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# Scientific Notation

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### Scientific Notation

1. 1. Scientific NotationImage Source: http://sphotos-a.xx.fbcdn.net
2. 2. Image Source: http://nerdsoftheroundtable.wordpress.comPowers of 10 Exponents, (called Scientific Notation), are used tospecify very large amounts, such as the distance between starsand Planets. Earth to Moon Distance is about 4 x 105km.
3. 3. Image Source: http://www.soest.hawaii.eduNegative Powers of 10 Exponents, (called Scientific Notation), areused to specify very small decimal amounts, such as the distancebetween Silicon atoms in a Silicon Crystal which is 2.35 x 10-10m.
4. 4. 1.496 x 108Image Source: http://www.inquisitr.com149 600 000 kmPower of 10 MagnitudeNumber between1 and 10 X
5. 5. Keep in mind at all times the following:1.496 x 108= 149 600 000Normal Numbers bigger than 1, or large numbers,always have a POSITIVE Power of 10.Values smaller than 1, usually decimal values,always have a NEGATIVE Power of 10.6.2 x 101= 626.234 x 10-1= 0.62342.31 x 10-3= 0.00231
6. 6. Move the Decimal Point eight to the RightMove the Decimal Point three to the Left.2.31 x 10-3= 0.002311.496 x 108= 149 600 000The Power of 10 value gives us key informationabout how many places to move theDecimal Point to make Number values.
7. 7. 1.5  104Scientific Notation involves moving decimals.1.5 0 0 0Because the exponent is Positive4, move the decimal point 4 placesto the right.Add in Zeroes to fill the empty gaps.5.8  10-40 0 0 0 5.8Because the exponent is a Negative4, move the decimal point 4 placesto the left.Add in Zeroes to fill the empty gaps.0.0005815 000====
8. 8. 2.756  105Scientific Notation involves moving decimals.2.7 5 6 0 0Because the exponent is Positive5, move the decimal point 5 placesto the right.Add in Zeroes to fill the empty gaps.3.76  10-30 0 0 3.76Because the exponent is a Negative3, move the decimal point 3 placesto the left.Add in Zeroes to fill the empty gaps.0.00376275 600====
9. 9. 7.74521  105Scientific Notation involves moving decimals.7.7 4 5 2 1Because the exponent is Positive5, move the decimal point 5 placesto the right.No Zeroes needed to fill empty gaps.6  10-30 0 0 6.Because the exponent is a Negative3, move the decimal point 3 placesto the left.Add in Zeroes to fill the empty gaps.0.006774 521====
10. 10. 1.5  1041 5 0 0 0The Number is Greater than 10,so the Exponent will be Positive.15 000=Move the Decimal point to the LEFTto create a number between 1 and 10.Remove Zeroes that are not needed.1.5 0 0 0=We moved 4 places soPower of 10 is four : 104=4 places
11. 11. Does 1.5  104 15 000 ?=1.5  1041.5 0 0 0Because the exponent is Positive4, move the decimal point 4 placesto the right.Add in Zeroes to fill the empty gaps.15 000==It is a Good Idea to check all Scientific NotationAnswers by working backwards from the answerto the Original given value we had at the start.Originally we started off with 15 000, so we are right!Our Answer to Question Original Starting Value
12. 12. 4.3  10-30 .0 0 4 3The Number is a decimal less than 1,so the Exponent will be Negative.0.0043=Move the Decimal point to the RIGHTto create a number between 1 and 10.Remove Zeroes that are not needed.0 0 0 4.3=We moved 3 places soPower of 10 is three : 10-3=3 places
13. 13. 5.0  10-30 .0 0 5 0The Number is a decimal less than 1,so the Exponent will be Negative.0.0050= Move the Decimal point to the RIGHTto create a number between 1 and 10.Remove Zeroes that are not needed.NEVER REMOVE ZEROES THATCAME AFTER A DECIMAL POINT.0 0 0 5.0=We moved 3 places soPower of 10 is three : 10-3=3 places
14. 14. 1  103 or 1031 0 0 0The Number is Greater than 10,so the Exponent will be Positive.1000=Move the Decimal point to the LEFTto create a number between 1 and 10.Remove Zeroes that are not needed.1.0 0 0=We moved 3 places soPower of 10 is three : 103=3 places
15. 15. 8  1008The Number is NOT Greater than 10,so the Exponent will NOT be Positive.8=8 is already a number between 1 and 10.so we move the decimal ZERO places.There are no Zeroes that need removal.8=We moved 0 places soPower of 10 is zero : 100=
16. 16. Express 3.45 x 106 as a number value.On the calculator, scientific notation isdone with the or button.3.45 x 106 is typed as 3.45 6and appears as 3.45*10^6 or 3.45E6x10nx10nPressing “enter” gives : 3 450 000