Powers of Ten

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MSH! Classes - Powers of Ten

Powers of Ten

Material of many levels of sophishistication is presented on this page. Some of it should be familiar. Some of it should be completely new.

The Usual Powers of Ten
The Funny Looking (at First) Powers of Ten Needed To Write 1 through 10
Apply A Pattern - The Exponents Used to Write 2, 20, 200

NOTES:

No points have been marked on this page for BREAKs. Decide for yourself when to break.
Keep both notes open and your calculator open.
If you only have the computer calculator, use it to verify the easier examples. A scientific or graphing calculator will work for all.
You might find the word list on NAME THAT NUMBER (PART I) to be of value.
You might find the table on place value to be useful.

Some of the Integer Powers of Ten

This list extends infinitely at each end.

Examine the list, generalize or make an observation about a pattern or patterns you see, and record your observations below the list.

	1 quadrillion
	100 trillion
	10 trillion
	1 trillion
	100 billion
	10 billion
	1 billion
	100 million
	10 million
	1 million
	100 thousand
	10 thousand
	1 thousand
	1 hundred
	ten
	one
	1 tenth
	1 hundredth
	1 thousandth
	10-thousandth
	100-thousandth
	1 billionth

$Answer$

Please state your observations.

Writing 2, 3, 4 As Powers of Ten

Each number may be written as a power of ten.

The larger a number is, the larger the power of 10 required to represent it. THERE IS NO WAY WITHOUT KNOWLEGDE OF LOGS OR A CALCULTOR OR MATH TABLES FOR THE READER TO DETERMINE THE EXPONENTS LISTED BELOW. The reader of this page is not expected to study logs now!

	one
	two
	three
	four
	five
	six
	seven
	eight
	nine
	ten

$Answer$

Please state your observations.

Powers of e, the base of Natural Logs
e to- the- ln(number) is this number,

e^-1.609437912 is 	0.2
e^-1.203972804 is 	0.3
e^-0.916290732 is 	0.4
e^-0.693147181 is 	0.5
e^-0.510825624 is 	0.6
e^-0.356674944 is 	0.7
e^-0.223143551 is 	0.8
e^-0.105360516 is 	0.9
e^-0.010050336 is 	0.99

e⁰is 	1

e^0.693147181 is 	2
e^1.098612289 is 	3
e^1.386294361 is 	4
e^1.609437912 is 	5
e^1.791759469 is 	6
e^1.945910149 is 	7
e^2.079441542 is 	8
e^2.197224577 is 	9
e^2.302585093 is 	10
e^2.397895273 is 	11
e^2.48490665 is 	12

e^2.564949357 is 	13
e^2.63905733 is 	14
e^2.708050201 is 	15
e^2.772588722 is 	16
e^2.833213344 is 	17
e^2.890371758 is 	18
e^2.944438979 is 	19
e^2.995732274 is 	20
e^3.044522438 is 	21
e^3.091042453 is 	22
e^3.135494216 is 	23

e^3.17805383 is 	24
e^3.218875825 is 	25
e^3.258096538 is 	26
e^3.295836866 is 	27
e^3.33220451 is 	28
e^3.36729583 is 	29
e^3.401197382 is 	30
e^3.433987204 is 	31
e^3.465735903 is 	32
e^3.496507561 is 	33
e^3.526360525 is 	34

A Log Is An Exponent

Writing 2, 20, 200 As Powers of Ten

Using the integer powers of ten and the decimal or fractional powers of ten, any number may be written.

1. Please state your observations.

2. Use only the tables above and your observations to answer. Ten to what power is 20,000?

$Answer$

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MSH! Classes - Powers of Ten

A Log Is An Exponent

MATHEMATICAL CONCEPTS, inc.