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A 40 000 in Scientific Notation

# 40 000 in Scientific Notation

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A recent viral math meme had people scrambling to figure out how much money that phrase is. That viral math meme was (ironically) calculated by a math teacher at a high school in Connecticut, just one of many jokes that happen every college application season, when the price of a college education skyrockets. This time, the joke is more consequential because it’s no longer a rare joke.

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When converting a number into scientific notation, we must remember a few rules. First, the decimal must be between the first two non-zero numbers. The number prior to the multiplication symbol is known as the significant or mantissa. The numbers of digits in the significant depends on the application and are known as significant figures. The significant figures calculator can assist in this situation. The value of the exponent depends on whether or not the decimal place is moved to the right or left to return to the original number. An example on how to convert a number into scientific notation is done in the next section.

Conversion between different scientific notation representations of the same number with different exponential values is achieved by performing opposite operations of multiplication or division by a power of ten on the significand and an subtraction or addition of one on the exponent part. The decimal separator in the significand is shifted x places to the left (or right) and x is added to (or subtracted from) the exponent, as shown below. (Source: en.wikipedia.org)

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A shorthand method of writing very small and very large numbers is called scientific notation, in which we express numbers in terms of exponents of 10. To write a number in scientific notation, move the decimal point to the right of the first digit in the number. Write the digits as a decimal number between 1 and 10. Count the number of places n that you moved the decimal point. Multiply the decimal number by 10 raised to a power of n. If you moved the decimal left as in a very large number, $n$ is positive. If you moved the decimal right as in a small large number, $n$ is negative.

Scientific notation, used with the rules of exponents, makes calculating with large or small numbers much easier than doing so using standard notation. For example, suppose we are asked to calculate the number of atoms in 1 L of water. Each water molecule contains 3 atoms (2 hydrogen and 1 oxygen). The average drop of water contains around $1.32\times {10}^{21}$ molecules of water and 1 L of water holds about $1.22\times {10}^{4}$ average drops. Therefore, there are approximately $3\cdot \left(1.32\times {10}^{21}\right)\cdot \left(1.22\times {10}^{4}\right)\approx 4.83\times {10}^{25}$ atoms in 1 L of water. We simply multiply the decimal terms and add the exponents. Imagine having to perform the calculation without using scientific notation! (Source: courses.lumenlearning.com)

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