NETS 11496 Glencoe G7 SE MS Math 09 LA02_LA05_874046 wa 04-16-08 Edit wa 06-26-08 1st pp NETS 11496 Glencoe G7 SE MS Math 09 LA02_LA05_874046 wa 04-16-08 Edit wa 06-26-08 1st pp

MAIN IDEAExpress numbers in scientific notation and in standard form.

New Vocabularyscientific notation

Math Onlineglencoe.com• Personal Tutor• Self-Check Quiz• Extra Examples

Key ConceptScientific Notation

Words A number is expressed in scientific notation when it is written as the product of a factor and a power of 10. The factor must be greater than or equal to 1 and less than 10.

Symbols a × 10 n , where 1 ≤ a < 10 and n is an integer

Examples 425,000,000 = 4.25 × 10 8

Scientific Notation

More than 425 million pounds of gold has been discovered in the world. If all this gold were in one place, it would form a cube seven stories on each side.

1. Write 425 million in standard form.

2. Complete: 4.25 × ? = 425 million.

When you deal with very large numbers like 425,000,000, it can be difficult to keep track of the zeros. You can express numbers such as this in scientific notation by writing the number as the product of a factor and a power of 10.

Express Large Numbers in Standard Form

1 Express 2.16 × 10 5 in standard form.

2.16 × 10 5 = 2.16 × 100,000 10 5 = 100,000

= 216,000 Move the decimal point 5 places to the right.

Express each number in standard form.

a. 7.6 × 10 6 b. 3.201 × 10 4

Scientific notation is also used to express very small numbers. Study the pattern of products at the right. Notice that multiplying by a negative power of 10 moves the decimal point to the left the same number of places as the absolute value of the exponent.

1.25 × 10 2 = 125

1.25 × 10 1 = 12.5

1.25 × 10 0 = 1.25

1.25 × 10 –1 = 0.125

1.25 × 10 –2 = 0.0125

1.25 × 10 –3 = 0.00125

LA2 Looking Ahead

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NETS 11496 Glencoe G7 SE MS Math 09 LA02_LA05_874046 wa 04-16-08 Edit wa 06-26-08 1st pp NETS 11496 Glencoe G7 SE MS Math 09 LA02_LA05_874046 wa 04-16-08 Edit wa 06-26-08 1st pp

Move the Decimal PointThe exponent tells you how many places to move the decimal point.• If the exponent is

positive, move the decimal point to the right.

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

Express Small Numbers in Standard Form

2 Express 5.8 × 10 –3 in standard form.

5.8 × 10 –3 = 5.8 × 0.001 10–3 = 0.001

= 0.0058 Move the decimal point 3 places to the left.

c. 4.7 × 10 –5 d. 9.0 × 10 –4

To write a number in scientific notation, place the decimal point after the first nonzero digit. Then find the power of 10.

Express Numbers in Scientific Notation Express each number in scientific notation.

3 1,457,000

1,457,000 = 1.457 × 1,000,000 The decimal point moves 6 places to the left.

= 1.457 × 10 6 The exponent is positive.

4 0.00063

0.00063 = 6.3 × 0.0001 The decimal point moves 4 places to the right.

= 6.3 × 10 –4 The exponent is negative.

e. 35,000 f. 0.00722

To compare numbers in scientific notation, first compare the exponents. With positive numbers, any number with a greater exponent is greater. If the exponents are the same, compare the factors.

Compare Numbers in Scientific Notation

5 OCEANS The Atlantic Ocean has an area of 3.18 × 10 7 square miles. The Pacific Ocean has an area of 6.4 × 10 7 square miles. Which ocean has the greater area?

Since both exponents are the same, compare the factors.

3.18 < 6.4 → 3.18 × 10 7 < 6.4 × 10 7

So, the Pacific Ocean has the greater area.

g. Replace � with <, >, or = to make 4.13 × 10 –2 � 5.0 × 10 –3 a true

sentence.

Lesson 1 Scientific Notation LA3

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Disc Distance (mm)CD 1.6 × 10 -3 DVD 7.4 × 10 -4

Category Sales ($)Camping 1.547 × 10 9 Golf 3.243 × 10 9 Tennis 3.73 × 10 8

Source: National Sporting Goods Assoc.

Examples 1, 2(pp. LA2–LA3)

Express each number in standard form.

1. 3.754 × 10 5 2. 8.34 × 10 6

3. 1.5 × 10 –4 4. 2.68 × 10 –3

Examples 3, 4(p. LA3)

Express each number in scientific notation.

