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# Decimal Multiplication

## Multiply decimals like whole numbers, then place the decimal point.

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Practice Decimal Multiplication

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Decimal Multiplication

Micah is preparing to go on a climbing trip and needs to buy climbing rope. The cost of the rope is 1.59 per foot. He wants to buy 195.5 feet of rope. How much will the rope cost? In this concept, you will learn how to multiply a decimal number with another decimal number. ### Multiplying Decimals One way to multiply decimals is using area models. Another more efficient way to multiply two decimals is to ignore the decimal and multiply the numbers as if they were whole numbers first. Afterwards, add the decimal point back into the product. It is important to place the decimal point in the correct place. Here is another multiplication problem. \begin{align*}4.7 \times 2.1 = \underline{\;\;\;\;\;\;\;\;\;\;\;\;}\end{align*} First, ignore the decimal point and multiply the numbers as if they were two whole numbers. \begin{align*}\begin{array}{rcl} && \quad 4.7\\ && \underline{\times \; 2.1\;}\\ && \quad \ 47\\ && \underline{+ 940\;\;}\\ && \ \ \ 987 \end{array}\end{align*} Then, place the decimal point into the product. Count the number of decimal places both multipliers. 4.7 has 1 decimal place. 2.1 also has 1 decimal places. There are a total of 2 decimal places. Move the decimal point 2 places to the left. Remember that the decimal point is located to the right of the ones place in a whole number. If you need to move the decimal point more places than there are digits, you can always use zero placeholders. \begin{align*}9.\underleftarrow{87}\end{align*} The product of 4.7 times 2.1 is 9.87. Check to see if the decimal point was placed correctly by estimating the product of 4.7 times 2.1. First, round the decimal numbers to the nearest whole number. 4.7 rounds to 5. 2.1 rounds to 2. Then, multiply to find an estimate product. \begin{align*}5 \times 2 = 10\end{align*} Next, compare the products. The actual product should be close to the estimate product. 9.87 is close to 10. The decimal point was placed in the right location. ### Examples #### Example 1 Earlier, you were given a problem about Micah on the climbing trip. Micah wants to buy 195.5 feet of rope that costs1.59 per foot. Multiply 195.5 by 1.59 to find the total cost of the rope. First, ignore the decimal point and multiply the numbers as if they were two whole numbers. \begin{align*}\begin{array}{rcl} && \ \ \ \ \ \ 195.5\\ && \ \ \ \ \underline{\times \;1.59}\\ && \ \ \ \ \ 17595\\ && \ \ \ \ \ 9775\\ && \underline{+ 1995\;\;\;\;}\\ && \ \ \ 310845 \end{array}\end{align*} Then, place the decimal point into the product. There are a total of 3 decimal places in the multiplicands. Move the decimal point 3 places to the left. \begin{align*}310.\underleftarrow{845}\end{align*} The cost of the rope should be310.845, but remember that dollars are only calculated to the hundredths place. Round the decimal to the nearest hundredths place.

\begin{align*}\begin{array}{rcl} && 310.8\underline{4}5 \approx 310.85\\ && \qquad \quad \uparrow \end{array}\end{align*}

Micah will spend \$310.85 on climbing rope.

#### Example 2

Multiply the decimals.

\begin{align*}0.134 \times 0.567 = \underline{\;\;\;\;\;\;\;\;\;\;\;\;}\end{align*}

First, ignore the decimal point and multiply the numbers as if they were two whole numbers.

\begin{align*}\begin{array}{rcl} && \ \ \ \ 0.134\\ && \underline{\times \; 0.567}\\ && \quad \ \ \ 938\\ && \ \ \ \ \ 804\\ && \underline{+670\;\;\;\;}\\ && \ \ \ 75978 \end{array}\end{align*}

Then, place the decimal point into the product. Count the number of decimal places both multipliers. 0.134 has 3 decimal places. 0.567 also has 3 decimal places. There are a total of 6 decimal places. Move the decimal point 6 places to the left. Remember that the decimal point is located to the right of the ones place in a whole number. Use a zero placeholder if needed.

\begin{align*}0.\underleftarrow{075978}\end{align*}

The product of 0.134 times 0.567 is 0.075978

#### Example 3

Multiply the decimals.

\begin{align*}3.1 \times 4.9 = \underline{\;\;\;\;\;\;\;\;\;\;\;\;}\end{align*}

First, ignore the decimal point and multiply the numbers as if they were two whole numbers.

\begin{align*}\begin{array}{rcl} && \quad \ \ 3.1\\ &&\ \underline{\times \;\; 4.9\;}\\ &&\quad \ 279\\ && \underline{+124\;\;\;}\\ && \ \ \ 1519 \end{array}\end{align*}

Then, place the decimal point into the product. There are a total of 2 decimal places in the multiplicands. Move the decimal point 2 places to the left.

\begin{align*}15.\underleftarrow{19}\end{align*}

The product of 3.1 times 4.9 is 15.19.

