Large Numbers

A simple example is that 10,000 can be written as 10 to the fourth power.

10,000 = 10⁴

Next, you can see how 30,000 can be written as 3 times 10,000; and since 10,000 is 10 to the fourth, then 30,000 can be written as 3 times 10 to the fourth.

30,000 = 3 x 10,000 = 3x10⁴

Here is a different way of figuring this change. If you start with 30,000 and you were to move the decimal place to the left until it was next to the 3, which is the first non-zero digit in the number, you would have moved the decimal four places. The number of places the decimal has to move becomes the exponent for the 10. So 30,000 is equal to 3 times 10 to the fourth power, the same as before.

30,000 = 30,000. = 3x10⁴
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Here is another example. Thirty-four thousand can be written as 3.4 times 10,000, which in turn can be written as 3.4 times 10 to the fourth.

34,000 = 3.4 x 10,000 = 3.4x10⁴

Looking at it another way, you must move the decimal point four places to get it in position just to the right of the first non-zero digit in the number (the 3). So 34,000, with the decimal point moved over four places, becomes 3.4 times 10 to the fourth.

34,000 = 34,000. = 3.4x10⁴
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The same process is shown for changing 34,567 into scientific notation. In scientific notation the decimal always goes just to the right of the first non-zero digit.

34,567 = 3.4567 x 10,000 = 3.4567x10⁴

34,567 = 34,567. = 3.4567x10⁴
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