Answer:-
Scientific notation is a concise way of representing very large or very small numbers in mathematics and scientific fields. It is particularly useful when dealing with numbers that have numerous digits, making it easier to handle and comprehend such values. In scientific notation, a number is expressed as a product of a coefficient and a power of 10. This format simplifies complex numbers, allowing for easier calculations and comparisons. In this article, we will explore how to express 78 million in scientific notation.
Scientific notation follows a standardized format: N x 10^M, where N represents the coefficient, and M denotes the exponent of 10. The coefficient N is always a number greater than or equal to 1 and less than 10. The exponent M can be positive or negative, indicating whether the number is very large or very small, respectively. For example, the number 78 million can be expressed in scientific notation as 7.8 x 10^7.
To represent 78 million (78,000,000) in scientific notation, we follow these steps:
Step 1: Identify the coefficient (N)
The coefficient (N) is the first non-zero digit in the original number. In the case of 78 million, the coefficient is 7.8.
Step 2: Determine the exponent (M)
The exponent (M) represents the power of 10 required to convert the original number into scientific notation. To find M, count the number of places you move the decimal point from its original position to create a number between 1 and 10. In this instance, 78 million is written as 7.8 x 10^7, so the decimal point moves seven places to the left to create 7.8.
Step 3: Combine the coefficient and exponent
The scientific notation for 78 million is the coefficient multiplied by 10 raised to the power of the exponent: 7.8 x 10^7.
Conclusion:
In conclusion, scientific notation provides a convenient and standardized way to express large or small numbers, such as 78 million. By writing numbers in the form N x 10^M, where N is a number between 1 and 10 and M is the appropriate exponent, we can represent unwieldy values like 78 million in a compact and easily manageable format.
The scientific notation for 78 million is 7.8 x 10^7. It is important to remember that scientific notation is not only useful in mathematical and scientific fields but also in everyday life situations where dealing with very large or very small numbers is common. By mastering scientific notation, we can better communicate and comprehend such numbers, making complex calculations and comparisons much more straightforward.
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