8.4 Use Scientific Notation

5SE 3CIENTIFIC .OTATION
'OAL
9OUR .OTES
+ 2EAD AND WRITE NUMBERS IN SCIENTIFIC NOTATION
6/#!"5,!29
3CIENTIFIC NOTATION ʘՓLiÀʈÃÊÜÀˆÌÌi˜Êˆ˜ÊÃVˆi˜ÌˆvˆVÊ
˜œÌ>̈œ˜Ê܅i˜ÊˆÌʈÃʜvÊ̅iÊvœÀ“Ê VÊÊ£ä˜Ê܅iÀiÊÊ
£Êγ ÊVʐʣäÊ>˜`ʘʈÃÊ>˜Êˆ˜Ìi}iÀ°
3#)%.4)&)# ./4!4)/.
! NUMBER IS WRITTEN IN SCIENTIFIC NOTATION WHEN IT IS
OF THE FORM Ê VÊÊ£ä˜Ê WHERE γ C AND N IS AN
INTEGER
.UMBER
3TANDARD FORM
3CIENTIFIC NOTATION
3IXTEEN MILLION
Ê £È]äää]äääÊ
Ê £°ÈÊÊ£äÇÊ
4WO HUNDREDTHS
Ê Ê Ê ÊÊÊä°äÓÊÊÊÊÊ Ê Ê
Ê ÓÊÊ£äÓÊ
%XAMPLE A Ê Ç°nÓÊ Ê ÈÊ
-OVE DECIMAL POINT Ê ÈÊ
PLACES TO THE Ê ÊÊÊʏivÌÊÊÊÊÊ %XPONENT IS Ê ÊÊÊÊÈÊÊÊÊÊ B Ê {°ä£Ê Ê ÎÊ
-OVE DECIMAL POINT Ê ÎÊ
PLACES TO THE Ê Àˆ}…ÌÊ %XPONENT IS Ê ÎÊ %XAMPLE 7RITE NUMBERS IN SCIENTIFIC NOTATION
7RITE NUMBERS IN STANDARD FORM
A Ê Î]n™™]äää]äääÊ
%XPONENT IS Ê ÊÊÊʙÊÊÊÊÊ -OVE DECIMAL POINT
Ê ™Ê PLACES TO THE
Ê Àˆ}…ÌÊ B Ê ä°ääää™ä™ÇÊ
%XPONENT IS Ê xÊ -OVE DECIMAL POINT
Ê xÊ PLACES TO THE
Ê ÊÊÊʏivÌÊÊÊÊÊ ,ESSON s !LGEBRA .OTETAKING 'UIDE
#OPYRIGHT Ú -C$OUGAL ,ITTELL(OUGHTON -IFFLIN #OMPANY
9OUR .OTES
#HECKPOINT #OMPLETE THE FOLLOWING EXERCISE
7RITE THE NUMBER IN SCIENTIFIC NOTATION 4HEN
WRITE THE NUMBER IN STANDARD FORM
n°™™ÊÊ£äÓÆÊÈä]ää£]äää
%XAMPLE /RDER NUMBERS IN SCIENTIFIC NOTATION
/RDER AND FROM LEAST
TO GREATEST
3OLUTION
3TEP 7RITE EACH NUMBER IN SCIENTIFIC NOTATION IF
NECESSARY
Ê {ÊÊ£ä{Ê
3TEP /RDER THE NUMBERS &IRST ORDER THE NUMBERS WITH
DIFFERENT POWERS OF 4HEN ORDER THE NUMBERS
WITH THE SAME POWER OF "ECAUSE Ê Ê YOU KNOW THAT
Ê Ó°nÊÊ£äxÊ IS LESS THAN BOTH Ê Î°ÓÊÊ£ä{Ê AND
Ê {ÊÊ£ä{Ê "ECAUSE Ê Ê YOU KNOW THAT
Ê Î°ÓÊÊ£ä{Ê IS LESS THAN Ê {ÊÊ£ä{Ê 3O Ê Ó°nÊÊ£äxÊ Ê Î°ÓÊÊ£ä{Ê Ê {ÊÊ£ä{Ê 3TEP 7RITE THE ORIGINAL NUMBERS IN ORDER FROM LEAST
TO GREATEST
Ê Ó°nÊÊ£äxÆÊΰÓÊÊ£ä{ÆÊä°äää{Ê
#HECKPOINT #OMPLETE THE FOLLOWING EXERCISE
/RDER AND FROM
LEAST TO GREATEST
£°ÇxÊÊ£äxÆÊÓÓx]äääÆÊ£]Ç{ä]äää
#OPYRIGHT Ú -C$OUGAL ,ITTELL(OUGHTON -IFFLIN #OMPANY
,ESSON s !LGEBRA .OTETAKING 'UIDE
9OUR .OTES
%XAMPLE #OMPUTE WITH NUMBERS IN SCIENTIFIC NOTATION
%VALUATE THE EXPRESSION 7RITE YOUR ANSWER IN SCIENTIFIC
NOTATION
A ­ ®­ ®
+ ­ + ®Ê
Ê#OMMUTATIVE PROPERTY
Ê Ç°n{Ê Ê £ä™Ê
0RODUCT OF POWERS
PROPERTY
AND ASSOCIATIVE
PROPERTY
B ­ ®
z
Ê Î°ÓÎÊ Ê ­£äÓ®ÎÊ
0OWER OF A PRODUCT
PROPERTY
Ê ÎÓ°ÇÈnÊ Ê £äÈÊ
0OWER OF A POWER
PROPERTY
­Ê ΰÓÇÈnÊÊ£ä£Ê ® Ê £äÈÊ
7RITE Ê ÎÓ°ÇÈnÊ IN
SCIENTIFIC NOTATION
Ê Î°ÓÇÈnÊ ­Ê £ä£ÊÊ£äÈÊ ®
!SSOCIATIVE PROPERTY
Ê Î°ÓÇÈnÊÊ£äÇÊ
0RODUCT OF POWERS
PROPERTY
]z ]
z
z
C ]]
Ê ÓÊ Ê £äÓÊ
0RODUCT RULE FOR
FRACTIONS
1UOTIENT OF POWERS
PROPERTY
#HECKPOINT 3IMPLIFY THE EXPRESSION
­ ®
(OMEWORK
{°ä{ä£ÊÊ£ä£{Ê
,ESSON s !LGEBRA .OTETAKING 'UIDE
]
z
Ê nÊÊ£ä£
#OPYRIGHT Ú -C$OUGAL ,ITTELL(OUGHTON -IFFLIN #OMPANY