TeXes Science Practice Test

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In scientific notation, how would 151,000,000,000 meters be properly expressed?

1.51 * 10^10 meters
1.51 * 10^11 meters
1.51 * 10^12 meters
15.1 * 10^11 meters

The correct answer is: 1.51 * 10^11 meters

To express a number in scientific notation, one must convert it to a format where it is represented as a product of a number between 1 and 10, multiplied by a power of ten. In the case of 151,000,000,000 meters, we need to identify how many places the decimal point must move to create a coefficient between 1 and 10. The correct process involves moving the decimal point left from its original position at the end of the number (after the last zero) to just after the first non-zero digit, which is 1 in this case. Moving the decimal point left 11 places transforms 151,000,000,000 into 1.51. Thus, this leads us to express the number as 1.51 multiplied by 10 raised to the power of 11. This is because shifting the decimal point left by 11 positions indicates that all the zeros represented must be accounted for by elevating ten to the power of 11. Therefore, the correct representation in scientific notation is 1.51 * 10^11 meters.