# Decimal Quotients Using Zero Placeholders

## Extending the place value of a decimal

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Decimal Quotients Using Zero Placeholders

Jerry is hosting a barbeque for his friends. He buys 10.5 pounds of ground meat to make hamburgers. He wants to make 20 hamburger patties for the party. How much meat will be in each patty if he divides the meat evenly?

In this concept, you will learn how to divide a decimal using zero place holders.

### Zero Placeholder

Not all decimal division problems will divide exactly. In some cases, a division problem will have a remainder. A remainder is the amount left over when the dividend is not equally divided by the divisor. The remainder is written as “R” followed by a number.

Here is a division problem with a remainder.

\begin{align*}\require{enclose} \begin{array}{rcl} && \quad \ \ 2.9 \ R4 \\ && 5 \enclose{longdiv}{14.9}\kern-.2ex\\ && \ \ \! \underline{-10}\\ && \quad \ \ \! 4 \hphantom{.} 9\\ && \ \ \ \underline{-4 \ 5}\\ && \quad \ \ \ \hphantom{.} 4 \end{array}\end{align*}

The quotient of 14.9 divided by 5 is 2.9 with a remainder of 4. You can continue dividing the dividend to find a more accurate quotient. Place a zero as a placeholder at the end of the decimal number in the division box.

Here is the same division problem with a zero placeholder.

\begin{align*}\require{enclose} \begin{array}{rcl} && \quad \ \ 2.98\\ && 5 \enclose{longdiv}{14.9{\color{red}0}}\kern-.2ex\\ && \ \: \! \underline{-10}\\ && \quad \ 4 \hphantom{.} 9\\ && \ \ \: \underline{-4 \ 5}\\ && \qquad 4{\color{red}0} \\ && \quad \ \ \! \underline{-40}\\ && \qquad \ \ 0 \end{array}\end{align*}

The quotient of 14.9 divided by 5 is 2.98. This means that 5 can go into 14.9 exactly 2.98 times.

Adding zero placeholders at the end of a decimal does not change the value of the decimal.

\begin{align*}14.9 = 14.9000\end{align*}

Zero placeholders can be used to continue dividing to get a more accurate quotient. You can also add as many zero placeholders as you need.

### Examples

#### Example 1

Earlier, you were given a problem about Jerry and the hamburgers.

Jerry wants to make 20 hamburger patties from 10.5 pounds of ground meat. Divide 10.5 by 20 to find the exact weight of each patty.

First, start dividing 10.5 by 20.

\begin{align*}\require{enclose} \begin{array}{rcl} && \qquad \ \: \! .5 \\ && 20 \enclose{longdiv}{10.5}\kern-.2ex\\ && \quad \! \, \! \underline{-10 \kern+.2ex 0}\\ && \qquad \ \hphantom{.}5 \end{array}\end{align*}

Then, add zero placeholders and continue to divide.

\begin{align*}\require{enclose} \begin{array}{rcl} && \qquad \ \ \kern+.1ex 525 \\ && 20 \enclose{longdiv}{10.5{\color{red}00}}\\ && \ \ \ \, \underline{-10 \kern+.2ex 0}\\ && \quad \ \quad \hphantom{.}5{\color{red}0}\\ && \quad \ \ \ \hphantom{.} \underline{-40}\\ && \qquad \ \ 10{\color{red}0}\\ && \quad \ \ \ \hphantom{.} \kern-.2ex\underline{-100}\\ && \qquad \quad \ \kern.2ex 0 \end{array}\end{align*}

Next, add the decimal point to the quotient.

\begin{align*}\require{enclose} \quad \ 0{\color{red}.}525\\ 20 \enclose{longdiv}{10.5{\color{red}00}}\end{align*}

Each patty will weigh exactly 0.525 pounds.

#### Example 2

Divide and use zero placeholders if needed.

\begin{align*}3.1 \div 8 = \underline{\;\;\;\;\;\;\;\;\;\;\;\;\;}\end{align*}

First, start dividing 3.1 by 8. Remember that 3.1 is the dividend and 8 is the divisor.

\begin{align*}\require{enclose} \begin{array}{rcl} && \quad \ \ \hphantom{.}3 \\ && 8 \enclose{longdiv}{3.1}\\ && \ \hphantom{.} \underline{-24}\\ && \quad \ \ 7 \end{array}\end{align*}

Then, add zero placeholders and continue to divide.

\begin{align*}\require{enclose} \begin{array}{rcl} && \quad \ \ \hphantom{.}3875\\ && 8 \enclose{longdiv}{3.1{\color{red}000}}\\ && \underline{-\ \, 24}\\ && \quad\ \ 7{\color{red}0}\\ && \quad \! \underline{-64}\\ && \quad \ \ \ \ 6{\color{red}0} \\ && \quad \ \underline{-56}\\ && \quad \quad \ \ \! 4{\color{red}0} \\ && \quad \ \ \ \underline{-40}\\ && \qquad \quad \! \! 0 \end{array}\end{align*}

Then, add the decimal point to the quotient.

\begin{align*}\require{enclose} \ \ \ 0{\color{red}.}3875\\ 8 \enclose{longdiv}{3.1{\color{red}000}}\\\end{align*}

The final answer for 3.1 divided by 8 is 0.3875.

Divide the following problems and use zero placeholders if needed.

