How to Abbreviate Large Numbers
Large numbers are abbreviated by using scientific notation. In the book "Mathematics for Teachers," Thomas Sonnabend writes that mathematician Archimedes, who lived between 287 to 212 B.C., was the first person to abbreviate a number. He did this after attempting to quantify the grains of sand it would take to fill up the universe. He used an exponent. An exponent tells you how many times to multiply the base number against itself. Scientific notation uses exponents to abbreviate large numbers into equations.
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Instructions
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To the Left of the Decimal
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Imagine a very large number written out in full, or physically write it out on a piece of scratch paper. For example, write 5,400,000,000.
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2
Move the decimal point from the end of the number to the left to create a number that falls between one and 10. For example, 5,400,000,000 becomes 5.4.
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3
Count the number of places you needed to shift the decimal point to create the number between one and 10. In the example, you needed to move the decimal point nine spaces from the first significant digit, 5.
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4
Calculate the exponent that would add up to a billion after multiplying it nine times. Your exponent is 10. Ten multiplied by itself nine times equals a billion.
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5
Write the digit you created by moving the decimal point against the exponent, and you have the abbreviation of the number 5,400,000,000. Write your number as 5.4 x 10^9.
To the Right of the Decimal
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6
Write out a very small number in full. For example, for the number fifty-four hundred thousandths, write it out as 0.00054
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7
Transfer the decimal point from the beginning of the number to a place in the sequence that creates a number that falls between one and 10. For example, 0.00054 becomes 5.4.
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8
Calculate the number of places you had to shift the decimal point to create the new number. In the example, you needed to move the decimal point four spaces.
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9
Calculate the number that would need to be multiplied to get to the ten thousandth position in the number sequence. This is the first significant number in 0.00054 -- that is, 5. Your exponent is 10. Ten multiplied by itself negative four times equals a ten thousandth.
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10
Write the digit you created by moving the decimal point against the exponent, and you have the abbreviation of the number 0.00054. Write your number as 5.4 x 10^-4.
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1
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