Scientific Notation- the VERY BIG - Grade 11...
Transcript of Scientific Notation- the VERY BIG - Grade 11...
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Scientific Notation- the VERY BIG and the very small
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Converting to Scientific Notation
Scientific notation is a way of easily and conveniently dealing with very large or very small numbers.
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Consider the mass of an electron:
0.000 000 000 000 000 000 000 000 000 000 910 kilograms
and the number of seconds in 1 year:
3,153,600,000 seconds
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The Very Large
Let's check out this number:
3,153,600,000 seconds
3.1536 x 10
31.536 x 10315.36 x 10
3153.6 x 10
31536 x 10
315360 x 10
3153600 x 10
31536000 x 10
315360000 x 10
31536000003.1536 x 10 x 10 x 10 x 10 x 10 x 10 x 10 x 10 x 10 =
= 3.1536 x 109
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The Very Small
0.000 000 000 000 000 000 000 000 000 000 910 kilograms
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Converting from Standard form to Scientific Notation
1) Find the decimal place.
2) Start at the left side of the number and put a box around the first number you come to. (This number will be between 1 and 9)
3) Put a new decimal point to the right of the box.
4) Rewrite this new number
5) Put a "x 10" after the new number
4) Count the number of places between the old decimal place and the new one.
5) Put this number as the exponent. (Remember + if you have to go to the left and - if you have to go right.)
0.000 000 000 000 000 000 000 000 000 000 910 kilograms
3,153,600,000 seconds
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What if the number already has an exponent?
347.66 x 104
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Try these:
a) 7, 960,000,000
b) 0.007485
c) 45.756
d) 998.6 x 102
e) 64.3 x 10-4
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Convert to standard form
3.65 x 104 seconds =
8.877 x 10 -3 metres =
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The numerical values we deal with in science represent measurements whose values are never known exactly.
CALCULATORS ARE STUPID
-Calculators treat the numbers we punch into them as "pure" mathematical entities.
-The result is that they frequently give answers that are physically ridiculous even though mathematically correct.
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CALCULATORS ARE STUPID!!
They do not ask if an answer makes sense.
That is your job!
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Significant Digits
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Important point:
-the concept of significant digits has less to do with mathematics than with our confidence in a measurement.
-When you measure something you are comparing it to something else.
-How many significant digits we have will depend on what we are measuring and what instrument we are using to do the measuring.
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• Number of significant figures = number of digits we are certain of plus one final uncertain digit.• Each measurement keeps only one uncertain digit.
Significant Digits or Significant Figures
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Significant Digits Rules
• All non-‐zero digits are significant.• All zeros between non-‐zero digits are significant.• Leading zeros in decimals are not significant.• Trailing zeros are significant if they are to the right of a decimal.• In numbers greater than 1, trailing zeros are not significant unless they are stated to be so.
Memorize These Rules
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• Try this addition. Do not use a calculator.5.4 m 3.45 m +0.656 m
??
Adding and Subtracting
What do you think the rule for Addition and Subtraction might be?
In each case the least significant digit is in red.
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• The sum or difference of an addition or subtraction equation is only as accurate as the least accurate measurement.
• In other words if a final uncertain digit is combined with a certain digit the result becomes uncertain itself.
• The answer to a calculation keeps only one uncertain digit.
Rules For Adding and Subtraction
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Try these:
1) 1.34 cm + 2.5 cm =
2) 34.557 m/s - 0.08 m/s =
3) 14.46 kg - 8 kg =
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• Try this multiplication. Do not use a calculator.14.25x6.43
Multiplication and Division
Can you think of the rule for multiplication?
The least significant digit is in red.
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• The resultant (i.e. product in our example) is only as accurate as the factor with the least number of significant digits.
• In other words if the final uncertain digit is multiplied or divided by a certain digit the result becomes uncertain.
• Answers to calculations keep only one uncertain digit.
Rules For Multiplication and Division
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Try these:
1) 7.64 x .5 =
2) 154.778 ÷ .33 =
3) 6.54 x 102 x 3.00 =
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• If the number to be rounded off is greater than of equal to 5, the next digit is increased by 1.
• If the digit to be dropped is less than 5, the preceding digit remains the same.
• If the digits to be dropped are to the left of the decimal point and zeros are used as their replacements express your answer in scientific notation.
As a general rule only round off at the END of a series of calculations.
Rules For Rounding Off
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Distance between the Sun and Earth = 149,000,000,000 meters
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Size of a Hydrogen Atom = 0.000000000053 meters
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http://www.khanacademy.org/video/scientific-notation-1?playlist=Algebra%20I%20Worked%20Examples
http://www.khanacademy.org/video/scientific-notation-2?playlist=Algebra%20I%20Worked%20Examples
http://www.khanacademy.org/video/scientific-notation-3?playlist=Algebra%20I%20Worked%20Examples
Or just go to khanacademy.org and search through for scientific notation.
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