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Numbers that are extremely large or extremely small are easier to work with and understand when they are written in scientific notation.
The first number in a scientific notation is the coefficient and it must be greater than or equal to 1 but less than 10.
The second number in a scientific notation is the base and it is always base 10 with an exponent.
To rewrite a number into scientific notation move the decimal to the first digit and leave off the zeroes. To find the exponent on the base, count the number of places left or right to the end of the number. If the decimal moves right, the exponent will be negative. If the decimal moves left, the exponent will be positive.
3,000,052 = 3.000052 * 10^6
.0000648 = 6.48 * 10^-5
5,100,000 = 5.1 *10^6
Move the decimal point until you end up with a whole number less than 10. Then write times 10 raised to the power of however many decimal places you moved. If you moved to the left, its a positive power. If you moved to the right, its a negative power.
3,000052 = 3.000052 x 10^6
.0000648 = 6.48 x 10^-5
5,100,000 = 5.1 x 10^6
3,000052 = `3.000052 xx 10^6`
.0000648 = `6.48 xx 10^-5`
5,100,000 = `5.1 xx 10^6`
3.000052 * 10^6
6.48 * 10^-5
Any number expressed in the form (n.ddd---)x10^m, where
n is coefficient with value 1 to 9
d is any digit having value 0 to 9
and m is the exponent (to the base 10) and is any number positive or ngative but not zero
to convert any number to scientific notation move the decimal point to left or right so that you get only one number (n) to the left of decimal point.
The positions of decimal moved to the left gives the positive value of exponent whereas the positions of decimal moved to the right gives the negative value of exponent.
Now coming to numbers:
3,000052 has no decimal point shown and hence it lies to the left of the rightmost digit. It has to be moved 6 positions to the right to get one number to the left. Hence
3,000052 = 3.000052x10^6
.0000648 has a decimal in the left most position and has to be moved to the right 5 positions to the right to get one number (6) to the left of the decimal point. Hence
.0000648 = 6.48x10^-5
5,100,000 has a decimal point to the left of the last zero on the right and has to be moved 6 positions to the left so as to get 5 on the left of the decimal point. Hence
5,100,000 = 5.1x10^6
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