Taking into account the definition of Scientific notation, the correct answer is the options C and D: 9.2×10⁻⁹ and 3.4×10⁻¹⁰ are less than 8.1×10⁻⁸.
Scientific notation
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 compare numbers in scientific notation, the number with the largest power of 10 is always the largest number.
If the powers of 10 are the same, then the number "a" should be compared.
Numbers that are less than 8.1×10⁻⁸
- 8.2×10⁻⁸: In this case, since the exponent is the same, the number "a" must be compared. Being 8.2>8.1, the number is greater than 8.1×10⁻⁸.
- 7.3×10⁻⁵: In this case, being the exponent -5>-8, then the number is greater than 8.1×10⁻⁸.
- 9.2×10⁻⁹: In this case, being the exponent -9<-8, then the number is less than 8.1×10⁻⁸.
- 3.4×10⁻¹⁰: In this case, being the exponent -10<-8, then the number is less than 8.1×10⁻⁸.
Finally, the correct answer is the options C and D: 9.2×10⁻⁹ and 3.4×10⁻¹⁰ are less than 8.1×10⁻⁸.
Learn more about scientific notation:
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