The document discusses scientific notation and operations involving numbers written in scientific notation. It explains that for addition or subtraction, the exponents must be the same. If exponents are different, the decimal must be moved in one number so that the exponents match before performing the operation. Examples are provided for adding and subtracting numbers with the same and different exponents, demonstrating the steps to obtain the final answer in proper scientific notation form.

1. OPERATIONS OF SCIENTIFIC
NOTATION

3. The coefficient must be greater than 1 and
less than 10 and contain all the significant
(non-zero) digits in the number
•12.5 × 106 is not in proper scientific notation, since the
coefficient is greater than 10.
•Neither is 0.125 × 107, since the coefficient is less than 1.

4. The base is always 10.
The exponent is the number of places the decimal
was moved to obtain the coefficient.

5. When adding or
subtracting numbers in
scientific notation, where
the exponents must be
the same.
Step 1 - add/subtract the decimal
Step 2 – Bring down the given exponent
on the 10

6. 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

7. TRY THIS:
The sum of 5.6 x 10
3
and
2.4 x 10
3
is:
A 8.0 x 10
3
B 8.0 x 10
6
C 8.0 x 10
-3
D 8.53 x 10
3
4.86 x 103 – 4.72 x
103
Subtract this:
Answer:
= 1.4 x 102

8. 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

9. 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.
MOVING THE DECIMAL
Step 1 – Rewrite so the exponents are the
same
Step 2 - add/subtract the decimal
Step 3 – Bring down the given exponent

10. Adding With Different
Exponents
• (4.12 x 106) + (3.94 x 104)
• (412 x 104) + (3.94 x 104)
• 412 + 3.94 = 415.94
• 415.94 x 104
• Express in proper form:
4.15 x 106
Subtracting With
Different Exponents
• (4.23 x 103) – (9.56 x 102)
• (42.3 x 102) – (9.56 x 102)
• 42.3 – 9.56 = 32.74
• 32.74 x 102
• Express in proper form:
3.27 x 103

11. A
B
C
D
7.8 x 10
5
minus 3.5 x 10
4
is
7.45 x 10
5
4.3 x 10
4
4.3 x 10
6
4.3 x 10
10
3.6 x 105 + 2.7 x 104
Add this:
= 3.87 x 105

12. ADDING AND
SUBTRACTING…
•The important thing to remember about
adding or subtracting is that the exponents
must be the same!
If the exponents are not the same then it is
necessary to change one of the numbers
so that both numbers have the same
exponential value.

13. 1)(3.45 x 103) + (6.11 x 103)
2)(4.12 x 106) + (3.94 x 104)
1)(8.96 x 107) – (3.41 x 107)
2)(2.9785 x 10-8) – (5.72x 10-10)