Over Lesson 9–4

Write 2–3 using a positive exponent.

A. (–3)2

B. 23

C.

D.

Over Lesson 9–4

Write a–1 using a positive exponent.

A. a

B. –a

C.

D.

Over Lesson 9–4

Write (–5)–4 using a positive exponent.

A.

B.

C. 54

D. (–5)4

Over Lesson 9–4

A. 45

B. 4–5

C. (–4)–5

D.

Over Lesson 9–4

A. 49–0

B. 7–2

C. 4–9

D.

Over Lesson 9–4

Evaluate z–3 if z = 5.

A. 125

B. –125

C.

D.

You have already compared and ordered integers. (Lesson 2–1)

• Express numbers in standard form and in scientific notation.

• Compare and order numbers written in scientific notation.

• standard form

• scientific notation

Express Numbers in Standard Form

A. Express 3 × 105 in standard form.

3 × 105= 3 × 100,000105 = 100,000

=300,000Move the decimal point 5 places to the right.

Answer: 300,000

Express Numbers in Standard Form

B. Express 4.395 × 104 in standard form.

4.395 × 104 = 4.395 × 10,000 104 = 10,000

= 43950Move

the decimal point 4 places to the right.

Answer: 43,950

Express Numbers in Standard Form

C. Express 6.79 × 10–6 in standard form.

6.79 × 10–6 = 6.79 × 0.000001 10–6 = 0.000001

=0.00000679 Move the decimal point 6 places to the left.

Answer: 0.00000679

A. 5,000

B. 50,000

C. 500,000

D. 5,000,000

A. Express 5 × 104 in standard form.

A. 2,614,000

B. 261,400

C. 0.000002614

D. 0.002614

B. Express 2.614 × 106 in standard form.

A. 80,300

B. 8.030

C. 0.000803

D. 0.0803

C. Express 8.03 × 10–4 in standard form.

Express Numbers in Scientific Notation

A. Express 800,000 in scientific notation.

800,000 = 8.0 × 100,000 The decimal point moves 5 places.

Answer: 8.0 × 105

= 8.0 × 105

The exponent is positive.

Express Numbers in Scientific Notation

B. Express 64,000 in scientific notation.

64,000 = 6.4 × 10,000The decimal

point moves 4 places.

Answer: 6.4 × 104

= 6.4 × 104 The exponent is positive.

Express Numbers in Scientific Notation

C. Express 0.0119 in scientific notation.

0.0119 = 1.19 × 0.01 The decimal point moves 2 places.

Answer: 1.19 × 10–2

= 1.19 × 10–2

The exponent is negative.

A. 6.5 × 105

B. 6.5 × 10–4

C. 6.5 × 104

D. 65 × 103

A. Express 65,000 in scientific notation.

A. 9.5 × 106

B. 9.5 × 107

C. 95 × 106

D. 95 × 107

B. Express 95,000,000 in scientific notation.

A. 42 × 10–5

B. 4.2 × 10–4

C. 4.2 × 104

D. 4.2 × 10–3

C. Express 0.00042 in scientific notation.

Solve Problems Using Scientific Notation

DIMES A dime is 1.35 × 10–3 meters thick. What would the height of a stack of one million dimes be in scientific notation?

Understand You know that a dime is 1.35 × 10–3 meters thick and that there are 1 million dimes in the stack. You need to know how thick the stack is.

Plan Write 1 million in scientific notation. Multiply the thickness of a dime by the number of dimes in the stack to find the total thickness of the stack.

Solve 1 million = 1.0 × 106

thickness of = thickness of 1 dime × stack number in stack

= (1.35 × 10–3 m) × (1.0 × 106)

= 1.35 × 10–3 + 6 m

= 1.35 × 103 m

Solve Problems Using Scientific Notation

Check Check using mental math.

(1.35 × 10–3)(1 × 106) = (1.35 × 1.0)(10–3 × 106)

= 1.35 × 103

Answer: So, the height of the stack is 1.35 × 103 m.

A. 1.75 × 106 m

B. 1.75 × 109 m

C. 1.75 × 1012 m

D. 1.75 × 1015 m

A quarter is 1.75 × 10–3 meters thick. What would be the height of a stack of one billion quarters in scientific notation?

Order Numbers in Scientific Notation

SPACE The diameters of Neptune, Saturn, and Uranus are 4.9 × 104 km, 1.2 × 105 km, and 5.1 × 104 km, respectively. Order the planets from greatest to least diameter.

Step 1 Order the numbers according to their exponents.

Saturn has the greatest exponent so it is the largest.

Order Numbers in Scientific Notation

5.1 > 4.9

Uranus Neptune

5.1 × 104 > 4.9 × 104

Answer: So, the order is Saturn, Uranus, and Neptune.

Step 2 Order the numbers with the same exponent by comparing the factors.

A. Mercury, Earth, Jupiter

B. Mercury, Jupiter, Earth

C. Earth, Jupiter, Mercury

D. Earth, Mercury, Jupiter

The diameters of Earth, Jupiter, and Mercury are 1.55 × 108 km, 7.79 × 108 km, and 5.80 × 107 km, respectively. Order the diameters from smallest to largest diameter.