#### Example 3

\begin{align*}13.95 \div 6 = \underline{\;\;\;\;\;\;\;\;\;\;\;\;\;}\end{align*}

First, start dividing 13.95 by 6.

\begin{align*}\require{enclose} \begin{array}{rcl} && \quad \ \ 2 \hphantom{.}32\\ && 6 \enclose{longdiv}{13.95}\\ && \ \underline{-12}\\ && \quad \ \ \! 19\\ && \ \ \ \underline{-18}\\ && \quad \ \ \ 15 \\ && \quad \underline{-12}\\ && \qquad \ \! 3 \end{array}\end{align*}

Then, add zero placeholders and continue to divide.

\begin{align*}\require{enclose} \begin{array}{rcl} && \quad \ \ 2 \hphantom{.}325\\ && 6 \enclose{longdiv}{13.95 {\color{red}{0}}}\\ && \ \underline{-12}\\ && \quad \ \ \! 19\\ && \ \ \ \underline{-18}\\ && \quad \ \ \ 15 \\ && \quad \underline{-12}\\ && \qquad \ \! 3 {\color{red}{0}}\\ && \quad \ \ \underline{- 30}\\ && \qquad \ \ \, 0 \end{array}\end{align*}

Next, add the decimal point to the quotient.

\begin{align*}\require{enclose} \quad \ 2{\color{red}.}325\\ 6 \enclose{longdiv}{13.95{\color{red}{0}}}\end{align*}

The quotient of 13.95 divided by 6 is 2.325.

#### Example 4

\begin{align*}2.5 \div 2 = \underline{\;\;\;\;\;\;\;\;\;\;\;\;\;}\end{align*}

First, start dividing 2.5 by 2.

\begin{align*}\require{enclose} \begin{array}{rcl} && \quad 1 \hphantom{.}2\\ && 2 \enclose{longdiv}{2.5}\\ && \ \underline{-2}\\ && \quad \! 0 \hphantom{.}5\\ && \ \ \ \ \underline{-4}\\ && \quad \ \ \ \! 1 \end{array}\end{align*}

Then, add zero placeholders and continue to divide.

\begin{align*}\require{enclose} \begin{array}{rcl} && \quad 1 \hphantom{.}25 \\ && 2 \enclose{longdiv}{2.5{\color{red}{0}}}\\ && \ \underline{-2}\\ && \quad 05\\ && \ \ \ \, \underline{-4}\\ && \quad \ \ 1{\color{red}0}\\ && \ \ \ \, \underline{-10}\\ && \qquad 0 \end{array}\end{align*}

Next, add the decimal point to the quotient.

\begin{align*}\require{enclose} \quad 1{\color{red}.}25\\ 2 \enclose{longdiv}{2.5{\color{red}{0}}}\end{align*}

The quotient of 2.5 divided by 2 is 1.25.

#### Example 5

\begin{align*}1.66 \div 4 = \underline{\;\;\;\;\;\;\;\;\;\;\;\;\;}\end{align*}

First, start dividing 1.66 by 4.

\begin{align*}\require{enclose} \begin{array}{rcl} && \quad \ \ \ 41\\ && 4 \enclose{longdiv}{1.66}\\ && \ \underline{-16}\\ && \quad \ \ 06\\ && \quad \ \underline{-4}\\ && \qquad 2 \end{array}\end{align*}

Then, add zero placeholders and continue to divide.

\begin{align*}\require{enclose} \begin{array}{rcl} &&\quad \ \ \ 415\\ && 4 \enclose{longdiv}{1.66{\color{red}{0}}}\\ && \ \underline{- \, 16}\\ && \quad \ \ 06\\ && \quad \ \underline{-4}\\ && \quad \ \ \ \ 2{\color{red}0}\\ && \quad \ \underline{-20}\\ && \qquad \ \, 0 \end{array}\end{align*}

Next, add the decimal point to the quotient.

\begin{align*}\require{enclose} \quad \ 0{\color{red}.}415\\ 4 \enclose{longdiv}{1.66{\color{red}{0}}}\end{align*}

The quotient of 1.66 divided by 4 is 0.415.

### Review

Divide the following problems and use zero placeholders if needed.

1. \begin{align*}\require{enclose} 5 \enclose{longdiv}{17.6}\kern-.2ex\\\end{align*}
2. \begin{align*}\require{enclose} 4 \enclose{longdiv}{12.3}\kern-.2ex\\\end{align*}
3. \begin{align*}\require{enclose} 4 \enclose{longdiv}{14.4}\kern-.2ex\\\end{align*}
4. \begin{align*}\require{enclose} 5 \enclose{longdiv}{27.51}\kern-.2ex\\\end{align*}
5. \begin{align*}\require{enclose} 6 \enclose{longdiv}{13.6}\kern-.2ex\\\end{align*}
6. \begin{align*}\require{enclose} 6 \enclose{longdiv}{54.9}\kern-.2ex\\\end{align*}
7. \begin{align*}\require{enclose} 8 \enclose{longdiv}{4.18}\kern-.2ex\\\end{align*}
8. \begin{align*}\require{enclose} 8 \enclose{longdiv}{94.1}\kern-.2ex\\\end{align*}
9. \begin{align*}\require{enclose} 8 \enclose{longdiv}{10.04}\kern-.2ex\\\end{align*}
10. \begin{align*}\require{enclose} 4 \enclose{longdiv}{24.89}\kern-.2ex\\\end{align*}
11. \begin{align*}\require{enclose} 12 \enclose{longdiv}{27.9}\kern-.2ex\\\end{align*}

To see the Review answers, open this PDF file and look for section 4.11.

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### Vocabulary Language: English

TermDefinition
Divide To divide is split evenly into groups. The result of a division operation is a quotient.
Dividend In a division problem, the dividend is the number or expression that is being divided.
divisor In a division problem, the divisor is the number or expression that is being divided into the dividend. For example: In the expression $152 \div 6$, 6 is the divisor and 152 is the dividend.
Quotient The quotient is the result after two amounts have been divided.