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Chapter 4: Problem 92

Evaluate. $$ 6504 \div 100 $$

Short Answer

Expert verified
65.04

Step by step solution

01

Understand Division

Recognize that the division involves determining how many times 100 fits into 6504.
02

Simplify the Division by Removing Zeros

Since we are dividing by 100, we can simplify the calculation by moving the decimal point two places to the left. Essentially, dividing by 100 is the same as shifting the decimal point two places to the left in 6504.
03

Move the Decimal Point

Move the decimal point two places to the left in the number 6504. So, it becomes 65.04.
04

Write the Result

The result of dividing 6504 by 100 is 65.04.

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Key Concepts

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

Understanding Division
Let's start with the basic idea of division. Division is about splitting a number into equal parts. When we divide 6504 by 100, we're asking, 'How many times does 100 fit into 6504?' This process breaks down a large number into smaller, manageable pieces.
In simpler terms:
  • 6504 is the total amount we want to split.
  • 100 is the number of equal parts we want to create.
Understanding division helps us realize that it's just repeated subtraction or how many groups of the divisor (100) fit into the dividend (6504).
Shifting the Decimal Point
Now, let's make things easier by shifting the decimal point. When dividing by 100, notice that 100 ends with two zeros.
This means we can shift the decimal point two places to the left in the number 6504. Moving the decimal point left by two places simplifies the division without actually performing long division.
For example:
  • Starting with 6504, imagine a decimal point at the end: 6504.0.
  • Move the decimal point two places to the left: 65.04.
This technique saves time and makes calculations easier.
Simplifying Division
Finally, let's simplify our division. After shifting the decimal point, we now have 65.04 as the result of dividing 6504 by 100.
Simplifying division is crucial because:
  • It reduces large numbers to simpler forms.
  • Helps avoid potential mistakes in manual calculations.
In this scenario, shifting the decimal point was our method for simplifying. With 6504 divided by 100 turning into 65.04, we can say that simplifying helped us reach the answer quickly and accurately.
Always remember, simplifying through techniques like moving the decimal point is a great way to make division problems more manageable.

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Most popular questions from this chapter

Simplify by writing each expression with positive exponents. Assume that all variables represent nonzero real numbers. $$ \left(\frac{w z^{-5}}{w^{-3} z}\right)^{-2} $$

Simplify by writing each expression wth positive exponents. Assume that all variables represent nonzero real numbers. $$ \frac{\left(9^{-1} z^{-2} x\right)^{-1}\left(4 z^{2} x^{4}\right)^{-2}}{\left(5 z^{-2} x^{-3}\right)^{2}} $$

Fill in each blank with the correct response. In the term \(4 x^{6},\) the coefficient is _____ and the exponent is _____.

Match each number written in scientific notation I with the correct choice from Column II. Not all choices in Column II will be used. (I) (a) \(4.6 \times 10^{-4}\) (b) \(4.6 \times 10^{4}\) (c) \(4.6 \times 10^{5}\) (d) \(4.6 \times 10^{-5}\) (II) A. \(46,000\) B. \(460,000\) C. \(0.00046\) D. \(0.000046\) E. \(4600\)

Our system of numeration is called a decimal system. In a whole number such as 2846 each digit is understood to represent the number of powers of 10 for its place value. The 2 represents two thousands \(\left(2 \times 10^{3}\right),\) the 8 represents eight hundreds \(\left(8 \times 10^{2}\right),\) the 4 represents four tens \(\left(4 \times 10^{1}\right),\) and the 6 represents six ones (or units) \(\left(6 \times 10^{\circ}\right)\) \(2846=\left(2 \times 10^{3}\right)+\left(8 \times 10^{2}\right)+\left(4 \times 10^{1}\right)+\left(6 \times 10^{0}\right) \quad\) Expanded form $$ \text {Keeping this information in mind,} $$ Divide 2846 by \(2,\) using paper-and-pencil methods: \(2 \longdiv { 2 8 4 6 }\)
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