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Chapter 4: Problem 27

Write each number in standard notation. 2.3 \times 10^{2}

Short Answer

Expert verified
The number 2.3 脳 10^2 written in standard notation is 230.

Step by step solution

01

Understanding Scientific Notation

Scientific notation is a way of expressing numbers that are too large or too small to be conveniently written in standard form. Here, the number is 2.3 脳 10^2. The base number is 2.3 and the exponent is 2.
02

Conversion to Standard Notation

To convert the number to standard notation, we move the decimal point in the base number to the right by the number of places indicated by the exponent. In this case, since the exponent is 2, we move the decimal in 2.3 two places to the right.
03

Writing the Result

With the decimal point moved two places to the right, the base number becomes 230. Hence, 2.3 脳 10^2 in standard notation is 230.

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Key Concepts

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

Standard Notation
Standard notation is the regular way of writing numbers without using exponents. It鈥檚 how we typically see numbers in everyday life. For example, the number three hundred is written as 300 in standard notation. Utilizing standard notation makes it easier to understand and compare numbers, especially when dealing with practical situations, such as counting objects or measuring distances.

By converting numbers from scientific notation to standard notation, you can visualize and use these numbers effectively in real-world applications without the complexities of exponential terms.
Exponents
Exponents are used to express repeated multiplication of a number by itself. They are written as a small number (the exponent) to the upper right of the base number. For instance, in the expression \(10^2\), 10 is the base, and 2 is the exponent, which means 10 multiplied by itself: 10 脳 10 = 100.

In scientific notation, exponents help simplify long numbers by showing how many times the base number is multiplied. Understanding exponents is crucial as they transform large and small figures into a manageable format.
Decimal Point Movement
The concept of moving the decimal point is key to converting scientific notation to standard notation. To perform this conversion, look at the exponent on the base 10. For instance, in \(2.3 \times 10^2\), the exponent is 2.

This tells you to move the decimal point in the number 2.3 two places to the right:
  • First move: 2.3 becomes 23.
  • Second move: 23 becomes 230.


Always remember:
  • If the exponent is positive, move the decimal to the right, making the number larger.
  • If negative, move it to the left, making the number smaller.
Understanding how to move the decimal based on the exponent allows for accurate conversions from scientific to standard notation.

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Most popular questions from this chapter

Graph the function \(f(x)=-x^{2} .\) What do you discover?

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