5.1 Add and Subtract Large Number
Scientific Notation
Common Core Standards
8. EE.1 Know and apply the properties of integer exponents to generate
equivalent numerical expressions. For example, 32 × 3–5 = 3–3 = 1/33 = 1/27.
8.EE.4 Perform operations with numbers expressed in scientific notation,
including problems where both decimal and scientific notation are used.
Use scientific notation and choose units of appropriate size for
measurements of very large or very small quantities (e.g., use millimeters
per year for seafloor spreading). Interpret scientific notation that has been
generated by technology.
WARM-UP
1) Convert into standard or decimal form.
5.2 × 10
4
2) Convert into scientific notation.
604,000
Evaluate the expressions.
3)
604,000 + 52,000
4) 6.04 × 105 + 5.2 × 10 4
Add and Subtract Large Number
Scientific Notation
What are the rules for adding and
subtracting scientific notation?
(4 × 103 ) + (2 × 102 )
4,000 + 200 = 4,200 = 4.2 × 103
NOTES
The most straightforward way to add or subtract with
scientific notation is to convert each back to its
regular form.
Examples
Evaluate the expressions and write in scientific notation.
(7.5 × 101) + (2 × 102 )
3
2
(6.3 × 10 ) − (5 × 10 )
EXAMPLES
A scientist found 2 asteroids with masses of 4.06 x 108
and 2 x 107 kilograms. Find the total mass and write
your answer in scientific notation.
EXAMPLES
One elephant weighed 1.36 x 104 lbs and the other
weighed 9 x 103 lbs. Find the difference in the total
weights and write your answer in scientific notation.
NOTES
If the powers of ten are the same there is sometimes a
shortcut: Just add or subtract the decimals and keep
the power of ten.
Examples
Evaluate the expressions and write in scientific notation.
(4.5 × 10 4 ) + (2 × 10 4 )
(7.3 × 105 ) − (5.1× 105 )
EXAMPLES
A scientist found 2 asteroids with masses of 5.3 x 108
and 4 x 108 kilograms. Find the difference in their
masses and write your answer in scientific notation.
PRACTICE
Evaluate the expressions and write in scientific notation.
(8.4 × 105 ) − (7.1× 103 )
(9.16 × 103 ) + (2.5 × 10 4 )
EXAMPLES
Evaluate the expressions and write in scientific notation.
(9 × 105 ) − (7.4 × 105 )
FINAL QUESTION
One elephant weighed 1.06 x 104 lbs and the other
weighed 7.5 x 103 lbs. Find the total weight and write
your answer in scientific notation.