Transcript Adding and Subtracting Numbers in Scientific Notation

Adding and Subtracting
Numbers in Scientific Notation
Adding/Subtracting when
Exponents are Equal
• When the exponents are the same:
easy peasy:
• just add/subtract the numbers then
carry the base 10 and the exponent
through.
If the Exponents are the
same:
When adding
2.46 X
103 +
3.476 X
103
or subtracting
numbers in
scientific
notation, the
exponents must
be the same.
2.46 X 103 + 3.476 X 103
2.46 + 3.476 X 103
Then just rearrange
the numbers and carry
through the Power of
10
Example 1
2.56 X 103 + 6.964 X 103
Given: 2.56 X 103 + 6.964 X 103
2.56 + 6.964 = 9.524
Answer: 9.524 X 103
Example 2
9.49 X 105 – 4.863 X 105
Given: 9.49 X 105 – 4.863 X 105
Subtract: 9.49 – 4.863 = 4.627
Answer: 4.627 X 105
Adding/Subtracting when
the Exponents are
Different
If the Exponents are
different:
1. Turn the expression into Standard
Notation
2. Calculate
3. Turn the result back into Scientific
Notation
Example 1
Given: 2.46 X 106 + 3.476 X 103
Turn problem into Standard Notation:
2.46 X 106 = 2,460,000
3.476 X 103 = 3,476
Calculate:
2,460,000 + 3,476 = 2,463,476
Turn answer into Scientific Notation:
2.463476 X 106
Example 2
• Given: 5.762 X 103 – 2.65 X 10-1
• Turn problem into Standard Notation:
5.762 X 103 = 5,762
2.65 X 10-1 = .265
• Calculate:
5,762 - .265 = 5761.735
• Turn answer into Scientific Notation:
5.761735 X 103
Need a Challenge??
(You can skip this part if
you want and do the
problems at the end)
• When adding or subtracting numbers
in scientific notation, the exponents
must be the same.
• Therefore…………
• If they are different, you must move
the decimal either right or left so
that they will have the same
exponent.
Need a Challenge??
…continued
It does not matter which number you
use to change the exponent, but
remember that before you can do the
calculation, both Powers of 10 have to
have the same exponent on the 10.
Need a Challenge??
…continued
Remember!!!
• For each move of the decimal
to the right,
you have to add -1 to the exponent.
0.3 X 103 = 3.0 X 102
• For each move of the decimal
to the left,
you have to add +1 to the exponent.
0.3 X 103 = 0.03 X 104
Same
problem
as
before!
Need a Challenge??
…continued
Given: 5.762 X 103 – 2.65 X 10-1
Shift decimal 4
places to the
left for 10-1 to
become 103.
Exponents
don’t match!
.000265 X 10(-1+4)
Subtract: 5.762 X 103- .000265 X 103
5.762 - .000265 X 103
Answer: 5.761735 X 103
Same
problem
as
before!
Need a Challenge??
…continued
Given: 2.46 X 106 + 3.476 X 103
Shift decimal 3
places to the
left for 106.
.
.003476 X 103+3
Add: 2.46 X 106 + .003476 X 106
Answer: 2.463476 X 106
Try a
new
problem!
Need a Challenge??
…continued
Given: 7.4 X 102 + 2.735 X 106
.00074 X 10(2+4)
Shift decimal 4
places to the
left for 106.
.
Add: .00074 X 106 + 2.735 X 106
.00074 + 2.735 X 106
Answer: 2.73574 X 106
Practice Worksheet
(solve using either method)
1.
2.
3.
4.
2 × 103 + 3.6 × 104 = 3.8 x 104
7 × 105 – 5.2 × 104 = 6.48 x 105
3.4 x 102 + 4.57 x 103 = 4.91 x 103
8.41 x 10-5 – 7.9 x 10-6 = 7.62 x 10-5