5. 4,510,000 6. 0.00673

7. 0.000092 8. 11,620,000

9. PHYSICAL SCIENCE Light travels 300,000 kilometers per second. Write this

number in scientific notation.

Example 5(p. LA3)

10. TECHNOLOGY The distance between tracks on a

CD and DVD are shown in the table. Which disc

has the greater distance between tracks?

Replace each � with <, >, or = to make a true sentence.

11. 2.3 × 10 5 � 1.7 × 10 5 12. 0.012 � 1.4 × 10 –1

For Exercises

13–2223–3233–38

See Examples

1, 23, 45

HOMEWORK HELPHELP Express each number in standard form.

13. 6.1 × 10 4 14. 5.72 × 10 6 15. 3.3 × 10 –1 16. 5.68 × 10 –3

17. 9.014 × 10 –2 18. 1.399 × 10 5 19. 2.505 × 10 3 20. 7.4 × 10 –5

21. SPIDERS The diameter of a spider’s thread is 1.0 × 10 –3 inch. Write this

number in standard form.

22. DINOSAURS The Gigantosaurus dinosaur weighed about 1.4 × 10 4 pounds.

Write this number in standard form.

Express each number in scientific notation.

23. 499,000 24. 2,000,000 25. 0.006 26. 0.0125

27. 50,000,000 28. 39,560 29. 0.000078 30. 0.000425

31. CHESS The number of possible ways that a player can play the first four

moves in a chess game is 3 billion. Write this number in scientific

notation.

32. SCIENCE A particular parasite is approximately 0.025 inch long. Write this

number in scientific notation.

SPORTS For Exercises 33 and 34, use the table.

Determine which category in each pair had a

greater amount of sales.

33. golf or tennis 34. camping or golf

LA4 Looking Ahead

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Metric MeasuresPrefix Meaningatto 10 -18 giga 10 9 kilo 10 3 nano 10 -9 peta 10 15 pico 10 -12

Volcanic Eruptions

Volcano, Year Eruption Rate ( m 3 /s)

Mount St. Helens, 1980

2.0 × 10 4

Ngauruhoe, 1975 2.0 × 10 3 Hekla, 1970 4.0 × 10 3 Agung, 1963 3.0 × 10 4

Source: University of Alaska

Replace each � with <, >, or = to make a true sentence.

35. 1.8 × 10 3 � 1.9 × 10 –1 36. 5.2 × 10 2 � 5000

37. 0.00701 � 7.1 × 10 –3 38. 6.49 × 10 4 � 649 × 10 2

39. MEASUREMENT The table at the right shows the values

of different prefixes that are used in the metric system.

Write the units attometer, gigameter, kilometer,

nanometer, petameter, and picometer in order from

greatest to least measure.

40. NUMBER SENSE Write the product of 0.00004 and 0.0008

in scientific notation.

41. NUMBER SENSE Order 6.1 × 10 4 , 6100, 6.1 × 10 –5 , 0.0061, and 6.1 × 10 –2

from least to greatest.

PHYSICAL SCIENCE For Exercises 42 and 43,

use the table.

The table shows the maximum amounts of

lava in cubic meters per second that erupted

from four volcanoes.

42. How many times greater was the

Mount St. Helens eruption than the

Ngauruhoe eruption?

43. How many times greater was the Hekla

eruption than the Ngauruhoe eruption?

Write each number in standard form.

44. (8 × 10 0 ) + (4 × 10 –3 ) + (3 × 10 –5 )

45. (4 × 10 4 ) + (8 × 10 3 ) + (3 × 10 2 ) + (9 × 10 1 ) + (6 × 10 0 )

H.O.T. Problems 46. CHALLENGE Convert the numbers in each expression to scientific notation.

Then evaluate the expression. Express in scientific notation and in

decimal notation.

a. (420,000)(0.015)

__ 0.025

b. (0.078)(8.5)

__ 0.16(250,000)

47. REASONING Which is a better estimate for the number of times per year

that a person blinks: 6.25 × 10 –2 times or 6.25 × 10 6 times? Explain your

reasoning.

48. OPEN ENDED Describe a real-life value or measure using numbers in

scientific notation and in standard form.

49. MATHWRITING IN Explain the relationship between a number in

standard form and the sign of the exponent when the number is written

in scientific notation.

Lesson 1 Scientific Notation LA5

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