × 105

268,000 = 2.68 × 10,000 The decimal point moves 5 places.

= 2.68 × 105

The exponent is positive.

A. 2.3 × 102

B. 2.3 × 103

C. 23.0 × 103

D. 0.23 × 104

Express 2,300 in scientific notation.

Express 0.00000028 in scientific notation.

Express Numbers in Scientific Notation

Answer: 2.8 × 10

–7

0.00000028 = 2.8 × 0.0000001 The decimal point moves 7 places.

= 2.8 × 10

–7 The exponent is negative.

A. 0.3 × 10–5

B. 3.0 × 10–5

C. 30 × 10–5

D. 300 × 10–5

Express 0.00003 in scientific notation.

Compare Numbers in Scientific Notation

PLANETS Earth has an average radius of 6.38 × 103 kilometers. Mercury has an average radius of 2.44 × 103 kilometers. Which planet has the greater average radius?

6.38 > 2.44 6.38 × 103 > 2.44 × 103

Answer: So, Earth has the greater average radius.

A. Sound travels faster at sea level.

B. Sound travels faster at 20,000 feet.

C. Sound travels the same speed at sea level and at 20,000 feet.

SOUND At sea level, the speed of sound is about 1.225 103 kilometers per hour. At 20,000 feet, the speed of sound is 1.062 103 kilometers per hour. Does sound travel faster at sea level or at 20,000 feet?