## Standard Form

### Standard form is a way of representing a number in a concise and consistent format

Standard form is a way of representing a number in a concise and consistent format. In mathematics, standard form refers to the representation of numbers using powers of 10. It allows us to express large or small numbers in a more manageable and uniform way.

In standard form, a number is written in the form of A × 10^n, where A is a number greater than or equal to 1 and less than 10, and n is an integer. The number A is called the coefficient or mantissa, while n represents the power of 10 to which it is multiplied.

For example, let’s consider the number 731,000. In standard form, it can be written as 7.31 × 10^5. Here, the coefficient A is 7.31, which is between 1 and 10, and the exponent n is 5.

Standard form is particularly useful when dealing with very large or very small numbers, such as those encountered in scientific notation or exponential growth/decay problems. It provides a compact representation and allows for easier comparison and arithmetic operations.

To convert a number to standard form, you need to determine the coefficient and the exponent. Start by moving the decimal point in the original number until you have a number between 1 and 10. The number of places you move the decimal point will determine the value of the exponent. If you move the decimal point to the left, the exponent becomes positive, and if you move it to the right, the exponent becomes negative.

Here’s an example:

Let’s convert the number 0.0000254 to standard form:

1. Move the decimal point to the right until you have a number between 1 and 10. In this case, we need to move it 5 places to the right.

0.0000254 becomes 2.54

2. Determine the exponent based on the number of places you moved the decimal point. Since we moved it 5 places to the right, the exponent becomes -5.

Therefore, in standard form, 0.0000254 can be written as 2.54 × 10^(-5).

Remember, standard form allows for consistent and concise representation of numbers, making them easier to work with in mathematical calculations.

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