Express the number in standard notation.
$9.427 \times 10^{-6}$
Answer (2)
To convert 9.427 × 1 0 − 6 to standard notation, move the decimal point 6 places to the left, resulting in 0.000009427 . This method accurately represents the small value in a more comprehensible format. Understanding scientific notation is essential for dealing with very large or very small numbers in mathematics.
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To convert 9.427 × 1 0 − 6 to standard notation, move the decimal point 6 places to the left.
Add zeros as needed to the left of the number.
Moving the decimal point 6 places to the left gives 0.000009427 .
The number in standard notation is 0.000009427 .
Explanation
Understanding the Problem We are given the number 9.427 × 1 0 − 6 in scientific notation and we want to express it in standard notation.
Converting to Standard Notation To convert from scientific notation to standard notation, we need to move the decimal point 6 places to the left because the exponent is -6. This means we will add zeros to the left of 9 as needed.
Writing in Standard Notation Starting with 9.427, we move the decimal point 6 places to the left: 1 place: 0.9427 2 places: 0.09427 3 places: 0.009427 4 places: 0.0009427 5 places: 0.00009427 6 places: 0.000009427 So, 9.427 × 1 0 − 6 = 0.000009427 .
Final Answer Therefore, the number 9.427 × 1 0 − 6 in standard notation is 0.000009427 .
Examples
Scientific notation is useful in many real-world scenarios. For example, in astronomy, the distance to a star might be 3.8 × 1 0 16 meters. In biology, the size of a bacterium might be 2.5 × 1 0 − 6 meters. Converting these numbers to standard notation helps us understand their magnitude in a more intuitive way. In this case, 2.5 × 1 0 − 6 meters is 0.0000025 meters, which is a very small number.
