scientific notation as a way scientists condense very large or small figures

It shows Scientific notation

1. Designed by Peter Taremwa, Kabojja International High School
Scientific Notation

2. How wide is our universe?
210,000,000,000,000,000,000,000 miles
(210 sextillion miles)
Scientists work with such large numbers
and often need a way to shorten them.

3. •Scientific Notation provides this
shortened form
And is generally written in the form
a x 10
n
where a is between 1 and 10
and n is an integer

4. Example 1. Writing the width of the
universe in scientific notation.
210,000,000,000,000,000,000,000 miles
We ask the questions
1. Where is the decimal point now?
After the last zero.
2. Where would you put the decimal to make this
number be between 1 and 10?
Between the 2 and 1 (this gives us a )

5. 3. How many decimal places did you
move the decimal?
2.10,000,000,000,000,000,000,000.
23 places (therefore n=23)
Since the original number is more than 1, the
power(n) is positive.
The scientific notation is
2.1 x 10
23

6. Example 2. Express 0.0000000902 in
scientific notation.
1. Where would the decimal go to make the
number be between 1 and 10?
a = 9.02
2. The decimal was moved how many places to
reach 9?
n = 8 places
Since the original number is less than 1, n is
negative.
9.02 x 10
-8

7. Questions:
1.Write the following numbers in scientific
notation
a.28750.9
b.0.00018
c.4,580,000
d.0.0028125

8. Expressing numbers in full form or
decimal form
a.1.6 x 10
-5
in decimal notation.
For -n, n is the number of zeros before the
non zero digits in the number
0.000016 (5 zeros)
b. Express 4.798 x 10
-2
in full notation
/decimal notation.
0.04798

9. b. Express 4.798 x 10
6
in full
notation /decimal notation.
For +n, n is the number of decimal
places after before the decimal point
0.000016 (5 zeros)
this gives
4,798,000

10. Bonus
Write in PROPER scientific notation.
(Notice the number is not between 1 and 10)

1) 234.6 x 10
9
2) 0.0642 x 10
4