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.

18

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

19

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