Transcript Adding and Subtracting Numbers in Scientific Notation

Adding and Subtracting
Numbers in Scientific Notation
January 2, 2014
When adding or
subtracting numbers
in scientific
notation, the
exponents must be
the same.
Adding/Subtracting when
Exponents are THE SAME
Step 1 - add/subtract the decimal
Step 2 – Bring down the given exponent
on the 10
Example 1
(2.56 X 103) + (6.964 X 103)
Step 1 - Add:
2.56 + 6.964 =
9.524
Step 2 – Bring down exponent :
9.524 x 103
Example 2
(9.49 X 105) – (4.863 X 105)
Step 1 - Subtract:
9.49 – 4.863 =
4.627
Step 2 – Bring down exponent:
4.627 x 105
Adding/Subtracting when
the Exponents are
DIFFERENT
• When adding or subtracting numbers
in scientific notation, the exponents
must be the same.
• If they are different, you must move
the decimal so that they will have the
same exponent.
Moving the Decimal
It does not matter which number you
decide to move the decimal on, but
remember that in the end both
numbers have to have the same
exponent on the 10.
Adding/Subtracting when the
Exponents are DIFFERENT
Step 1 – Rewrite so the exponents are the
same
Step 2 - add/subtract the decimal
Step 3 – Bring down the given exponent on
the 10
Example 3
(2.46 X 106) + (3.4 X 103)
Step 1 – Rewrite with the same exponents
3.4 X 103 
0.0034 X 103+3
New Problem: (2.46 X 106) + (0.0034 X 106)
Step 2 – Add decimals
2.46 + 0.0034 =
2.4634
Step 3 – Bring Down Exponents
2.4634 X 106
Example 4
(5.762 X 103) – (2.65 X 10-1)
Step 1 – Rewrite with the same exponents
2.65 X 10-1 
0.000265 X 10(-1+4)
New Problem : (5.762 X 103) – (0.000265 X 103)
Step 2 – Subtract Decimals
5.762 – 0.000265 =
5.762
Step 3 – Bring down decimals
5.762 X 103
Practice
1) (3.45 x 103) + (6.11 x 103)
2) (4.23 x 103) – (9.56 x 102)
1) (4.12 x 106) + (3.94 x 104)
1) (8.96 x 107) – (3.41 x 107)