Converting to Scientific Notation Step – by – Step
Lets try the numbers 2346000000000 and 0.00003242
1. Locate the Decimal point in your number:
1st one is 2346000000000.
(Circle the Decimal point)
2nd one is 0.00003242
2. Move the decimal either left or right so the number becomes greater then 1, but
less then 10. (When you are done moving the decimal there should be one non-zero
number in front of the decimal.)
1st one is now 2.346
2nd one is now 3.242
3. Place a X 10 to the right of the number.
1st one is now 2.346 X 10
2nd one is now 3.242 X 10
4. Count the number of places the decimal moved.
1st one moved 12 places left.
2nd one moved 5 places right.
5. Put this number as an exponent on the X 10.
1st one is now 2.346 x 1012
2nd one is now 3.242 x 105
6. Check to see if the exponent should be positive (+) or negative (-).
If the number got smaller when you moved the decimal, then make the exponent larger
(or positive) to compensate.
ie. 1st one was 2346000000000 and became 2.346. Since it got smaller, the power has to
be positive to compensate for the smaller number.
2346000000000 = 2.346 x 1012
If the number got larger when you moved the decimal, then make the exponent smaller
(or negative) to compensate.
ie. 2nd one was 0.00003242 and became 3.242 which is larger. Since it got larger, the
power has to become a negative to compensate.
0.00003242 = 3.242 x 10-5
Another way to remember the rule is:
Move the decimal left = positive exponent.
Move the decimal right = negative exponent.
Practice for Scientific Notation
Convert the following numbers to scientific notation.
1.
a) 56349
2.
a) 0.000000454
b) 2300
b) 0.0002300
c) 120.5600
c) 0.001001
d) 17.0009
d) 0.0973
e) 10
e) 0.08
f) 7.3
f) 0.2300740
Convert the following to regular numbers.
3
a) 1.45 * 102
4
a) 2.44 * 10-3
b) 3.88 * 103
b) 3.66 * 10-1
c) 2.77 * 1014
c) 7.700 * 10-8
d) 7.2001 * 106
d) 8 * 10-12
e) 9.900 * 104
e) 4.000 * 10-2
f) 1 * 1015
f) 1.01 * 10-6