Scientific notation is used to express numbers that are very large or extremely small as a coefficient raised to a power of 10. The exponent for 10 can be a positive number (for large numbers) or a negative number (for small numbers). For example, the mass of the earth is about 1,317,000,000,000,000,000,000,000 pounds. This would be extremely difficult to write out each time. Using scientific notation, we would write the same number as 1.317 x 10²⁴

Rules for writing large numbers in scientific notation:

Write 123,456,000 in scientific notation.

1. All whole numbers have a decimal point. For whole numbers, such as 123,456,000, there is a decimal point at the far right end of the number. (123,456,000.)
2. Move the decimal point to the left so that the number to the left of the decimal point is greater than or equal to 1 and smaller than 10. For example, we would move our decimal point from the end of the number to between the 1 and 2. (1.23456000). 1, (the number to the left of the decimal point) is greater than or equal to 1 and smaller than 10.
3. The next step is to count the number of spaces we moved the decimal point. We moved the decimal point 8 spaces to the left. This number, 8, will become our exponent in the power of 10. Our exponent will be 10⁸.
4. When writing scientific notation, don't write trailing zeroes. Without the trailing zeroes, our number is 1.23456. Now, multiply this number by the power of 10 we calculated earlier. In scientific notation, our number is written as 1.23456 x 10⁸

Rules for writing small numbers in scientific notation:

Write .000000123 in scientific notation.

1. This works the same as for large numbers, we just move the decimal point to the right instead of the left and our exponent will have a negative number.
2. Move the decimal point to the right so that the number to the left of the decimal point is greater than or equal to 1 and smaller than 10. For example, we would move our decimal point from the beginning of the number to between the 1 and 2. (0000001.23). 1, (the number to the left of the decimal point) is greater than or equal to 1 and smaller than 10.
3. The next step is to count the number of spaces we moved the decimal point. We moved the decimal point 7 spaces to the right. This number, 7, will become our exponent in the power of 10, but this time it will have a negative value. Our exponent will be 10^-7.
4. When writing scientific notation, don't write leading zeroes. Without the leading zeroes, our number is 1.23. Now, multiply this number by the power of 10 we calculated earlier. In scientific notation, our number is written as 1.23 x 10^-7

Write the following numbers in scientific notation. Answers are included at the bottom of this tutorial.

1. 1,897,432,000
2. 3,874,000
3. 1,000,000,000,000,000
4. 256,000,000,000
5. 875,932,745
6. .00023498456
7. .0000000000001
8. .0002034056
9. .0000021583000
10. .864391

Answers:

1. 1.897432 x 10⁹
2. 3.874 x 10⁶
3. 1 x 10¹⁵
4. 2.56 x 10¹¹
5. 8.75932745 x 10⁸
6. 2.3498456 x 10^-4
7. 1 x 10^-13
8. 2.034056 x 10^-4
9. 2.1583 x 10^-6
10. 8.64391 x 10^-1