Answer:-
To express a number in scientific notation, we need to represent it as a product of a coefficient and a power of 10. In the case of 0.763, we can express it in scientific notation as follows:
0.763 = 7.63 × 10^(-1)
In scientific notation, the coefficient is always a number between 1 and 10 (inclusive) and the exponent represents the power of 10 by which the coefficient should be multiplied. In this case, the coefficient is 7.63, and the exponent is -1.
To understand how we arrived at this representation, let's break down the steps:
The coefficient should be a number between 1 and 10. To obtain it, we move the decimal point in 0.763 until we have a number between 1 and 10. In this case, we moved the decimal point one place to the right, resulting in 7.63.
The exponent represents the number of places we moved the decimal point in step 1. If we moved the decimal point to the right, the exponent is negative, indicating that the number is less than 1. In this case, we moved the decimal point one place to the right, so the exponent is -1.
Now that we have the coefficient and the exponent, we can express 0.763 in scientific notation as 7.63 × 10^(-1).
Scientific notation is a concise way of representing very large or very small numbers, making it easier to work with such values in mathematical calculations or scientific contexts. It allows us to express numbers using powers of 10, which simplifies arithmetic operations and helps us grasp the magnitude of a number more easily.
In the case of 0.763 expressed in scientific notation, we can see that the number is less than 1, as indicated by the negative exponent. The magnitude of the number is conveyed by the coefficient, which is 7.63. The exponent -1 tells us that the decimal point is located one place to the left of the coefficient.
By using scientific notation, we can effectively represent numbers with many decimal places or large orders of magnitude. It is commonly used in fields such as physics, chemistry, and astronomy, where working with very large or very small numbers is common.
In summary, the number 0.763 can be expressed in scientific notation as 7.63 × 10^(-1). This representation conveys the value of the number and its magnitude in a compact and standardized format, making it useful for mathematical calculations and scientific communication.
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