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Chapter 2: Problem 77

What is the quotient of 48.05 and \(10^{2} ?\)

Short Answer

Expert verified
The quotient of 48.05 and \(10^{2}\) is 0.4805.

Step by step solution

01

Simplify the Denominator

Simplify \(10^{2}\) by multiplying 10 by itself, which results in 100.
02

Division

Now, divide 48.05 by 100. This can be done by moving the decimal two places to the left.

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Key Concepts

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

Decimal Division
Decimal division involves dividing numbers where one or both are decimals. Decimals have a decimal point, which is a crucial part to understand in division. When you divide a decimal by a whole number or another decimal, you need to line up the numbers by the decimal point. This helps to maintain order and accuracy during calculations.
To divide decimals:
  • Align the numbers by their decimal points.
  • If you are dividing by a decimal, multiply both numbers by the same power of ten to make the divisor a whole number.
  • Perform the division as you would with whole numbers.
  • Place the decimal point in the quotient directly above the decimal in the dividend.
Moving the decimal is easier when you understand how powers of ten work, which is crucial in decimal division.
Place Value
Place value is a fundamental concept in mathematics and plays a significant role in decimal division. Each number has a position, or place value, depending on its placement relative to the decimal point.
To understand place value in decimals:
  • Each digit to the left of the decimal represents whole numbers: tens, hundreds, etc.
  • Each digit to the right of the decimal point represents fractional parts: tenths, hundredths, etc.
  • The position dictates its value, which is essential for accurate calculations.
In a division, you align numbers by decimal points because you're aligning their place values. If you misalign them, then the values can be misrepresented, giving an incorrect answer. Attention to place value ensures precision in decimal calculations.
Powers of Ten
Powers of ten are essential when performing operations like decimal division. They help simplify calculations by focusing on moving the decimal point. Understanding powers of ten makes manipulating numbers, especially in divisions, easier.
  • Powers of ten are expressed as exponents, like \(10^2\).
  • Each power increases the number of zeroes: \(10^1\) is 10, \(10^2\) is 100.
  • In division, dividing by \(10^n\) means moving the decimal point to the left "n" times.
So in this exercise, dividing \(48.05\) by \(10^2\), assessed as 100, requires moving the decimal two places to the left, simplifying this part of the calculation.
Quotients
A quotient is the result of division. In mathematical terms, it's what you get when one number is divided by another. Quotients can be whole numbers or decimals, depending on the division.
  • For whole number division, the quotient is also a whole number.
  • In decimal division, the quotient often includes decimals to show the exact value.
  • You place the decimal in the quotient directly above where it appears in the dividend once the division is complete.
In the given problem, dividing \(48.05\) by \(100\) results in \(0.4805\). Thus, \(0.4805\) is the quotient. Understanding the notion of a quotient is crucial for learning division deeply and accurately.

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