College

Multiplying Decimals: Multiply each set of decimals. Show your work.

1)
[tex]\[
\begin{array}{r}
40.9 \\
\times \quad 2.1 \\
\end{array}
\][/tex]

2)
[tex]\[
\begin{array}{r}
65.9 \\
\times \quad 26.4 \\
\end{array}
\][/tex]

3)
[tex]\[
\begin{array}{r}
85.6 \\
\times \quad 80.5 \\
\end{array}
\][/tex]

4)
[tex]\[
\begin{array}{r}
80.6 \\
\times \quad 2.5 \\
\end{array}
\][/tex]

5)
[tex]\[
\begin{array}{r}
92.5 \\
\times \quad 80.8 \\
\end{array}
\][/tex]

6)
[tex]\[
\begin{array}{r}
59.1 \\
\times \quad 1.4 \\
\end{array}
\][/tex]

7)
[tex]\[
\begin{array}{r}
45.8 \\
\times \quad 41.3 \\
\end{array}
\][/tex]

8)
[tex]\[
\begin{array}{r}
7.8 \\
\end{array}
\][/tex]

(Note: The last multiplication in problem 8 appears incomplete. Please check the original document for any missing information.)

Answer :

Sure! Let's work through each of these multiplication problems step by step.

1) 40.9 × 2.1
- Align the numbers by their decimal points.
- Ignore the decimals and multiply 409 by 21.
- Calculate 409 × 21 = 8589.
- Count the total decimal places in the original numbers (1 in 40.9 and 1 in 2.1, totaling 2).
- Place the decimal point two places from the right in 8589, resulting in 85.89.

2) 65.9 × 26.4
- Align the numbers by their decimal points.
- Ignore the decimals and multiply 659 by 264.
- Calculate 659 × 264 = 173976.
- Count the decimal places (1 in 65.9 and 1 in 26.4, totaling 2).
- Place the decimal point two places from the right in 173976, making it 1739.76.

3) 85.6 × 80.5
- Align the numbers by their decimal points.
- Ignore the decimals and multiply 856 by 805.
- Calculate 856 × 805 = 690880.
- Count the decimal places (1 in 85.6 and 1 in 80.5, totaling 2).
- Place the decimal point two places from the right in 690880, resulting in 6890.80 (can be rounded to 6890.80).

4) 80.6 × 2.5
- Align the numbers by their decimal points.
- Ignore the decimals and multiply 806 by 25.
- Calculate 806 × 25 = 20150.
- Count the decimal places (1 in 80.6 and 1 in 2.5, totaling 2).
- Place the decimal point two places from the right in 20150, making it 201.50.

5) 92.5 × 80.8
- Align the numbers by their decimal points.
- Ignore the decimals and multiply 925 by 808.
- Calculate 925 × 808 = 747400.
- Count the decimal places (1 in 92.5 and 1 in 80.8, totaling 2).
- Place the decimal point two places from the right in 747400, resulting in 7474.00.

6) 59.1 × 1.4
- Align the numbers by their decimal points.
- Ignore the decimals and multiply 591 by 14.
- Calculate 591 × 14 = 8274.
- Count the decimal places (1 in 59.1 and 1 in 1.4, totaling 2).
- Place the decimal point two places from the right in 8274, making it 82.74.

7) 45.8 × 41.3
- Align the numbers by their decimal points.
- Ignore the decimals and multiply 458 by 413.
- Calculate 458 × 413 = 189154.
- Count the decimal places (1 in 45.8 and 1 in 41.3, totaling 2).
- Place the decimal point two places from the right in 189154, resulting in 1891.54.

8) 0 × 7.8
- Any number multiplied by 0 is 0.

These are the results for each multiplication problem.

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