2.36x 10^-2 / 8.4x10^2 express in scientific notation

The 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.

To divide numbers in scientific notation, you must first divide the numbers that are not powers of 10, that is, the numbers a. And then you divide the powers of ten by subtracting the exponents.

This case

In this case, you have to divide 2.36×10⁻²÷ 8.4×10².

So, first of all, dividing 2.36 and 8.4 you get:

2.36÷ 8.4= 0.28

And subtracting the powers of both scientific numbers we get:

(-2) - (2)= -4

So, the scientific number obtained is:

0.28×10⁻⁴

Now convert 0.28 to scientific notation by moving the decimal point one place to the right and multiplying by 10⁻¹, which groups to the power of 10⁻⁴ using the Associative Property of Multiplication. This is:

2.8×10⁻¹×10⁻⁴

To multiply the powers of 10 you must add the exponents:

2.8×10⁻¹⁺⁽⁻⁴⁾= 2.8×10⁻¹⁻⁴= 2.8×10⁻⁵

Finally, 2.36×10⁻²÷ 8.4×10² results 2.8×10⁻⁵.

Learn more about scientific notation:
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