Dividing Scientific Notation | MathHelp.com
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To divide numbers that are in written in scientific notation, such as 6.5 x 10 cubed divided by 9.8 times 10 to the 9th, we first divide the decimals, in this case 6.5 divided by 9.8, to get 0.663265306. And let’s go ahead and round this decimal to the nearest hundredth (underline the hundredth place). Since the 3 to the right of the rounding place is less than 5, we round down, so we have 0.66. Next, we divide the powers of 10, in this case 10 cubed divided by 10 to 9th. And since we’re dividing two powers that have like bases, we subtract the exponents and leave the base the same, to get 10 to the 3 - 9, or 10 to the -6th. So we have 0.66 times 10 to the -6th. Finally, we’re asked to write our answer in scientific notation. Notice that our decimal, 0.66, is not between 1 and 10, so our number is not in scientific notation. In this situation, we multiply 0.66 by 10, which moves the decimal point one place to the right, and we have 6.6. Now our decimal is between 1 and 10. However, if we multiply the decimal by 10, then we must divide the power of 10 by 10, in order to balance things out. So we have 10 to -6th divided by 10 to the 1st, which means that we subtract the exponents, -6 – 1, to get -7. So we have 6.6 times 10 -7th, which is our final answer, written in scientific notation.
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