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Chapter 1: Problem 9

Write the following numbers in scientific notation and in E-notation. 39,900,000

Short Answer

Expert verified
In scientific notation: 3.99 x 10^7; in E-notation: 3.99E7.

Step by step solution

01

Identify Significant Figures

The number given is 39,900,000. To convert this into scientific notation, we first determine the significant figures. In this case, they are 3.99.
02

Determine the Exponent

Count how many places the decimal point needs to move to the left to place it where only one non-zero digit is to the left of the decimal. Moving it 7 places gives us 3.99.
03

Express in Scientific Notation

Express the number in the form \[a \times 10^n\] where \(a\) is a number between 1 and 10. Thus, 39,900,000 becomes \[3.99 \times 10^7\].
04

Convert to E-notation

Scientific notation can also be expressed in E-notation, which is often used in calculators and computer programs. In E-notation, the number 3.99 x 10^7 is written as 3.99E7.

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Key Concepts

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

Significant Figures
Significant figures are the digits in a number that contribute to its precision. These are important when representing a number in scientific notation.
For the number 39,900,000, the significant figures are 3.99. Here's how:
  • Ignore the trailing zeros because they don't add precision when trailing without a decimal point.
  • Focus on the non-zero digits and the zeros between them, which contribute to precision.
In 39,900,000, the significant figures identify the magnitude of the number. It helps in expressing the number as 3.99 in scientific notation.
Exponents
An exponent tells how many times a number, known as the base, is multiplied by itself. In scientific notation, the base is always 10.
For example, in the number 39,900,000 the exponent is determined by how many places the decimal moves:
  • Start with the number 39,900,000.
  • Move the decimal 7 places to the left to transform it into 3.99.
  • This movement of the decimal results in the exponent 7, as it indicates the base 10 is used seven times.
Thus, 39,900,000 can be expressed in scientific notation as 3.99 x 10^7, where 10^7 is the exponential component.
E-notation
E-notation is a simpler way to express numbers in scientific notation, especially useful in digital formats, like calculators.
It eliminates the need for writing 'x 10^' and uses 'E' to denote the power of 10.
For instance:
  • The scientific notation 3.99 x 10^7 converts to 3.99E7 in E-notation.
  • The 'E' signifies 'Exponent' and the number following it represents the power of 10.
E-notation is often favored in computing and programming because it's a straightforward way to handle very large or very small numbers consistently and without confusion.

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