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Chapter 5: Problem 97

Convert to scientific notation. $$ 0.000000603 $$

Short Answer

Expert verified
6.03 \times 10^{-7}

Step by step solution

01

Identify the Decimal Point

Locate the decimal point in the number. For the given number, the decimal point is at the start before the first significant digit: 0.000000603.
02

Move the Decimal Point

Move the decimal point to the right of the first non-zero digit. For 0.000000603, move the decimal point 7 places to the right to get: 6.03.
03

Determine the Exponent

Count how many places the decimal was moved. Since the decimal point was moved 7 places to the right, the exponent will be -7.
04

Write in Scientific Notation

Combine the significant figure and the exponent to form the number in scientific notation. This gives: \[ 6.03 \times 10^{-7} \].

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Key Concepts

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

decimal point
Understanding the decimal point is essential when working with scientific notation. The decimal point separates the whole number part of a number from the fractional part. For instance, in the number 0.000000603, the decimal point is located just before the first digit.
To convert such a number into scientific notation, you need to move the decimal point to the first non-zero digit. This ensures the number is written in a more manageable format.
For our specific example, moving the decimal point gives us the significant figure 6.03.
significant digits
Significant digits are the digits that carry meaning contributing to a number's precision. They include all digits except:
  • Leading zeros
  • Trailing zeros when they are merely placeholders.
In the number 0.000000603, the significant digits are 603 because they are the digits that tell us the precision of the measurement.
When writing in scientific notation, we focus on these significant digits. This means that 0.000000603 becomes 6.03 in scientific notation, emphasizing the meaningful figures.
exponent
The exponent in scientific notation shows how many times the decimal point is moved to place it after the first non-zero digit.
In our example, moving the decimal point 7 places to the right gives us 6.03. Since we are increasing a smaller number, the exponent will be negative.
Thus, the number is represented as \[ 6.03 \times 10^{-7} \].
This indicates that you must move the decimal point 7 places back to the left to return to the original number 0.000000603.

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