Unit 4: Dividing Decimals
Topic A: Dividing Decimals
Dividing decimals uses the same method that you learned for dividing whole numbers.
Vocabulary Review
[latex]\require{enclose} \begin{array}{r} \text{quotient}\\ \text{divisor}\enclose{longdiv}{\text{dividend}} \\ \end{array}[/latex]
dividend ÷ divisor = quotient
Using the above diagram, write the definitions.
Divisor:
Dividend:
Quotient:
Remember to use zeros to hold the places in the quotient if there is no other digit.
[latex]\begin{array}{r}\downarrow \phantom{0}\\1\mathbf{0}4\\9\enclose{longdiv}{936} \\9\downarrow \;\;\\\hline 03\phantom{0}\\0\downarrow\\\hline 36\\36\\ \hline0\end{array}[/latex]
Where Do You Place the Decimal Point?
Dividing decimals follows almost the same steps as dividing whole numbers. Here you will be shown two ways to figure out where to place the decimal point.
Method One
One way is to estimate the quotient using rounded whole numbers.
Example A
[latex]17.7 \div3[/latex]
Estimate: 17.7 ÷ 3 ≈ 18 ÷ 3 = 6
This tells us that the correct answer will be around 6 (which is one whole number place).
We know that the answer will not be around 0.6 and it will not be around 60.
If we take the decimals out and just divide the digits, the answer is 59.
[latex]\begin{array}{r}59\\3\enclose{longdiv}{177}\end{array}[/latex]
The estimate shows that the the decimal point will come after one whole number.
17.7 ÷ 3 = 5.9
Example B
[latex]137.88\div18[/latex]
Estimate: 137.88 ÷ 18 ≈ 140 ÷ 20 = 7
The answer will be around 7. It will not be around 0.7 or 70 or 700.
If we take the decimals out and just divide the digits, the answer is 7.66.
[latex]\begin{array}{r}7.66\\18\enclose{longdiv}{137.88}\end{array}[/latex]
The estimate shows that the the decimal point will come after one whole number.
137.88 ÷ 18 = 7.66
To check the accuracy of your division, multiply the quotient by the divisor.
dividend ÷ divisor = quotient
quotient × divisor = dividend
The product will equal the dividend if your arithmetic is correct.
23.72 ÷ 8 = 2.965 [latex]\begin{array}{rr}&2.965\\ \times&8\\ \hline &23.720\end{array}[/latex]
Exercise 1
The division has been done. Your task is to put the decimal point in the quotient by doing a whole number estimate of the question.
- [latex]\begin{array}{r}10.8\\2\enclose{longdiv}{21.6}\\ \end{array}[/latex] [latex]\left(\begin{array}{r}10\\2\enclose{longdiv}{20}\\ \end{array}\right)[/latex]
- [latex]\begin{array}{r}1.3\\8\enclose{longdiv}{10.4}\\ \end{array}[/latex] [latex]\left(\begin{array}{r}1\\8\enclose{longdiv}{10}\\ \end{array}\right)[/latex]
- [latex]\begin{array}{r}236\\6\enclose{longdiv}{14.16}\\ \end{array}[/latex]
- [latex]\begin{array}{r}53\\7\enclose{longdiv}{37.4}\\ \end{array}[/latex]
- [latex]\begin{array}{r}434\\4\enclose{longdiv}{173.6}\\ \end{array}[/latex]
- [latex]\begin{array}{r}345\\5\enclose{longdiv}{17.25}\\ \end{array}[/latex]
- [latex]\begin{array}{r}864\\7\enclose{longdiv}{60.48}\\ \end{array}[/latex]
- [latex]\begin{array}{r}182\\6\enclose{long