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Q: How is the way the decimal point moves when you divide a number by a power of ten the same as when you multiply?

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It is not. For positive powers of ten, the decimal point moves to the right when multiplying and to the left when dividing. For negative powers of ten the point moves in the opposite directions.

Multiply it by 100. This moves the decimal point so that your answer is no longer in decimal form :)

It moves three places to the right.

It moves to the right because the decimal point moves to the left.

The decimal place "moves" one space to the left.

When you divide by ten the decimal point moves one place to the left.

One to one

Multiply the coefficient by 10, moves decimal to the right, changes the exponent to be 1 less. Divide the coefficient by 10, moves decimal to the left, changes the exponent to be 1 more.

The decimal point moves one place to the left when dividing by 10.

Multiplying a real number by a positive power of ten moves the decimal point that number (the exponent) of places to the right. Multiplying by a negative power of ten moves it to the left. For example, the -3 power of 10 is 1/1000; multiplying by that moves the decimal point 3 places to the left.

What you are asking is not clear, but I think that you're asking, "Why do you use x10 with scientific notation (Correct me if I'm wrong). The x10 is used because if you multiply something by ten, the decimal place of the number moves one to the right. If you divide a number by ten the decimal place moves one to the left. The x10(to whatever number) is just an easier way to symbolize that decimal place moving

What you are asking is not clear, but I think that you're asking, "Why do you use x10 with scientific notation (Correct me if I'm wrong). The x10 is used because if you multiply something by ten, the decimal place of the number moves one to the right. If you divide a number by ten the decimal place moves one to the left. The x10(to whatever number) is just an easier way to symbolize that decimal place moving

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