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Here are some tips for Scientific Notation, which aligns with Arizona state standards:
Scientific notation is an easier way to express very large numbers or very small numbers.
Examples of using scientific notation:
Which one do you think is easier to read, the number written out or the number written using scientific notation?
Original statement: Jupiter is 483400000 miles away from the sun. With scientific notation: Jupiter is 4.834 × 108 miles away from the sun. Original statement: The radius of a chlorine atom is 0.00000000012 meters. With scientific notation: The radius of a chlorine atom is 1.2 × 10-10 meters.
For 4.834 × 108, 4.834 is called the significant value and 8 is called the exponent.
For 1.2 × 10-10, 1.2 is called the significant value and -10 is called the exponent.
Significant values must be greater or equal to 1 and less than 10.
Example 1: Write numbers in normal notation
Convert from scientific notation into normal notation.
a. 8.49 × 105 The exponent is 5 which means that we move the decimal point on the significant value to the right by 5 zeros.
8.49 × 105 = 849000
b. 6.023 × 10-4 The exponent is -4 which means that we move the decimal point on the significant value to the left by 4 zeros.
6.023 × 10-4 = 0.0006023
Example 2: Write numbers in scientific notation
Convert from normal notation into scientific notation. Use '*' for the multiplication sign.
a. 4646000000 Count how many decimal places you have to move so that you have a number between 1 and 10.
You have to move the decimal point 9 places to the left to get 4.646
So the significant value is 4.646 and the exponent is 9.
46460000000 = 4.646 * 109
b. 0.0000003507 Count how many decimal places you have to move so that you have a number between 1 and 10.
You have to move the decimal point 7 places to the right to get 3.507
So the significant value is 3.507 and the exponent is -7.
0.0000003507 = 3.507 * 10-7
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