#### Example 4

Multiply the decimals.

\begin{align*}1.2 \times 5.1 = \underline{\;\;\;\;\;\;\;\;\;\;\;\;}\end{align*}

First, ignore the decimal point and multiply the numbers as if they were two whole numbers.

\begin{align*}\begin{array}{rcl} && \quad 1.2\\ && \underline{\times \; 5.1\;}\\ && \quad \ 12\\ && \underline{+60 \;\;}\\ && \ \ \ 612 \end{array}\end{align*}

Then, place the decimal point into the product. There are a total of 2 decimal places in the multiplicands. Move the decimal point 2 places to the left.

\begin{align*}6.\underleftarrow{12}\end{align*}

The product of 1.2 times 5.1 is 6.12.

#### Example 5

Multiply the decimals.

\begin{align*}3.21 \times 6.7 = \underline{\;\;\;\;\;\;\;\;\;\;\;\;}\end{align*}

First, ignore the decimal point and multiply the numbers as if they were two whole numbers.

\begin{align*}\begin{array}{rcl} && \quad \ \ 3.21\\ && \ \ \underline{\times \;\; \; 6.7}\\ && \quad \ 2247\\ && \underline{+1926\;\;}\\ && \ \ \ 21507 \end{array}\end{align*}

Then, place the decimal point into the product. There are a total of 3 decimal places in the multiplicands. Move the decimal point 3 places to the left.

\begin{align*}21.\underleftarrow{507}\end{align*}

The product of 3.21 times 6.7 is 21.507.

### Review

Multiply the following decimals.

1. \begin{align*}4.3 \times 0.12 = \underline{\;\;\;\;\;\;\;\;\;\;\;\;}\end{align*}
2. \begin{align*}2.3 \times 3.4 = \underline{\;\;\;\;\;\;\;\;\;\;\;\;}\end{align*}
3. \begin{align*}0.34 \times 0.56 = \underline{\;\;\;\;\;\;\;\;\;\;\;\;}\end{align*}
4. \begin{align*}2.7 \times 3.2 = \underline{\;\;\;\;\;\;\;\;\;\;\;\;}\end{align*}
5. \begin{align*}6.5 \times 2.7 = \underline{\;\;\;\;\;\;\;\;\;\;\;\;}\end{align*}
6. \begin{align*}0.23 \times 0.56 = \underline{\;\;\;\;\;\;\;\;\;\;\;\;}\end{align*}
7. \begin{align*}1.23 \times 0.4 = \underline{\;\;\;\;\;\;\;\;\;\;\;\;}\end{align*}
8. \begin{align*}0.5 \times 0.76 = \underline{\;\;\;\;\;\;\;\;\;\;\;\;}\end{align*}
9. \begin{align*}0.23 \times 0.8 = \underline{\;\;\;\;\;\;\;\;\;\;\;\;}\end{align*}
10. \begin{align*}3.45 \times 1.23 = \underline{\;\;\;\;\;\;\;\;\;\;\;\;}\end{align*}
11. \begin{align*}1.45 \times 0.23 = \underline{\;\;\;\;\;\;\;\;\;\;\;\;}\end{align*}
12. \begin{align*}0.89 \times 0.9 = \underline{\;\;\;\;\;\;\;\;\;\;\;\;}\end{align*}
13. \begin{align*}0.245 \times 0.8 = \underline{\;\;\;\;\;\;\;\;\;\;\;\;}\end{align*}
14. \begin{align*}34.5 \times 0.7 = \underline{\;\;\;\;\;\;\;\;\;\;\;\;}\end{align*}
15. \begin{align*}18.7 \times 0.9 = \underline{\;\;\;\;\;\;\;\;\;\;\;\;}\end{align*}
16. \begin{align*}22.3 \times 0.76 = \underline{\;\;\;\;\;\;\;\;\;\;\;\;}\end{align*}
17. \begin{align*}21.7 \times 0.4 = \underline{\;\;\;\;\;\;\;\;\;\;\;\;}\end{align*}.
18. \begin{align*}14.5 \times 0.68 = \underline{\;\;\;\;\;\;\;\;\;\;\;\;}\end{align*}
19. \begin{align*}20.1 \times 0.3 = \underline{\;\;\;\;\;\;\;\;\;\;\;\;}\end{align*}
20. \begin{align*}34.23 \times 0.18 = \underline{\;\;\;\;\;\;\;\;\;\;\;\;}\end{align*}
21. \begin{align*}0.189 \times 0.9 = \underline{\;\;\;\;\;\;\;\;\;\;\;\;}\end{align*}
22. \begin{align*}0.341 \times 0.123 = \underline{\;\;\;\;\;\;\;\;\;\;\;\;}\end{align*}
23. \begin{align*}0.451 \times 0.12 = \underline{\;\;\;\;\;\;\;\;\;\;\;\;}\end{align*}
24. \begin{align*}0.768 \times 0.123 = \underline{\;\;\;\;\;\;\;\;\;\;\;\;}\end{align*}
25. \begin{align*}0.76 \times 0.899 = \underline{\;\;\;\;\;\;\;\;\;\;\;\;}\end{align*}

To see the Review answers, open this PDF file and look for section 4.9.

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### Vocabulary Language: English

TermDefinition
Horizontally Horizontally means written across in rows.
Hundreds grid A hundreds grid is a grid of one hundred boxes used to show hundredths when working with decimals.
Product The product is the result after two amounts have been multiplied.
Vertically Vertically means written up and down in columns.