MAIN IDEA Express numbers in scientific notation and in standard form. New Vocabulary scientific notation Math Online glencoe.com • Personal Tutor • Self-Check Quiz • Extra Examples Key Concept Scientific 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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LA02 LA05 874046 - Glencoeglencoe.com/sites/north_carolina/support_student...Express Large Numbers in Standard Form 1 Express 2.16 × 10 5 in standard form. 2.16 × 10 5 = 2.16 ×
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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
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
LA02_LA05_874046.indd 2 5/26/09 5:23:12 PM
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