Taking into account the definition of Scientific notation, the correct way to write the distance in scientific notation is option B. 4.217×10⁵ km.
First of all, scientific notation is a quick way to represent a number using powers of base 10. This notation is used to be able to express very large or very small numbers very easily.
The numbers are written as a product:
a×10ⁿ
where:
- a is a real number greater than or equal to 1 and less than 10, to which a decimal point is added after the first digit if it is a non-integer number.
- n = a whole number, which is called an exponent or an order of magnitude. Represents the number of times the point decimal is shifted. It is always an integer, positive if it is shifted to the left, negative if it is shifted to the right.
In this case, to write the number 421,700 in scientific notation, the following steps are performed:
- The decimal point is moved to the left as many spaces until it reaches the right of the first digit. This number will be the value of a in the previous expression. Then a = 4.21700= 4.217
- The base 10 is written with the exponent equal to the number of spaces that the decimal point moves. This is a positive number because the decimal point is shifted to the left, and it will have a value of n = 5.
So, the correct way to write the distance in scientific notation is option B. 4.217×10⁵ km.
Learn more about scientific notation:
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