Understanding Very Large Numbers and Very Small

When we consider the estimated

200,000,000,000 (200 billion)

stars in the Milky Way Galaxy

estimated 100,000,000,000,000 (100 trillion) cellsin the adult human body

We are forced to use numbers so large we cannot comprehend their meaning.

Let’s try to use our imaginations to place some of these large numbers in perspective.

We will use money as a teaching tool to illustrate the magnitude of large numbers. Whether you stack it, spread it, line it up,

or spend it, we hope you’ll think of money and large numbers in a

new way

Money Stacks

The thickness of a single one dollar bills measures .0043 inches or .0000000679 miles.

The height of a stack of 100 one dollar bills measures .43 inches.

The height of a stack of 1,000 one dollar bills measures 4.3 inches.

The height of a stack of 1,000,000 one dollar bills measures 4,300 inches or 358 feet – about the height of a 30 to 35 story

building.

The height of a stack of 100,000,000 (one hundred million) one dollar bills measures 35,851 feet or 6.79 miles.

This would reach from the earth’s surface to the approximate altitude at which

commercial jetliners fly

1,000,000,000

The height of a stack of 1,000,000,000 (one billion) one dollar bills measures 358,510 feet or 67.9 miles.

This would reach from the earth’s surface into the lower portion of the troposphere – one of the major outer layers of earth’s atmosphere.

The height of a stack of 100,000,000,000 (one hundred billion) one dollar bills measures6,786.6 miles.

A column of bills this high would extend 28 times higher than the orbiting International Space Station.

The height of a stack of 100,000,000,000,000 (one hundred trillion) one dollar bills measures

6,786,616 miles. This would reach from the earth to the moon and back????times.

14

Money Lines

The length of a single one dollar bills measures 6.14 inches.

The length of 100 one dollar bills laid end-to-end measures 614 inches or 51.17 feet.

The length of 1,000 one dollar bills laid end-to-end measures 512 feet. This would approximate the length of some of the longer homerun balls hit by professional baseball players. (The world record for the longest homerun, estimated at 643 feet,

was set in 1961 by Mickey Mantle.)

The length of 1,000,000 (one million) one dollar bills laid end-to-end extends 96.9 miles. This would easily traverse the 21 miles across the English Channel from the shores of England to the shores of France and back more than two and a half times.

The length of 100,000,000 (one hundred million) one dollar bills laid end-to-end measures 9,690 miles. This would reach from Washington D.C., USA to Sydney, Australia.

The length of 100,000,000,000 (one hundred billion) one dollar bills laid end-to-end measures 9,690,656 miles. This would extend around the earth ???????? times.

387

The length of 100,000,000,000,000 (one hundred trillion) one dollar bills laid end-to-end measures 9,690,656,566 miles.

This would reach from the earth to the planet Saturn and back six times. (Assuming Saturn at its nearest point to earth)

Duration of Shopping SpreesWhile Spending $20 per SecondStarting Amount

(Dollars) Duration of Shopping Spree

1 1 second

100 5 seconds

1,000 50 seconds

10,000 500 seconds

100,000 5000 seconds or 1 hour, 23 minutes

1,000,000 500,000 or 13 hours ,48 minutes

10,000,000 5,000,000 or 138 hours, ( 5days , 19 hours)

100,000,000 50,000,000 or 57 days, 21 hours

1,000,000,000 500,000,000 or 578 days ( 1 year, 214 days)

1,000,000,000,000 500,000,000,000 or 1, 585 years

How many times has your heart beat in your life?

Average person heart beats 72

beats per minutes…..

72 x 60 x 24 x 365 x your agebpm x min x hr x days x year

72 x 60 x 24 x 365 x 491854316800

529804800

Now …. Very small numbers

Cut in half….

How small will the slice get?

Cut 1 14 cm 5.5 in Size of child’s hand

Cut 2 7 cm 2.75 in Fingers, ears,toes

Cut 3 3.5 cm 1.38 in Mushroom, eye

Cut 4 1.75 cm .69 in Keys, rings insects

Cut 6 .44 cm .17 in Poppy seed

Cut 8 1mm .04 in Thread

Cut 10 .25mm .01 in

Cut 12 .06mm .002 in Human hair

Cut 14 .015 mm .006 in Width of paper

Cut 18 1 micron .0004 in Bacteria

Cut 19 .5 micron .000018 in Visible light waves

Cut 31 .0001 micron .0000000045 in

A strip of paper 28 cm long

The Size of an Atom!!!

Why Scientific Notation?

Scientific notation is needed any time you need to express a number that is

very big or very small.

Suppose for example you wanted to figure out how many drops of water were in a river 12 km long, 270 m wide, and 38 m deep(assuming one drop is one millilitre).

There is a more compact and meaningful to write the answer  than to write 123120000000000 called scientific notation.

123120000000000

What is Scientific Notation?

SCIENTIFIC NOTATION A NUMBER IS WRITTEN IN

SCIENTIFIC NOTATION IFIT IS OF THE FORM C X 10N,

WHERE 1 ≤ C < 10 AND N IS ANINTEGER.

Who created scientific notation?

Scientific notation was not "created",in the sense of someone coming up with something new.

The fact that  3 X 104  happens to equal 30000 is a mathematical truth, not a creation.

Today we are going to learn to change a number from decimal notation to scientific notation.

And we are going to learn to change a number from scientific notation to decimal notation.