scientific notation - Joplin Pre

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Transcript scientific notation - Joplin Pre

SCIENTIFIC
NOTATION
Unit 3
Objective 7
WARM UP
Try to quickly tell which number is larger:
8567000000000 or 35460000000000
WARM UP
Try to quickly tell which number is larger:
0.00000000291 or 0.00000001834
SCIENTIFIC NOTATION – WHY???

Often, the sizes of numbers become so large or small
that it becomes tedious to write out all the zeroes, and
it is difficult to quickly judge the size of the number.
Scientific notation helps overcome these problems!
PARTS OF SCIENTIFIC NOTATION
A number correctly written in scientific notation has two
components:

A coefficient that is multiplied in front of the power of
ten. The coefficient must be greater than or equal to 1
and less than 10.

A power of 10 with an integer exponent.
PARTS OF SCIENTIFIC NOTATION
integer
exponent
M 10
coefficient
n
power of 10
EXAMINE THIS!
WHICH ARE CORRECTLY WRITTEN IN SCIENTIFIC NOTATION?

The earth is approximate 93,000,000 miles
from the sun. What is the distance in scientific
notation?
A.
9.3 x 106
B.
93 x 106
C.
.93 x 108
D.
9.3 x 107
SCIENTIFIC NOTATION!
COEFFICIENT GREATER THAN 10
COEFFICIENT LESS THAN 1
SCIENTIFIC NOTATION!
PART A:
REWRITING LARGE NUMBERS (POSITIVE EXPONENT)
PRACTICE
1.) 1.56 x 104
PART A:
REWRITING LARGE NUMBERS (POSITIVE EXPONENT)
PRACTICE
2.) 3.721 x 109
PART A:
REWRITING LARGE NUMBERS (POSITIVE EXPONENT)
PRACTICE
3.) 8 x 107
PART B:
REWRITING SMALL NUMBERS (NEGATIVE EXPONENT)
PRACTICE
1.) 4 x 10-3
PART B:
REWRITING SMALL NUMBERS (NEGATIVE EXPONENT)
PRACTICE
2.) 5.981 x 10-10
PART B:
REWRITING SMALL NUMBERS (NEGATIVE EXPONENT)
PRACTICE
3.) 3.8 x 10-5
POWERS OF TEN
 Each
time you move the decimal point in a number, you are
multiplying or dividing by ten – depending on the direction
you move the decimal point.
 Each
time you move the decimal point to the RIGHT, you are
multiplying the coefficient by 10.
 Each
time you move decimal point to the LEFT, you are
dividing the coefficient by 10.
Convert the following to scientific notation.
1) 120,400
5) .2
9) 56,000,000
2) 11,110,000
6) .45013
10) .00026
3) 230
7) 14,100,000
11) .000000698
4) 5601
8) .089
12) .0012