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Chapter 5: Problem 6

Perform the indicated operations. $$-2.43 \div(0.3)$$

Short Answer

Expert verified
-8.1

Step by step solution

01

Write the problem in fractional form

To divide by a decimal, first convert the expression into a fraction. Write \(\frac{-2.43}{0.3}\).
02

Eliminate the decimals

Multiply both the numerator and the denominator by 10 to eliminate the decimals. This gives \(\frac{-2.43 \times 10}{0.3 \times 10} = \frac{-24.3}{3}\).
03

Perform the division

Divide the numerator by the denominator: \(-24.3 \div 3 = -8.1\).

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Fractional Form
When dealing with decimal numbers in division problems, it can be easier to convert the problem using fractions first. This helps in simplifying the calculations. To do this, take the original problem \(-2.43 \(\div\) 0.3\) and write it as a fraction: \(\frac{-2.43}{0.3}\). Converting the division to a fraction sets us up for the next steps, making the problem more manageable.
Eliminating Decimals
Decimals can make calculations tough, but we can get rid of them by multiplying both parts of our fraction by the same power of 10. Here, we multiply the numerator and the denominator by 10. In our example, this means \(-2.43 \(\times\) 10\) and \((0.3 \(\times\) 10\). This changes our fraction to \(\frac{-24.3}{3}\). Now, there are no more decimals, and the math becomes simpler.
Basic Arithmetic Operations
Once we've eliminated the decimals, we perform basic division to get our answer. With the new fraction \(\frac{-24.3}{3}\), we simply divide the numerator by the denominator. This means we calculate \(-24.3 \(\div\) 3\). Performing the division gives us a result of \-8.1\. So, \(-2.43 \(\div\) 0.3 = -8.1\). Breaking problems into manageable steps and converting decimals to fractions can make complex calculations much easier to handle, and mastering these steps is key to solving similar problems successfully.

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Most popular questions from this chapter

For Exercises \(35-42,\) multiply the numbers by the powers of 10 and \(0.1 .\) $$-80.2 \times 0.01$$

Divide. Round the answer to the indicated place value. Use the rounded quotient to check. $$237.1 \div 2.13 \text { tenths }$$

The batting averages for five legends are given in the table. Rank the players' batting averages from lowest to highest. (Source: Baseball Almanac) $$\begin{array}{|l|l|} \hline \text { Player } & \text { Average } \\ \hline \text { Joe Jackson } & 0.3558 \\ \hline \text { Ty Cobb } & 0.3664 \\ \hline \text { Lefty O'Doul } & 0.3493 \\ \hline \text { Ted Williams } & 0.3444 \\ \hline \text { Rogers Hornsby } & 0.3585 \\ \hline \end{array}$$

Suppose that Deanna owns 50 shares of stock in Company \(\mathrm{A}\), valued at \(\$ 132.05\) per share. She decides to sell these shares and use the money to buy stock in Company B, valued at \(\$ 27.80\) per share. Assume there are no fees for either transaction. a. How many full shares of Company B stock can she buy? b. How much money will be left after she buys the Company B stock?

Divide. Round the answer to the indicated place value. Use the rounded quotient to check. $$27.88 \div 2.46 \text { thousandths }$$
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