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Chapter 5: Problem 16

Write each number in scientific notation. $$ 78,330 $$

Short Answer

Expert verified
7.8330 脳 10^4

Step by step solution

01

Identify the significant figures

Locate the digits that are the significant figures. For 78,330, the significant figures are 78330.
02

Place the decimal point

Place the decimal point after the first significant figure to rewrite the number. This gives: 7.8330
03

Count the decimal places moved

Determine how many places the decimal point has been moved to convert 78,330 to 7.8330. The decimal point has moved 4 places to the left.
04

Write in scientific notation

Combine the result from Step 2 with a power of 10, where the exponent is the number of places the decimal point has moved. This gives: 7.8330 脳 10^4

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Key Concepts

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

Understanding Significant Figures
Significant figures are the digits in a number that contribute to its precision. They include all non-zero digits, any zeros between significant digits, and trailing zeros in a decimal number.
In our example, the number 78,330 has five significant figures: 7, 8, 3, 3, and 0. Understanding which digits are significant is crucial for writing numbers in scientific notation.
Decimal Point Placement
The decimal point acts as the divider between the whole number part and the fractional part of a number. When converting a number into scientific notation, you must place the decimal point after the first significant figure.
  • For 78,330, the decimal point is moved to place it after the 7, making it 7.8330.
  • This process helps in rewriting large numbers into a more manageable format, aligning with the purpose of scientific notation.
Understanding how to correctly place the decimal point is essential for accurately representing numbers in scientific format.
Recognizing and Using Exponents
Exponents in scientific notation show how many times you need to multiply the base number by 10.
  • Starting from our example, once the decimal point is moved to create 7.8330, we count how many places it moved from the original number.

  • For 78,330, the decimal point moved four places to the left, therefore, the exponent is 4.
  • This means 78,330 can be written as 7.8330 脳 10^4.

Using exponents makes it easier to handle very large or very small numbers in calculations, making it a foundational tool in scientific and engineering fields.

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