Copyright, 1993 Dr. F.W. Boyle, Jr.

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Scientific numbers all have several things in common. 1) They represent relatively large or small real numbers. 2) The value in front of the decimal point is required to be between 1 and 9. 3) The sign of the exponent (power) of the 10 (ten) is for the purpose of converting the number from scientific notation back to the original number when necessary, i.e. adding or subtracting two numbers. The direction to move the decimal is to the right, adding zeros (0) as needed, when the sign is positive or absent and left, placing zeros (0) in front as needed when the sign is negative. 4) These numbers are always expressed as: a.bc x 10To figure the transformation from a real number into scientific notation, you must look carefully at the number being transformed.^{Y}where a, b, c are numbers and Y is a number representing the number of zeros (decimal places) that needed to be added to the left (-Y) or to the right (+Y or Y) to return the number to its more common form. An easy way to remember how to expand scientific notation is to look at the sign of the power. If the sign is negative (-Y), then write the number portion to the right and add zerosIN FRONTof the numbers. Then count from old decimal position toward the left to locate the new decimal point position. If the sign is positive (+Y or Y), write the number to the left and add zeros AFTER the number. Then count from the old decimal position toward the right to find the new decimal position. 5) a number which fits the format as shown in No. 4 is already in scientific notation and does not need transformation. 6) the exponent sign is negative if the decimal point position is moved to the right when going into scientific notation. The exponent sign is positive is the decimal point position is moved to the left going into scientific notation. These are the reverse of the moves discussed in No. 4 so be careful not to confuse which way the number is being transformed.

For example:

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One (1) place 123456.7Two (2) places 12345.67

Three (3) places 1234.567

Four (4) places 123.4567

Five (5) places 12.34567

Six (6) places 1.234567

Rewrite the number as a power of 10 (ten) using the new
number and adding the **x 10** portion as is shown below.

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One (1) place 00.00001234567Two (2) places 000.0001234567

Three (3) places 0000.001234567

Four (4) places 00000.01234567

Five (5) places 000000.1234567

Six (6) places 0000001.234567

Rewrite the number as a power of 10 (ten) using the new
number and adding the **x 10** portion as is shown below.

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Try the following numbers for practice in changing numbers into the scientific notation format.

A) 987.88 B) 0.00203 C) 1.005 D) 15432 E) 0.0003 F) 111.1 G) 0.00000001 H) 2.135