What is a rule for multiplying and Dividing by powers of 10?

Answer 1

Oh, dude, multiplying and dividing by powers of 10 is like the easiest math trick in the book. When you multiply, you just move the decimal to the right as many times as there are zeros in the power of 10. And when you divide, you move the decimal to the left. It's like magic, but with numbers.

Answer 2

For positive powers:

The rule is to move the digits in the place value columns left (for multiplication) or right (for division) the same number of columns as the power of 10.

However, on paper this is not easy to do so the effect on the decimal point relative to the digits is used instead: move the decimal point the same number of digits right (for multiplication) or left (for division); if there are less digits than required to be moved, insert zeros until the decimal point has moved the required number of digits.

If the power is negative reverse the direction of movement (eg with moving the decimal point, to multiply move the decimal point left and divide by moving the decimal point to the right).

Answer 3

The general rule for multiplication is to move the decimal point to the right, by as many digits as specified in the exponent (to the left for negative exponents). For division, it's the other way round - move the decimal point to the left for positive exponents, to the right for negative exponents. Examples:5.321 x 100 = 532.1 (exponent is 2)

5.321 x 0.01 = 0.05321 (exponent is -2)