5.4+Dividing+Decimals

Section 5.4 - Dividing Decimals
Without showing all of the work, when we covered long division, some problems did not come out even, meaning that there was a remainder.




 * Division with a Whole Number Divisor**

In the problem above, the divisor is 5. 763 is the dividend and the answer is the quotient.

The remainder occurs because there are no more digits to "bring down". However, if 763 were turned into 763.000 there would be. Adding zeroes after the decimal does not change the value, but does make it possible to continue this division problem without a remainder. You can continue to add zeroes until the problem comes out even or until you reach the desired place value. No more remainders.

Wherever the decimal point is in the dividend, that is where the decimal point goes in the quotient.




 * Division with a Decimal Number Divisor**

You must divide with a whole number divisor. If the divisor is a decimal number, multiply both the divisor and the dividend by the same power of ten (10, 100, 1000, etc.) until the divisor is a whole number (the dividend doesn't need to be). This is easier than it seems, because you can simply move the decimal point over to multiply by a power of ten. If you move the decimal in the divisor 3 places, move the decimal point in the dividend three as well. You may need to add zeroes as place holders. Then put the decimal point in the same place in the quotient and solve the problem.



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 * Division by Powers of Ten**

Just like multiplying a decimal number by ten moves the decimal point one place, dividing by 10 moves it one place in the other direction. You can divide any number by a power of ten (10, 100, 1000, etc.) just by moving the decimal point the number of places as zeroes in the divisor. That even works for a whole number: 3444 divided by 100 is 34.44


 * Converting Fractions to Decimals**

Although we already converted fractions and mixed numbers into decimals earlier in this chapter, those had denominators of 10 or 100.

All fractions, whether the denominator is a power of ten or not, can be converted to a decimal number by dividing. We waited this long to bring that out because it will usually require you to add a decimal point to complete the long division.

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 * Chapter Five Practice Problems**

**Where to from here?**
5.1 Decimals and Fractions 5.2 Adding and Subtracting Decimals 5.3 Multiplying Decimals 5.4 Dividing Decimals 5.5 Application Problems with Decimals Chapter Five Summary Chapter Five Homework