Name:_________ANSWER KEY_________________________ Date: ________________________ Period: _________
Scientific Notation & Multiplication
Remember that your answer should be
expressed in two parts, as in the model
to the right. The first part should be a
number less than 10 (eg: 2) and the
second part should be a power of 10
(eg: 102). If the first part is a number
greater than ten, you will have to convert
the first part. For extra practice, convert
your answer to standard form (long
form). In the above example, the
standard form answer would be 800,000.
Scientific notation
Standard form
1. (1 x 103) x (3 x 101) =
______3 x 104________
_______30000_________
2. (3.5 x 104) x (2 x 103) =
______7 x 107_________
______70000000_______
3. (2.46 x 105) x (4.2 x 10-3) =
______1.0 x 103_______
_______1000__________
4. (5.3 x 10-4) x (8.31 x 10-2) =
_______4.4 x 10-5_____
_______0.000044_______
Scientific Notation & Division
Subtract the 2nd exponent from the 1st
Divide the 1st number by the 2nd
(a little harder -we basically solve the problem as we did above, using multiplication. But we need to
"move" the bottom (denominator) to the top of the fraction. We do this by writing the negative value of
the exponent. Next divide the first part of each number. Finally, add the exponents).
Scientific notation
Standard form
5. (8 x 106) / (3 x 103) =
_______3 x 103________
________3000_________
6. (2 x 109) / (5.1 x 105) =
_______4 x 103_________
_______4000_________
7. (1.33 x 105) / (7.1 x 10-3) =
_______1.9 x 107_______
______19,000,000______
8. (4.7 x 10-4) / (9.25 x 10-2) =
________5.1 x 10-3_______
_______0.0051_________
Scientific Notation & Addition
The first step is to make sure the exponents are the same. We do this by changing the main number
(making it bigger or smaller) so that the exponent can change (get bigger or smaller). Then we can
add the main numbers and keep the exponents the same.
Scientific notation
Standard form
9. (3 x 106) + (4 x 104) =
______3 x 106__________
_______3,000,000______
10. (6.5 x 105) + (5.3 x 107) =
______5.4 x 107________
______54,000,000______
11. (1.3 x 101) + (2.1 x 10-3) =
______1.3 x 101_________
______13_____________
12. (2.7 x 10-3) + (7.65 x 10-2) =
_______7.9 x 10-2________
______0.079________
Scientific Notation & Subtraction
Just like addition, the first step is to make the exponents the same. Instead of adding the main
numbers, they are subtracted.
Scientific notation
Standard form
13. (2 x 102) - (3 x 101) =
_______1.7 x 102________
_______170___________
14. (3 x 106) - (4.5 x 105) =
_______3 x 106________
_______3000000_______
15. (2.45 x 10-2) - (7.1 x 10-1) =
_______-7 x 10-1_________
_______-0.7___________
16. (4.7 x 10-4) - (5.3 x 102) =
_______-5.3 x 102_________
_______-530__________
Make sure your final answers are always in scientific notation! Remember the rules!