How to Put Repeating Decimals Into Scientific Notation

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Putting repeating decimals into scientific notation will involve dividing to stop a decimal from repeating to an infinite place. Put repeating decimals into scientific notation with help from an experienced mathematics educator in this free video clip.

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Hello, my name is Walter Unglaub and this is how to put repeating decimals in scientific notation. So say we are dividing 1,000 by 3. In decimal form what we end up with is 333.333 continuing off into an infinite place after the decimal. We normally write this as 333.3 with a repetend bar over the 3 after the decimal place indicating that this number is repeated forever. We can rewrite this number in scientific notation by first considering the fact that we are in the 100s place so we write 3.33 and I'll just keep that 3 with the repetend bar times 10 to the power of 2 because we are in the 100s place now. Because these 3s are now to the right of the decimal place, we can just simply rewrite this as 3.3 with the repetend bar times 10 to the power of 2 or in compact scientific notation this simply becomes 3.3 with repetend bar, E2. If we wanted to write this without using the repetend bar, then we would have to decide what an appropriate number of significant figures or sig figs should be for this number. Normally, 3 to 4 sig figs is sufficient for most calculations. So if I use 3 sig figs, I'll simply write 3.33 E2 and this in compact scientific notation approximately equal to 1,000 divided 3. My name is Walter Unglaub and this is how to put repeating decimals into scientific notation.

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