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Chapter 2: Problem 29

Write as ordinary numbers: \(109 ; 1026 ; 3.6 \times 10^{13}\) \(5.9 \times 10^{-8}\)

Short Answer

Expert verified
109, 1026, 360,000,000,000,000, 0.000000059

Step by step solution

01

Understand the Number Types

Identify that the numbers include ordinary numbers (109 and 1026) and numbers in scientific notation (\(3.6 \times 10^{13}\) and \(5.9 \times 10^{-8}\)).
02

Writing Ordinary Numbers

Recognize that 109 and 1026 are already in ordinary form and require no conversion.
03

Convert Scientific Notation to Ordinary Number (Positive Exponent)

For \(3.6 \times 10^{13}\), move the decimal point 13 places to the right to get 360,000,000,000,000.
04

Convert Scientific Notation to Ordinary Number (Negative Exponent)

For \(5.9 \times 10^{-8}\), move the decimal point 8 places to the left to get 0.000000059.

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Key Concepts

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

Understanding Ordinary Numbers
Ordinary numbers are numbers we commonly use in everyday life, exactly as they appear. These numbers are not in any special format like scientific notation and can be whole numbers or decimals. When someone asks you to write a number in its ordinary form, it means you should represent it as it is typically used, without using exponents. For example:
  • 109 is already an ordinary number.
  • 1026 is also an ordinary number.
There is no need to do any further conversion as they are already in their simplest form.
Working with Positive Exponents in Scientific Notation
Scientific notation is a way of expressing very large or very small numbers more concisely. When dealing with scientific notation, a positive exponent indicates a large number. For example, in the case of the number \(3.6 \times 10^{13}\):
  • The positive exponent (13) tells us to move the decimal point 13 places to the right.
  • Start with the number 3.6. Adding 13 zeros to the right, you'll get 360,000,000,000,000.
This technique allows you to easily understand and write large numbers without writing countless zeros. Scientifically, it provides clarity and simplicity in calculations and data representation.
Exploring Negative Exponents in Scientific Notation
In scientific notation, a negative exponent signifies a very small number. It creates an opposite effect compared to positive exponents. Consider the number \(5.9 \times 10^{-8}\):
  • The negative exponent (-8) indicates we need to move the decimal point 8 places to the left.
  • Starting with 5.9, shift the decimal point left, which results in 0.000000059.
This adjustment accounts for many zeroes in numbers smaller than one, enabling clearer mathematical computation and interpretation. Furthermore, negative exponents are particularly useful in chemistry and physics where measurements can be exceedingly small.

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