Transcript Math 71 – 1.1
Math 50
6.3 – Multiplying Decimal Numbers; Exponents with Decimal Bases
1
Ex 1.
2.04 ⋅ 0.09
(−1.5)(2.91) −0.05
3
(1.7𝑥
3
)(6.2𝑥
2
)
2
Ex 2.
If you buy 4.5 pounds of oatmeal at $0.69 per pound, what is the total cost?
___________ means the price of each unit.
3
Ex 2.
If you buy 4.5 pounds of oatmeal at $0.69 per pound, what is the total cost?
___________ means the price of each unit.
4
Ex 2.
If you buy 4.5 pounds of oatmeal at $0.69 per pound, what is the total cost?
5
Ex 2.
If you buy 4.5 pounds of oatmeal at $0.69 per pound, what is the total cost?
unit price
6
Note that
2.3 ⋅ 10 = 23 2.3 ⋅ 100 = 230 2.3 ⋅ 1000 = 2300
Multiplying by a positive power of 10 (ex: 10 2 , 10 3 , 10 4 , place to the right.
etc.) moves the decimal 7
Note that
2.3 ⋅ 10 = 23 2.3 ⋅ 100 = 230 2.3 ⋅ 1000 = 2300
Multiplying by a positive power of
10
(ex:
10
2
, 10
3
, 10
4
,
place to the right.
etc.) moves the decimal 8
_____________________ is a convenient way to write really big or really small numbers as a decimal number between 1 and 10 multiplied by a power of 10.
9
write really big or really small numbers as a decimal number between 1 and 10 multiplied by a power of 10.
10
Scientific Notation So, there are two parts: 1. A decimal number whose absolute value is between 1 and 10 (including 1 but not 10).
2. 10 raised to an integer exponent.
ex: 3.27 × 10 3.27 × 10 3 3 is in scientific notation = 3.27 × 10 × 10 × 10 = 3270 ex: Is 24.6 × 10 4 in scientific notation?
No, since 24.6 is not between 1 and 10.
ex: Is −1.1 × 10 5 in scientific notation?
Yes (negative numbers are okay).
11
Scientific Notation So, there are two parts: 1. A decimal number whose absolute value is between 1 and 10 (including 1 but not 10).
2. 10 raised to an integer exponent.
ex: 3.27 × 10 3.27 × 10 3 3 is in scientific notation = 3.27 × 10 × 10 × 10 = 3270 ex: Is 24.6 × 10 4 in scientific notation?
No, since 24.6 is not between 1 and 10.
ex: Is −1.1 × 10 5 in scientific notation?
Yes (negative numbers are okay).
12
Scientific Notation So, there are two parts: 1. A decimal number whose absolute value is between 1 and 10 (including 1 but not 10).
2. 10 raised to an integer exponent.
ex: 3.27 × 10 3.27 × 10 3 3 is in scientific notation = 3.27 × 10 × 10 × 10 = 3270 ex: Is 24.6 × 10 4 in scientific notation?
No, since 24.6 is not between 1 and 10.
ex: Is −1.1 × 10 5 in scientific notation?
Yes (negative numbers are okay).
13
Scientific Notation So, there are two parts: 1. A decimal number whose absolute value is between 1 and 10 (including 1 but not 10).
2. 10 raised to an integer exponent.
ex: 3.27 × 10 3.27 × 10 3 3 is in scientific notation = 3.27 × 10 × 10 × 10 = 3270 ex: Is 24.6 × 10 4 in scientific notation?
No, since 24.6 is not between 1 and 10.
ex: Is −1.1 × 10 5 in scientific notation?
Yes (negative numbers are okay).
14
Scientific Notation So, there are two parts: 1. A decimal number whose absolute value is between 1 and 10 (including 1 but not 10).
2. 10 raised to an integer exponent.
ex: 3.27 × 10 3.27 × 10 3 3 is in scientific notation = 3.27 × 10 × 10 × 10 = 3270 ex: Is 24.6 × 10 4 in scientific notation?
