/*! This file is auto-generated */ .wp-block-button__link{color:#fff;background-color:#32373c;border-radius:9999px;box-shadow:none;text-decoration:none;padding:calc(.667em + 2px) calc(1.333em + 2px);font-size:1.125em}.wp-block-file__button{background:#32373c;color:#fff;text-decoration:none} Problem 43 Divide. $$\frac{62.5}{0.3}$$... [FREE SOLUTION] | 91影视

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Chapter 5: Problem 43

Divide. $$\frac{62.5}{0.3}$$

Short Answer

Expert verified
208.3333

Step by step solution

01

Understand the problem

You are asked to divide 62.5 by 0.3. This involves dividing a decimal by another decimal.
02

Convert to whole numbers

To simplify the division, convert both the numerator (62.5) and the denominator (0.3) to whole numbers by multiplying both by 10. This changes the division from \(\frac{62.5}{0.3}\) to \(\frac{625}{3}\).
03

Perform the division

Now, divide 625 by 3 using long division or a calculator. \(\frac{625}{3} = 208.3333...\).

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Key Concepts

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

Division of Decimals
Dividing decimals might seem tricky at first, but it becomes straightforward once you understand the process. In the given exercise, we are asked to divide 62.5 by 0.3. This involves some simple steps. First, understand that you are dealing with two numbers that have decimal points. The key to solving this problem is to eliminate the decimal points temporarily, making the division easier. Once you have clear whole numbers, you can carry out the division as you normally would. Later, you can reintroduce the decimal point in the final answer if necessary.
Long Division
Long division is a method that helps you divide large numbers easily by breaking down the division process into a series of easier steps. In this exercise, after converting decimals to whole numbers, we are left with 625 梅 3. To perform long division:
  • Divide the first digit of the dividend by the divisor.
  • Write the quotient above the dividend.
  • Multiply the quotient by the divisor and subtract the result from the dividend.
  • Bring down the next digit and repeat until all digits have been divided.
In our case, 3 goes into 6 two times (2 * 3 = 6), bringing down the next digit to continue dividing. Going through this process, we get 208.3333... as the result.
Converting Decimals to Whole Numbers
Converting decimals to whole numbers is crucial when dealing with decimal division. In our example \(\frac{62.5}{0.3}\), we start by eliminating the decimals. To do this, multiply both the numerator (62.5) and the denominator (0.3) by 10. This action shifts each decimal one place to the right, resulting in whole numbers (625 and 3, respectively). This conversion simplifies the problem and allows us to use traditional division methods. Always remember:
  • Count how many places you need to move the decimal to get a whole number.
  • Apply the same movement to both the numerator and the denominator.
This approach will consistently simplify your decimal division tasks.

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Most popular questions from this chapter

For Exercises \(85-90,\) refer to the table. The table gives the closing stock prices (in dollars per share) for the first day of trading for the given month. $$\begin{array}{l|c|c|c|c|c} \text { Stock } & \text { January } & \text { February } & \text { March } & \text { April } & \text { May } \\ \hline \text { IBM } & \$ 97.27 & \$ 99.00 & \$ 92.27 & \$ 95.21 & \$ 103.17 \\\ \hline \text { FedEx } & \$ 109.77 & \$ 111.89 & \$ 114.16 & \$ 106.07 & \$ 106.11 \\ \hline \end{array}$$ By how much did the FedEx stock decrease between January and May?

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Latasha has a bicycle, and the wheel has a 22 -in. diameter. If the wheels of the bike turned 1000 times, how far did she travel? Use 3.14 for \(\pi .\) Give the answer to the nearest inch and to the nearest foot (1 \(\mathrm{ft}=12 \text { in. })\)

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