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### Warmup

### Scientific Notation

Estimate the following amounts.

the number of bits on a computer hard disk (as of 2006)

the number of cells in the human body

the number of neuronal connections in the human brain Avogadro\'s number (the number of atoms in 12 grams of carbon-12)

the number of molecules in a cup of tea

age of the universe based on the current Big Bang model

the observable universe is how many light years across

the number of stars in the observable universe

Answers will be shown later in this lesson.

Algebra 1

What are these numbers?

Do you know this number,

300,000,000 m/sec.?

It\'s the speed of light !

Do you recognize this number,

0.000 000 000 753 kg?

This is the mass of a dust particle!

Which is easier to read?

- What about the number 145,000,000? The Department of Energy\'s (DOE) inventory of high level radioactive waste was approximately 145,000,000 pounds. 145,000,000 or 1.45 x 108?

A Shortcut

Scientists have developed a shorter method to express very large numbers. This method is calledscientific notation. Scientific notation is based on powers of the base number 10.

Scientists Using Scientific Notation While Studying Dinosaurs Video

Size of the Universe Demonstration of Scientific Notation

Power of Ten Video – Old but a Classic

To Change from Standard Form to Scientific Notation

(1) Write decimal one number in from the left so that the number is between 1 and 10.

(2) Write “x 10”

- Negative if the decimal moves left to original location; right is positive.

Where is the decimal “implied” if no decimal appears in a number? (example: 195)

Examples

Given: 4,750,000

Use 4.75 (moved 6 decimal places)

Answer: 4.75 X 106

The original number was greater than 1 so the exponent is positive.

Given: 0.000789

Use 7.89 (moved 4 decimal places)

answer: 7.89 x 10-4

The original number was less than 1 so the exponent is negative.

Examples

Given: 1.015 x 10-8

Answer:0.00000001015 (8 places to left)

Negative exponent move decimal to the left.

Given: 5.024 x 103

Answer: 5,024 (3 places to right)

Positive exponent move decimal to the right.

Real Life Examples

The Andromeda Galaxy (the closest one to our Milky Way galaxy) contains at least 200,000,000,000 stars.

On the other hand, the weight of an alpha particle, which is emitted in the radioactive decay of Plutonium-239, is0.000,000,000,000,000,000,000,000,006,645 kilograms.

Large Numbers

- the number of bits on a computer hard disk (as of 2006, about 1 x 1012 GB)
- the number of cells in the human body (more than 1 x 1014)
- the number of neuronal connections in the human brain (estimated at 1 x 1014)
- Avogadro\'s number (the number of atoms in 12 grams of carbon-12, ~ 6.022 × 1023)

There are around 8,360,000,000,000,000,000,000,000 molecules in a cup of tea!

The current Big Bang model of the Universe suggests that it is 13.7 billion years

or (4.3 × 1017 seconds) old.

The observable universe is 78 billion light years across (7.4 × 1026 meters), and contains about 5 × 1022 stars, organized into around 80 thousand million galaxies.

wavelength of green light: 5.5 × 10-7 m

- period of a 100 MHz FM radio wave: 1 × 10-8 s
- time taken by light to travel one meter: roughly 3 × 10-9 s
- radius of a hydrogen atom: 2.5 × 10-11 m
- the charge on an electron:

roughly 1.6 × 10-19 C (negative)

Between 1980 and 2011, hard disk sizes increased from 10 megabytes (1 × 107) to over 18 exabytes (1.8 x 1019 bytes).

Earth = 12.76 x 106 = 12,760,000 meters wide

Plant Cell = 12.76 x 10-6=0.00001276 m wide

The Andromeda Galaxy contains at least 200,000,000,000 stars.

- Alpha particle emitted in the radioactive decay of Plutonium-239, is 0.000,000,000,000,000,000,000,000,006,645 kg.
- Number of bits on a computer hard disk (as of 2006, about 1 x 1012 GB)
- Number of cells in the human body (more than 1 x 1014)
- Number of neuronal connections in the human brain (estimated at 1 x 1014)

Avogadro\'s number (the number of atoms in 12 grams of carbon-12, ~ 6.022 × 1023)

- There are around 8,360,000,000,000,000,000,000,000 molecules in a cup of tea.
- Time taken by light to travel one meter: roughly 3 × 10-9 sec
- The charge on an electron: roughly 1.6 × 10-19 C (negative)
- 1980 to 2011, hard disk sizes increased from 10 megabytes (1 × 107) to over 18 exabytes (1.8 x 1019 bytes).

On-Line Practice and More

On-line Practice Problems

Interactive Practice

Changing Numbers to Scientific Notation

http://www.aaamath.com/dec71i-dec2sci.html

Changing Numbers from Scientific Notation

http://www.aaamath.com/dec71i-dec2sci.html

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