Q: Must a decimal divisor and a decimal dividend have the same number of decimal places?

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The result of dividing 700,000,000 by 37 is approximately 18,918,919. The division can be done by dividing the whole number part of the dividend (700,000,000) by the divisor (37) and then adding any remaining decimal places of the dividend divided by the divisor.

The decimal point moves 3 places to the right.

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

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.

Moving a decimal point to the right is the same as multiplying a number by a power of ten. As long as both numbers are multiplied by the same amount, they will retain their same relationship.

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No.

It is moved 9 places.

The result of dividing 700,000,000 by 37 is approximately 18,918,919. The division can be done by dividing the whole number part of the dividend (700,000,000) by the divisor (37) and then adding any remaining decimal places of the dividend divided by the divisor.

The decimal point moves 3 places to the right.

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

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.

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.

Moving a decimal point to the right is the same as multiplying a number by a power of ten. As long as both numbers are multiplied by the same amount, they will retain their same relationship.

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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