Scientific Notation
Aim: How do we express a number using scientific notation?
Scientific notation (exponent) is a method used to express a number as the product of two factors without changing its value. The first factor is a number that is bigger than 1 and less than 10, while the second factor is a power of 10. For example, 1.70000 can be expressed as 1.7 x 10^5.
When expressing a number in scientific notation, significant figures become more clear, as the ambiguity as to the significant figures is removed.
Scientific Notation Examples
1) 9.8485 can be expressed as 9.8485 x 10^0
2) 100,480 = 1.00480 x 10^5
3) 0.00125 = 1.25 x 10^-3
4) 0.00018 = 1.8 x 10^-4
Using scientific notation is particularly useful when dealing with very large or very small numbers. For example, 2.11 x 10^9 can be expressed as 2,110,000,000 while 5.6 x 10^-5 can be written as 0.000056.
Significant Figures and Scientific Notation
When determining significant figures and performing operations with scientific notation, it's important to consider the digits in a measurement that are known with certainty and one estimated value. All non-zero digits are significant, while zeros may or may not be significant depending on their placement in the number.
Accuracy and Precision
Accuracy refers to the ability to obtain the same results repeatedly, while precision is the ability to obtain results that are close to the actual value.
Scientific Notation Calculator and Converter
A scientific notation exponent calculator or converter can be a helpful tool when working with scientific notation, significant figures, and performing operations with numbers expressed in scientific notation. These tools can simplify the process of working with very large or very small numbers, as well as determining significant figures and performing calculations accurately.
Overall, expressing numbers in scientific notation removes ambiguity as to the significant figures and allows for clearer representation of very large or very small numbers, making complex calculations and measurements more manageable.
