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1.8 x 10 1.8 x 10 Scientific notation can be used to write very large or very small numbers to be able to calculate them with a calculator. To write a number in scientific notation, write it as a product of two factors: (a decimal greater than or equal to 1 but less than 10) x (a power of 10). In other words there must be one non zero digit to the left of the decimal. Then count how many places the decimal was moved. That (number of places moved) is the exponent or power of 10. 180,000 becomes 4 5 1.8 x 10 1.8 x 10 3 6 1.8 x 10 1.8 x 10 180,000 becomes 1.8 x 105 because the decimal was moved five places.
1,800,000 becomes 4 5 1.8 x 10 1.8 x 10 3 6 4.53 x 10 4.53 x 10 1,800,000 becomes 1.8 x 106 because the decimal was moved six places. Remember count the places.
453,000 becomes
4 5 4.53 x 10 4.53 x 10 3 6 4.53 x 10 4.53 x 10 453,000 becomes 4.53 x 105 place because the decimal was moved five places.
453 becomes
4 1 4.53 x 10 4.53 x 10 2 3 4.53 x 10 4.53 x 10 453 becomes 4.53 x 10 to the 2nd place because the decimal was moved two places.
To write numbers between 0 and 1 in scientific notation, we use negative exponents. 0.004 becomes 4 x 10 to the negative third as the decimal was moved three places in a tiny direction.
0.000453 becomes -4 -1 4.53 x 10 4.53 x 10 -2 -3 4.53 x 10 4.53 x 10 0.000453 becomes 4.53 x 10 to the negative (a very small number) 4th power because the decimal moved four places before there was one non zero digit to the left.
0.00453 becomes -4 -1 4.53 x 10 4.53 x 10 -2 -3 4.53 x 10 4.53 x 10 0.00453 becomes 4.53 x 10-3 because the decimal moved three places before there was one non zero digit to the left.
0.453 becomes -4 -1 4.53 x 10 4.53 x 10 -2 -3 4.53 x 10 4.53 x 10 0.453 becomes 4.53 x 10 to the negative (a very small number) 1st power because the decimal moved only place before there was one non zero digit to the left.
0.0453 becomes -4 -1 4.53 x 10 4.53 x 10 -2 -3 4.53 x 10 4.53 x 10 0.0453 becomes 4.53 x 10-2 because the decimal moved two places before there was one non zero digit to the left.
0.0000453 becomes -4 -5 4.53 x 10 4.53 x 10 -2 -3 38,800 3,880 0.0000453 becomes 4.53 x 10-5 power because the decimal moved five places before there was one non zero digit to the left.
To change a number in scientific notation to standard form, reverse the process. Move the decimal to make it larger if the exponent is positive. Move the decimal to make is smaller if the exponent is negative. Remember a negative exponent is a faction/decimal.
3.88 x 102 becomes 388 38.8 38,800 3,880 To change a number in scientific notation to standard form, reverse the process. Move the decimal to make is larger if the exponent is positive. Move the decimal to make it smaller if the exponent is negative. Remember a negative exponent is a faction/decimal.
3.88 x 102 becomes 388 because the decimal moved two places to make it a larger number.
3.88 x 101 becomes... 388 38.8 38,800 3,880 To change a number in scientific notation to standard form, reverse the process. Move the decimal to make is larger if the exponent is positive. Move the decimal to make it smaller if the exponent is negative. Remember a negative exponent is a faction/decimal.
3.88 x 101 becomes... 38.8 because the decimal moved only one place larger (positive exponent).
3.88 x 104 becomes... 388 38.8 289,000,000 289,000 To change a number in scientific notation to standard form, reverse the process. Move the decimal to make it larger if the exponent is positive. Move the decimal to make it smaller if the exponent is negative. Remember a negative exponent is a faction/decimal.
3.88 x 104 becomes... 38,800 because the decimal moved four places larger (positive exponent).
2.89 x 106 2,890,000 28,900,000 289,000,000 289,000 2.89 x 108 2,890,000 28,900,000 289,000,000 289,000 2.89 x 106 2,890,000 28,900,000 289,000,000 289,000 2.89 x 105 2,890,000 28,900,000 0.00289 2890 2.89 x 10-3 0.289 0.0289 0.00289 2890 2.89 x 10-1 0.289 0.0289 0.00289 2890 2.89 x 10-2 0.289 0.0289 0.00289 2890 2.89 x 103 0.289 0.0289 |