Can you express correctly 0.000 1465 in scientific notation as?

Scientific notation is a way of expressing very large or very small numbers in a concise and standardized format. In scientific notation, a number is written in the form of “a x 10^b,” where “a” is a number between 1 and 10, and “b” is an integer representing the power of 10.

In the case of the number 0.000 1465, it can indeed be expressed in scientific notation. To do so, we first move the decimal point to the right until there is only one nonzero digit to the left of the decimal. This results in 1.465 x 10^-4, where “a” is 1.465 and “b” is -4.

Understanding Scientific Notation: A look at 0.000 1465

Let us delve deep into the world of scientific notation, a handy tool utilized by scientists, mathematicians, and students worldwide to express large or minute numbers with precision and simplicity. Our key focus will be to understand if the number 0.000 1465 can be accurately expressed in scientific notation.

What is Scientific Notation?

To begin, understanding scientific notation is essential. It is a mathematical approach used to denote numbers that are either too large or too small to be written practically in standard decimal notation. Significant figures are a crucial element of this approach, which can make working with numbers, especially in scientific computations, considerably easier.

The format of a number in scientific notation is a product of a number between 1 and 10 (including 1 but excluding 10) and a power of 10. It carries the format a × 10^b, wherein ‘a’ is a number, or a significand, between 1 and 10, and ‘b’ is the exponent indicating the actual place of the decimal point.

Conversion to Scientific Notation: Process

To convert a number into scientific notation involves moving the decimal point to a position where there’s only one non-zero digit left before the decimal. You then count the places moved, and this forms your exponent, ‘b’.

If you’re moving the decimal point to the right, as in small decimals, the exponent ‘b’ will be negative. Conversely, if you’re moving the decimal point to the left like in large numbers, the exponent ‘b’ will be positive.

Expressing 0.000 1465 in Scientific Notation

Now, let’s take a closer examination of the number 0.000 1465 and whether it can be accurately expressed in scientific notation.

When we follow the conversion rules as discussed above, we move the decimal point four places to the right, which yields the number 1.465. This implies an exponent of -4 because the decimal has been relocated to the right. Therefore, the scientific notation for 0.000 1465 is 1.465 × 10^-4.

Verifying Accuracy in the Conversion

The act of converting a number to scientific notation should not change its inherent value. Thus, to verify the accuracy of our conversion, if we perform the reverse process on our obtained scientific notation, we should regain the original number, 0.000 1465.

Executing this, 1.465 × 10^-4 essentially moves the decimal point of 1.465 four places to the left, as indicated by the negative exponent. And surely, this gives us the original value 0.000 1465.

Therefore, we can confidently proclaim that yes, the number 0.000 1465 can be correctly and accurately expressed in scientific notation as 1.465 × 10^-4.

Understanding methodologies such as these, aided by real examples, only serves to better comprehend and appreciate the scientific disciplines and mathematical procedures we employ, elevating our proficiency and fluency in these fields.

The number 0.0001465 can be correctly expressed in scientific notation as 1.465 x 10^-4.

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