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A grain of sand has a mass of approximately 0.00000003 grams. How would this number be expressed in scientific notation?

Answer :

Final answer:

The mass of a grain of sand weighing 0.00000003 grams is expressed in scientific notation as 3 × 10−7 grams or, when converting to kilograms, as 3 × 10−10 kilograms.

Explanation:

To express the mass of a grain of sand, which is 0.00000003 grams, in scientific notation, we convert it into the form of a significant number multiplied by a power of 10. In this case, the significant number is 3, and we need to find the power of 10 that will turn 3 into 0.00000003 grams when multiplied. To do so, we count the number of places we move the decimal point to the right until we reach the significant number 3. This gives us 3 × 10−7 grams, since we move the decimal point seven places. If we wish to express this in terms of the SI base unit of mass, which is the kilogram (kg), we have to account for the conversion from grams to kilograms. Knowing there are 1,000 grams in 1 kilogram, we can further convert our scientific notation to kilograms by shifting the exponent down by 3 to account for this relationship. So, 3 × 10−7 grams becomes 3 × 10−10 kilograms.

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