Download Wksht - Sci Notation

Name __________________________ Period ______
Scientific Notation
Scientists often deal with very small and very large numbers, which can lead to a lot of confusion
when counting zeros! We have learned a way to express these numbers as powers of 10 in order to
decrease their size when written.
Scientific notation takes the form shown here:
n
M x 10
In this example “M” is always a single digit number (not zero!) and “n” represents the number of decimal
places that were moved.
Example 1: Convert 1,500,000. to scientific notation.
- Move the decimal point 6 spaces to the left so it is between
the 1 and 5 to get…
6
o 1.5 x 10 (positive exponent!)
Example 2: Convert 0.00025 to scientific notation.
- Move the decimal 4 places to the right so it is between the
2 and the 5 to get…
-4
o 2.5 x 10 (negative exponent!)
Convert the following to scientific notation:
1) 0.005
_____________________
6) 0.25
_____________________
2) 5,050
_____________________
7) 0.025
_____________________
3) 0.0008
_____________________
8) 0.0025
_____________________
4) 1,000
_____________________
9) 500
_____________________
5) 1,000,000
_____________________
10) 5,000
_____________________
Convert the following to standard notation:
3
1) 1.5 x 10
_____________________
6) 0.25
_____________________
2) 5,050
_____________________
7) 0.025
_____________________
3) 0.0008
_____________________
8) 0.0025
_____________________
4) 1,000
_____________________
9) 500
_____________________
5) 1,000,000
_____________________
10) 5,000
_____________________
Calculations Using Significant Figures
When multiplying numbers in scientific notation, multiply the first part of the number (mantissa)
and add the exponents:
2
6
Example 1: (3.0 x 10 ) x (2.5 x 10 )
- Multiply 3.0 x 2.5 = 7.5
- Add 2 + 6 = 8
-
8
Answer = 7.5 x 10
When dividing numbers in scientific notation, divide the first part of the number and subtract exponents.
6
2
Example 2: (9.0 x 10 ) / (4.5 x 10 )
- Divide 9.0 / 4.5 = 2.0
- Subtract 6 - 2 = 4
-
4
Answer = 2.0 x 10
Perform the following calculations and show all answers in scientific notation!
3
5
6) (4 x 10 ) / (1 x 10 )
8
6
7) (7.6 x 10 ) x (8.2 x 10 )
1) (1.5 x 10 ) x (3.5 x 10 )
2) (2.0 x 10 ) x (2.0 x 10 )
5
-3
-3
6
2
8) (8.5 x 10 ) / (2.5 x 10 )
4
3
9) (7.0 x 10 ) x (7.0 x 10 )
3) (6.2 x 10 ) / (3.1 x 10 )
4) (5.0 x 10 ) / (2.5 x 10 )
7
-5
5) (6.8 x 10 ) x (2.2 x 10 )
-8
-4
11
-5
-3
-11
-9
10) (1.3 x 10 ) / (2.6 x 10 )