what is the number in scientific notation 0.000013

Natashya

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26-12-2024

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Scientific notation is a powerful tool for expressing very large or very small numbers concisely. It's particularly useful in fields like science and engineering where dealing with extremely tiny or gigantic values is commonplace. Let's explore how to convert the number 0.000013 into scientific notation.

Understanding Scientific Notation

Scientific notation expresses a number in the form a x 10^b, where 'a' is a number between 1 and 10 (but not including 10), and 'b' is an integer (whole number) representing the power of 10.

Converting 0.000013 to Scientific Notation

To convert 0.000013 to scientific notation, follow these steps:

1. Identify the coefficient (a): We need to move the decimal point to the right until we have a number between 1 and 10. In this case, moving the decimal point five places to the right gives us 1.3. Therefore, our coefficient (a) is 1.3.

2. Determine the exponent (b): We moved the decimal point five places to the right. Since we moved it to the right, the exponent (b) will be -5. Moving the decimal point to the right signifies a negative exponent because we are effectively dividing by powers of 10.

3. Write the number in scientific notation: Combining the coefficient and exponent, we get 1.3 x 10^-5.

Therefore, 0.000013 in scientific notation is 1.3 x 10^-5.

Examples of other numbers in scientific notation:

• Large Numbers: The distance from the Earth to the Sun (approximately 93,000,000 miles) is written as 9.3 x 10⁷ miles. Notice how the exponent is positive because the number is greater than 1.

• Small Numbers: The size of a bacterium (approximately 0.000001 meters) is represented as 1 x 10^-6 meters. Here, the negative exponent reflects the small size.

Why Use Scientific Notation?

• Conciseness: It simplifies the representation of very large or small numbers. Imagine trying to write out Avogadro's number (6.022 x 10²³) without scientific notation!

• Clarity: It avoids ambiguity and makes it easier to compare magnitudes of numbers.

This process can be applied to any number, big or small, making scientific notation an indispensable tool for scientists, engineers, and anyone working with numbers of varying scales. Remember to always keep your coefficient between 1 and 10 and adjust your exponent accordingly.