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Chapter 4: Problem 40

Divide. $$ \frac{83.57}{10} $$

Short Answer

Expert verified
8.357

Step by step solution

01

- Understanding Division by 10

When dividing a number by 10, the decimal point in the number shifts one place to the left.
02

- Apply the Division Rule

Take the number 83.57 and move the decimal point one place to the left. So, 83.57 becomes 8.357.
03

- Verify the Result

Double-check the calculation to ensure that the decimal point was moved correctly. 83.57 divided by 10 is indeed 8.357.

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Key Concepts

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

Understanding the Decimal Point
When dealing with numbers, the decimal point separates the integer part from the fractional part. Understanding how it works is crucial for mathematical operations, especially division.

For instance, in the number 83.57, '83' is the integer part and '57' is the fractional part. When we divide by powers of 10, such as 10, 100, or 1000, the position of this decimal point changes.
For division by 10, the rule is simple: move the decimal point one place to the left. In our exercise, shifting the decimal point in 83.57 one place to the left changes the number to 8.357.
Division Rules: Shifting the Decimal Point
Understanding the division rule for dividing by 10 is key for quick and accurate calculations.

The main rule is that for any number, dividing by 10 shifts its decimal point one place to the left. Consider the number 83.57:
  • Original number: 83.57
  • Shift decimal one place left -> New number: 8.357

It鈥檚 similar for other powers of 10:
  • Dividing by 100 shifts the decimal point two places left.
  • Dividing by 1000 shifts it three places left.

Moving the decimal point accurately ensures correct results, no matter how large or small the number.
Verification of the Result
Always double-check your work to ensure your calculations are correct. Verification is an essential step in mathematics.

To verify our division of 83.57 by 10:
  • First, we moved the decimal one place left, resulting in 8.357.
  • To check, multiply 8.357 by 10:
  • 8.357 脳 10 = 83.57
So our result 8.357 is indeed correct.
By retracing your steps or reversing the operation (as with multiplication), you can confirm the accuracy of your division.

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Most popular questions from this chapter

A construction worker is paid \(\$ 18.50\) per hour for the first \(40 \mathrm{hr}\) of work, and time and a half, or \(\$ 27.75\) per hour, for any overtime exceeding 40 hr per week. One week she works 46 hr. How much is her pay?

Add. $$ \begin{array}{r} 13.72 \\ 9.112 \\ 6542.7908 \\ +\quad 23.901 \\ \hline \end{array} $$

Estimate. Indicate which of the choices is an appropriate estimate. \(914 \div 0.921\) a) 10 b) 100 c) 1000 d) 1

After-School Supplies. Elijah wants to buy 35 boxes of crayons at \(\$ 1.89\) per box for the after-school program that he runs. Estimate the total cost of the crayons.

Add. $$ \begin{array}{r} 4203.28 \\ +\quad 3.39 \\ \hline \end{array} $$
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