Demonstrate how to write a number in scientific notation.
Show examples of how to add/subtract/multiply/divide numbers written in scientific notation.
This packet should help a learner seeking to represent numbers in scientific notation.
GENERAL RULES FOR CHANGING A NUMBER INTO SCIENTIFIC NOTATION
EXAMPLE 1:
Express the number 1,642,000 in scientific notation.
1,642,000 becomes 1.642000
For 1.642000, the decimal needs to move 6 times to the right to get back to the original number.
In scientific notation,
1,642,000 is 1.642000 x 10^{6} or 1.642 x 10^{6}
EXAMPLE 2:
Express the number 0.00000000520 in scientific notation.
0.00000000520 becomes 5.20
For 5.20, the decimal needs to move 9 times to the left to get back to the original number.
In scientific notation,
0.00000000520 is 5.20 x 10^{-9}
RULES FOR ADDITION AND SUBTRACTION
Addition Example
1.02 x 10^{12} + 3.01 x 10^{13} = ?
1.02 x 10^{12} + 30.1 x 10^{12} (you could also change both to 10^{13})
1.02 + 30.1 = 31.12
Answer: 31.12 x 10^{12}
Correct scientific notation: 3.112 x 10^{13}
Subtraction Example
1.2 x 10^{-3} - 2.5 x 10^{-5} = ?
1.2 x 10^{-3} - 0.025 x 10^{-3}
1.2 - 0.025 = 1.175
Answer and Correct scientific notation: 1.175 x 10^{-3}
RULES FOR MULTIPLYING
Multiplication Example
6.02 x 10^{23} x 2.15 x 10^{-5} = ?
(6.02 x 2.15) x (10^{23} x 10^{-5}) = 12.943 x 10 ^{23+ (-5)}
Answer: 12.943 x 10^{18}
Correct scientific notation: 1.2943 x 10^{19}
RULES FOR DIVIDING
Division Example
6.02 x 10^{23} / 2.15 x 10^{-5} = ?
(6.02 / 2.15) x (10^{23} / 10^{-5}) = 12.943 x 10 ^{23 - (-5)}
Answer and Correct scientific notation: 2.8 x 10^{28}