Discussion (Magnitude of a Measurement)Fact 1: The number 10n, for arbitrarily large positive integer n, is a big number in the sense that given a number M (no matter how big it is) there is a power of 10 that exceeds M.
Fact 2: The number 10-n, for arbitrarily large positive integer n, is a small number in the sense that given a positive number M (no matter how small it is), there is a (negative) power of that is smaller than M.
Discussion (Scientific Notation)
A positive, finite decimal s is said to be written in scientific notation if it is expressed as a product d x 10n where d is a finite decimal so that 1 ≤ d < 10, and n is an integer.
The integer n is called the order of magnitude of the decimal d x 10n
Consider the estimated number of stars in the universe: 6 × 1022. This is a 23-digit whole number with the leading digit (the leftmost digit) 6 followed by 22 zeroes. When it is written in the form 6 × 1022, it is said to be expressed in scientific notation.
The finite decimal 234.567 is equal to every one of the following:
However, only the first is a representation of in scientific notation.
Are the following numbers written in scientific notation? If not, state the reason.
Let’s say we need to determine the difference in the populations of Texas and North Dakota. In 2012, Texas had a population of about 26 million people and North Dakota had a population of about 6.9 x 104.
Let’s say that we need to find the combined mass of two hydrogen atoms and one oxygen atom, which is normally written as H2O or otherwise known as “water.”
Let M = 993, 456, 789, 098, 765. Find the smallest power of 10 that will exceed M.
The chance of you having the same DNA as another person (other than an identical twin) is approximately 1 in 10 trillion (one trillion is a 1 followed by 12 zeros). Given the fraction, express this very small number using a negative power of 10.
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