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Standard Form

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Standard Form

What is standard form. (scientific notation)
Writing large and small numbers in standard form
Converting between a 'normal number' and 'standard form'
Using a calculator for standard form (using EXP)

Rounding numbers in standard form

Khan Video Tutorial: Video 1 | Video 2 | Video 3 | Examples

Activity
Standard form to normal numbers (www.transum.org)
And normal to standard form

Class notes | pdf

Standard Form Conversions
p376 Ex 26.01 p66, Ex 5.01

Standard Form Calculations
p380 Ex 26.02 p69, Ex 5.02

Word problems p70, Ex 5.03

Scale of the Universe
Scale of the universe2 link to http://scaleofuniverse.com

You tube Powers of ten

NuLake p8,9,10

 

 

Big & Small Numbers

In the metric system there are standard ways of talking about big and small numbers. "kilo" for a thousand, "mega" for a million, and so on. See the chart below.

For example, if a long rope measures one thousand meters, it is easier to say it is a kilometer long, and even easier to write it down as km.

 

 

Example 2: if we weigh something on a set of scales and it shows 2,000 grams, we can call that 2 kilograms, or even 2 kg.

 

Example 3: If the doctor wants you to take 5 thousandths of a litre of medicine (thousandth=one thousand times smaller), he is more likely to say "take 5 milliliters", or write it down as 5ml.

In that example we used kilo as a prefix to the word meter,
and we used k as a symbol for kilo in front of m as the symbol for
meter.

 

Common Big and Small Numbers

Name
The Number Prefix Symbol
trillion
1,000,000,000,000
tera T
billion
1,000,000,000
giga G
million
1,000,000
mega M
thousand
1,000
kilo k
hundred
100
hecto h
ten
10
deka da
unit
1
   
tenth
0.1 deci d
hundredth
0.01 centi c
thousandth
0.001 milli m
millionth
0.000 001 micro µ
billionth
0.000 000 000 001 nano n
trillionth
0.000 000 000 000 001 pico p

 

Some Very Big, and Very Small Numbers

Name
The Number Prefix Symbol
 
Very Big !    
septillion
1,000,000,000,000,000,000,000,000
yotta Y
sextillion
1,000,000,000,000,000,000,000
zetta Z
quintillion
1,000,000,000,000,000,000
exa E
quadrillion
1,000,000,000,000,000
peta P
  Very Small !    
quadrillionth
0.000 000 000 000 001 femto f
quintillionth
0.000 000 000 000 000 001 atto a
sextillionth
0.000 000 000 000 000 000 001 zepto z
septillionth
0.000 000 000 000 000 000 000 001 yocto y

Big Numbers We Have Named

Name
As a Power of 10
As a Decimal
Thousand
103

1,000

Million
106

1,000,000

Billion
109

1,000,000,000

Trillion
1012

1,000,000,000,000

Quadrillion
1015

etc ...

Quintillion
1018
 
Sextillion
1021
 
Septillion
1024
 
Octillion
1027
 
Nonillion
1030
 
Decillion
1033
 
Undecillion
1036
 
Duodecillion
1039
 
Tredecillion
1042
 
Quattuordecillion
1045
 
Quindecillion
1048
 
Sexdecillion
1051
 
Septemdecillion
1054
 
Octodecillion
1057
 
Novemdecillion
1060
 
Vigintillion
1063
 

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Small Numbers We Have Named

Name
As a Power of 10
As a Decimal
thousandths
10-3

0.001

millionths
10-6

0.000 001

billionths
10-9

0.000 000 001

trillionths
10-12

etc ...

quadrillionths
10-15
 
quintillionths
10-18
 
sextillionths
10-21
 
septillionths
10-24
 
octillionths
10-27
 
nonillionths
10-30
 
decillionths
10-33
 
undecillionths
10-36
 
duodecillionths
10-39
 
tredecillionths
10-42
 
quattuordecillionths
10-45
 
quindecillionths
10-48
 
sexdecillionths
10-51
 
septemdecillionths
10-54
 
octodecillionths
10-57
 
novemdecillionths
10-60
 
vigintillionths
10-63
 

 

The Powers of 10

Link to  http://micro.magnet.fsu.edu/primer/java/scienceopticsu/powersof10/

Standard Form

Standard form is a simple way of writing very large or very small numbers without having to include all the zero placeholders.
Standard form is also called scientific notation, (used in science, especially physics)

eg 420 000 000 km

4.2 x 108 km

eg 254 80 000 000 000 m

2.548 x 1013 m

eg 18 040 000 000

1.804 x 1010

eg 0.000 00048 m

4.8 x 10-7m

eg 0.000 000 005 46 m

5.46 x 10-9m

eg 0.0001

1 x 10-4

eg 10 000 000

1 x 107

Note: Decimal place is ONE digit from the start of the number in standard form
Large numbers have a positive power
Small numbers have a negative power

 

 

Converting to standard form

eg convert 5 240 000 000 into standard form

 

 

steps

5.240 000 000

Move the decimal to be 1 digit from the start of the number

5.240 000 000 (9 places)

Count the number of places the decimal point was moved

5.24

Remove the zero place holders

5.24 x 109

The number of places the decimal was moved becomes the power on the ten (positive because a large number)

 

 

 

 

eg convert 0.0000083 into standard form

 

 

steps

0.000008.3

Move the decimal to be 1 digit from the start of the number (ignore zero place holders)

0.000008.3 (6 places)

Count the number of places the decimal point was moved

8.3

Remove the zero place holders

8.3 x 10-6

The number of places the decimal was moved becomes the power on the ten (Negative because a small number)

   

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Using a Calculator

The EXP calculator stands for 'times 10 to the power'

eg to enter 5.24 x 106 type in 5.24 EXP 6 (note do not enter 'x')

Or enter using the power function: 5.24 x 10 6

Check you get 5 240 000

 

 

 

Do these calculations
(give answers in standard form)

Mouse over below to check answers

1) 4.2 x 106   x   5.1 x 1012
2.142 x 1019
2) (9.23 x 1018)   ÷  (2.1 x 104)
4.395 x 1014 (3sf)
3) (5.3 x 106)10
1.75 x 1067 (3sf)
4) 9.2 x 106   ÷    3.56 x 10-5
2.58 x 1011 (3sf)
5) 3.8845 x 10126   x   5.1 x 1041 (a tricky one)
1.98 x 10168 (3sf)
Ignore the power of 100, do the calculation then add 100 onto the power

 

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