Express the number in standard notation.
$8.4 \times 10^{-6}$
Answer (2)
To convert 8.4 × 1 0 − 6 to standard notation, we move the decimal six places to the left. This results in the value 0.0000084 . Thus, the number in standard notation is 0.0000084 .
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We are given the number 8.4 × 1 0 − 6 in scientific notation.
To convert to standard notation, we move the decimal point 6 places to the left.
Adding leading zeros as needed, we get 0.0000084.
Therefore, the number in standard notation is 0.0000084 .
Explanation
Understanding Scientific Notation We are given a number in scientific notation, 8.4 × 1 0 − 6 , and we want to express it in standard notation. Scientific notation is a way of writing very large or very small numbers in a compact form. Standard notation is the usual way we write numbers.
Converting to Standard Notation To convert from scientific notation to standard notation, we need to move the decimal point in the number 8.4 to the left by 6 places, because the exponent of 10 is -6. Moving the decimal point to the left corresponds to dividing by powers of 10.
Moving the Decimal Point Starting with 8.4, we move the decimal point 6 places to the left. This means we will need to add some leading zeros:
1 place: 0.84 2 places: 0.084 3 places: 0.0084 4 places: 0.00084 5 places: 0.000084 6 places: 0.0000084
So, 8.4 × 1 0 − 6 = 0.0000084 .
Final Answer Therefore, the number 8.4 × 1 0 − 6 in standard notation is 0.0000084.
Examples
Scientific notation and standard notation are useful in many real-world applications. For example, in science, the size of a bacteria might be 2 × 1 0 − 6 meters, which is 0.000002 meters. In finance, very small interest rates or very large sums of money are often expressed using scientific notation to make them easier to read and understand. Understanding how to convert between scientific and standard notation helps us to work with these numbers effectively.
