2. Perform the division as if the numbers were whole numbers. You may need to add zeros to the back of the dividend to complete the division

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1 Math Section 5. Dividing Decimals 5. Dividing Decimals Review from Section.: Quotients, Dividends, and Divisors. In the expression,, the number is called the dividend, is called the divisor, and is called the quotient. is equivalent to is equivalent to is equivalent to divide by Steps for Dividing Decimal Numbers. The divisor (the outside number) needs to be a whole number. If the divisor contains a decimal you will need to move the decimal point to the end of the divisor. i. Count the number of times you will need to move the decimal point so that it is at the end of the divisor. ii. You will need to move the decimal point of the dividend (the inside number) the exact same number of times.. Perform the division as if the numbers were whole numbers. You may need to add zeros to the back of the dividend to complete the division. Place the decimal point in the quotient immediately above the decimal point in the dividend. (Carry the decimal point up.) Example : Divide by. Solution:.5. Since we are in the decimal chapter, we will not stop when we have a remainder. Instead we will add a decimal point and a zero to the back of the dividend. We will continue to divide and add zeros to the back of the dividend until we get a remainder of zero or the problem tells us to round to a specific decimal place. Hence,.5.

2 Math Section 5. Dividing Decimals You Try It : Divide by 5. Example : Divide Solution: Hence, You Try It : Divide..55 Example : Divide..6.9 Solution:.6.9 Since we have a decimal point in the divisor, we will need to move the decimal point to the end. In this case the decimal point needs to move TWO times to move to the end. This means we will need to move the decimal point in the dividend, TWO times to the right as well becomes Hence, You Try It : Divide

3 Math Section 5. Dividing Decimals Review of Dividing Signed Numbers Like Signs: The quotient to two numbers with like signs is positive. Unlike Signs: The quotient to two numbers with unlike signs is negative. Example : Divide... Solution: Since we have unlike signs, we know that our answer should be negative... Since we have a decimal point in the divisor, we will need to move the decimal point to the end. In this case the decimal point needs to move THREE times to move to the end. This means we will need to move the decimal point in the dividend, THREE times to the right as well..... becomes We will need to add a decimal point and zeros behind the to complete the division Hence,...5. Don t forget to put the negative sign in your answer! You Try It : Divide...5

4 Math Section 5. Dividing Decimals Example 5: Convert 7 to a decimal. Round your answer to the nearest hundredth. Solution: 7 7. Since the directions ask us to round, we do not need to keep dividing until we get no remainder. Instead, we will divide to one place value past where the problem is asking us to round. For example, this question asks us to round to the nearest hundredth. Therefore we must divide until we have a thousandths place (one place value past a hundredth). The reason we need one more place value past what is asked is because we need a testing digit to be able to see how to round the rounding digit. (See Section. for a review on rounding.) We will add a decimal point to the back of the dividend,, and add zeros behind the decimal point as needed. So we have rounding digit testing digit You Try It 5: Convert 5 7 to a decimal. Round your answer to the nearest hundredth. Consider: Dividing a number by n will move the decimal point n places to the left. EX:

5 Math Example 6: Simplify Section 5. Dividing Decimals Solution: According to the rule, dividing by should move the decimal point FOUR places to the left You Try It 6: Simplify Note: Multiplying and have very similar steps. The only difference is for one you move RIGHT and for the other you move LEFT. Multiplying by Powers of Ten Multiplying a number by n will move the decimal point n places to the RIGHT. When multiplying by n, your answer will be larger than the dividend. This is why the decimal is moving to the RIGHT. Dividing a number by n will move the decimal point n places to the LEFT. When dividing by n, your answer will be smaller than the dividend. This is why the decimal is moving to the LEFT. 5

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