No, since 24.6 is not between 1 and 10.
ex: Is −1.1 × 10 5 in scientific notation?
Yes (negative numbers are okay).
15
Scientific Notation So, there are two parts: 1. A decimal number whose absolute value is between 1 and 10 (including 1 but not 10).
2. 10 raised to an integer exponent.
ex: 3.27 × 10 3.27 × 10 3 3 is in scientific notation = 3.27 × 10 × 10 × 10 = 3270 ex: Is 24.6 × 10 4 in scientific notation?
No, since 24.6 is not between 1 and 10.
ex: Is −1.1 × 10 5 in scientific notation?
Yes (negative numbers are okay).
16
Scientific Notation So, there are two parts: 1. A decimal number whose absolute value is between 1 and 10 (including 1 but not 10).
2. 10 raised to an integer exponent.
ex: 3.27 × 10 3.27 × 10 3 3 is in scientific notation = 3.27 × 10 × 10 × 10 = 3270 ex: Is 24.6 × 10 4 in scientific notation?
No, since 24.6 is not between 1 and 10.
ex: Is −1.1 × 10 5 in scientific notation?
Yes (negative numbers are okay).
17
Scientific Notation So, there are two parts: 1. A decimal number whose absolute value is between 1 and 10 (including 1 but not 10).
2. 10 raised to an integer exponent.
ex: 3.27 × 10 3.27 × 10 3 3 is in scientific notation = 3.27 × 10 × 10 × 10 = 3270 ex: Is 24.6 × 10 4 in scientific notation?
No, since 24.6 is not between 1 and 10.
ex: Is −1.1 × 10 5 in scientific notation?
Yes, since |-1.1|=1.1 is between 1 and 10.
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Ex 3.
Write the number in standard form, then write its word name.
7.81 × 10 9
7,810,000,000 seven billion eight hundred ten million
−1.5 × 10 13
-15,000,000,000,000 negative fifteen trillion
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Ex 3.
Write the number in standard form, then write its word name.
7.81 × 10 9
7,810,000,000 seven billion eight hundred ten million
−1.5 × 10 13
-15,000,000,000,000 negative fifteen trillion
20
Ex 3.
Write the number in standard form, then write its word name.
7.81 × 10 9
7,810,000,000 seven billion eight hundred ten million
−1.5 × 10 13
-15,000,000,000,000 negative fifteen trillion
21
Ex 3.
Write the number in standard form, then write its word name.
7.81 × 10 9
7,810,000,000 seven billion eight hundred ten million
−1.5 × 10 13
-15,000,000,000,000 negative fifteen trillion
22
Ex 3.
Write the number in standard form, then write its word name.
7.81 × 10 9
7,810,000,000 seven billion eight hundred ten million
−1.5 × 10 13
-15,000,000,000,000 negative fifteen trillion
23
Ex 4.
Write each number in scientific notation.
91,000
𝟗. 𝟏 × 𝟏𝟎 𝟒
108,300,000
𝟏. 𝟎𝟖𝟑 × 𝟏𝟎 𝟖 24
Ex 4.
Write each number in scientific notation.
91,000
𝟗. 𝟏 × 𝟏𝟎 𝟒
108,300,000
𝟏. 𝟎𝟖𝟑 × 𝟏𝟎 𝟖 25
Ex 4.
Write each number in scientific notation.
91,000
𝟗. 𝟏 × 𝟏𝟎 𝟒
108,300,000
𝟏. 𝟎𝟖𝟑 × 𝟏𝟎 𝟖 26
Ex 4.
Write each number in scientific notation.
91,000
𝟗. 𝟏 × 𝟏𝟎 𝟒
108,300,000
𝟏. 𝟎𝟖𝟑 × 𝟏𝟎 𝟖 27
Ex 4.
Write each number in scientific notation.
91,000
𝟗. 𝟏 × 𝟏𝟎 𝟒
108,300,000
𝟏. 𝟎𝟖𝟑 × 𝟏𝟎 𝟖 28