More on Multiplying Decimals

Read this text. Pay attention to the "How To" overview of the steps needed to multiply decimals. Complete the practice problems and check your answers.

Answers

 

EXAMPLE 5.15

Solution
  (3.9)(4.075)
Determine the sign of the product. The signs are the same. The product will be positive.
Write the numbers in vertical format, lining up the numbers on the right. \begin{array}{r}4.075 \\\times 3.9 \\\hline\end{array}
Multiply the numbers as if they were whole numbers, temporarily ignoring the decimal points. \begin{array}{r}4.075 \\\times \, \, 3.9 \\\hline 36675 \\\text{12225} \, \, \, \\\hline 158925\end{array}
Place the decimal point. Add the number of decimal places in the factors (1+3). Place the decimal point 4 places from the right.

\begin{array}{rl}4.075 & \text{3 places} \\ \underline{\times \, \, 3.9} &\text{1 place} \\ 36675 \\ \underline{\text{12225} \, \, \, }\\\color{cyan}{\underbrace{\color{black}{158925}}} & \text{4 places} \end{array}
The product is positive. (3.9)(4.075)=15.8925

 

EXAMPLE 5.16

Solution
  (-8.2)(5.19)
The signs are different. The product will be negative.
Write in vertical format, lining up the numbers on the right.  \begin{array}{r}5.19 \\\times 8.2 \\\hline\end{array}
Multiply.  \begin{array}{r}5.19 \\\times 8.2 \\\hline 1038 \\\text{4152 } \, \, \\\hline 42558\end{array}
Place the decimal point 3 places from the right.

 \begin{array}{r}5.19 \\\times 8.2 \\\hline 1038 \\\text{4152 } \, \, \\\hline 42.558\end{array}
The product is negative.  (-8.2)(5.19)=-42.558

 

EXAMPLE 5.17

  (0.03)(0.045)
The product is positive.  
Write in vertical format, lining up the numbers on the right. \begin{array}{r}0.045 \\\times 0.03 \\\hline\end{array}
Multiply. \begin{array}{r}0.045 \\\times 0.03 \\\hline 135\end{array}

The decimal point must be 5 places from the right.

Add zeros as needed to get the 5 places.
The product is positive. (0.03)(0.045) = 0.00135

 

TRY IT 5.29

27.4815

 

TRY IT 5.30

87.6148


TRY IT 5.31

-13.427

 

TRY IT 5.32

38.122


TRY IT 5.33

0.00348



TRY IT 5.34

0.00603