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Q: Why can you move the decimal point in the divisor to th right as long as you move the decimal point in the dividend the same number of places to the right?

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No.

No.

It is moved 9 places.

The decimal point moves 3 places to the right.

You always move the decimal to the right when dividing by a number which is not a whole number. For example: In the problem 100 divided by .01, you would move the decimal two places to the right for divisor and dividend leaving you with 10000 divided by 1.

If the dividend is between 2.25*10k and 10k+1 where k is any integer, then the decimal point does not move while if the dividend is between 10k and 2.25*10k then the decimal point moves 1 place to the left.

To divide by a decimal, make the divisor a whole number by moving the decimal point to the right; the dividend must also be changed by moving its decimal point the same number of digits to the right. So to divide 0.5 by 0.57, make the divisor 0.57 into 57 by moving the decimal point two digits to the right, then also move the decimal point of the dividend (0.5) two places to the right to give 50. Thus: 0.5 / 0.57 = 50 / 57 ~= 0.88

That is because if you do the same thing to the divisor as the dividend then nothing changes. Say you have 2 divided by 4; if you multiply both by 10 you have 20/40 which is the same thing. So if you have 2.36 divided by 4.19 that is the same as 236/419 since you multiplied both by 100.

0.4

Because not to do so would change the relationship between them 3.45/12.3 = 345/1230 = 0.2805 (approx) If you multiplied the dividend by 100 and the divisor by ten (doing just enoguh to remove the decimal places) then the relationship (the ratio) changes 345/ 123 = 2.8049 (approx)

If you move the decimal point the same direction and number of places for the dividend and the divisor, this accomplishes the same thing as multiplying (or dividing) a numerator and denominator by the same number (in this case it is a power of ten). Moving the decimal place to the right by one place effectively multiplies the number by 10, and moving the decimal place to the left by one place is the same as dividing the number by 10. Example: 12345.6 / 10 = 1234.56

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