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Scientific Notation: A Review Physics 1st 6wks How wide is our observable universe? 210,000,000,000,000,000,000,000 miles (22 zeros) This number is written in decimal or standard notation. When numbers get this large, it is easier to write them in scientific notation. Scientific Notation A number is expressed in scientific notation when it is in the form a x 10n where 𝟏𝟎 > 𝒂 ≥ 𝟏 and n is an integer Write the width of the universe in scientific notation. 210,000,000,000,000,000,000,000 miles Where is the decimal point now? After the last zero. Where would you put the decimal to make the a comply with 𝟏𝟎 > 𝒂 ≥ 𝟏? Between the 2 and the 1 2.10,000,000,000,000,000,000,000. How many decimal places did you move the decimal? 23 When the original number is more than 1, the exponent is positive. The answer in scientific notation is 2.1 x 1023 1) Express 0.0000000902 in scientific notation. Where would the decimal go to make the number before the power of ten be 𝟏𝟎 > 𝒂 ≥ 𝟏? (Note: Preserve all non-zero numbers as well as any sandwiched zeroes between them) 9.02 The decimal was moved how many places? 8 When the original number is less than 1, the exponent is negative. 9.02 x 10-8 Write 28750.9 in scientific notation. 1. 2. 3. 4. 2.87509 x 10-5 2.87509 x 10-4 2.87509 x 104 2.87509 x 105 2) Express 1.8 x 10-4 in decimal (aka “standard”) notation. 0.00018 3) Express 4.58 x 106 in decimal notation. 4,580,000 On the graphing calculator, scientific notation is done by hitting the button then the button (some have their own button 4.58 x 106 is typed 4.58 6 Scientific Notation on the Screen • When you use the EE feature to input the “x 10” portion of a scientific notation value in calculator it will be displayed as Which correctly depicts 0.016 or 1.6 x 10-2 • You can also type “10^” symbol in the calculator to replace the “x 10” portion and see this instead (but that’s up to you) • However if you used the ^ symbol by itself, and say this • You really typed 0.390625 instead of 0.016 4) Use a calculator to evaluate: 4.5 x 10-5 1.6 x 10-2 Type 4.5 -5 1.6 -2 You must include parentheses if you don’t use those buttons!! (4.5 x 10 -5) (1.6 x 10 -2) 0.0028125 Write in scientific notation. 2.8125 x 10-3 5) Use a calculator to evaluate: 7.2 x 10-9 1.2 x 102 On the calculator, the answer is: 6E -11 The answer in scientific notation is 6 x 10 -11 The answer in decimal/standard notation is 0.00000000006 6) Use a calculator to evaluate (0.0042)(330,000). On the calculator, the answer is 1386. The answer in decimal/standard notation is 1386 The answer in scientific notation is 1.386 x 103 7) Use a calculator to evaluate (3,600,000,000)(23). On the calculator, the answer is: 8.28 E +10 The answer in scientific notation is 8.28 x 10 10 The answer in decimal/standard notation is 82,800,000,000 Write (2.8 x 103)(5.1 x 10-7) in scientific notation. 1. 2. 3. 4. 14.28 x 10-4 1.428 x 10-3 14.28 x 1010 1.428 x 1011 Write in PROPER scientific notation. (Notice the number is not between 1 and 10) 8) 234.6 x 9 10 2.346 x 1011 9) 0.0642 x 104 6.42 x 10 2 Write 531.42 x 105 in scientific notation. 1. 2. 3. 4. 5. 6. 7. .53142 x 102 5.3142 x 103 53.142 x 104 531.42 x 105 53.142 x 106 5.3142 x 107 .53142 x 108 Going from scientific notation to decimal/standard notation – with a positive exponent • When you see a number in scientific notation like 9.87 x 104 the exponent will tell you how many times to move the decimal to the right to put it back into decimal notation • The positive exponent means the number is a “large number”, that is one that is not less than one. • Therefore 9.87 x 104 is equal to 98700 Write 8.04 x 105 in decimal notation. A. B. C. D. E. 804 8040 80400 804000 8040000 Going from scientific notation to decimal notation – with a negative exponent • When you see a number in scientific notation like 9.87 x 10-4 the exponent will tell you how many times to move the decimal to the left to put it back into decimal notation • The negative exponent means it is a “small” number, that is a number less than one. • Therefore 9.87 x 10-4 is equal to 0.000987 Write 8.04 x 10-2 in decimal notation. A. B. C. D. E. 804 80.4 0.804 0.0804 0.00804 An interesting situation… • When you see a number in scientific notation like 9.87 x 100 • The zero exponent means that the decimal point is not moved at all. • Therefore 9.87 x 100 is equal to 9.87 • There will virtually never be a reason why we would do that in Physics since we use Scientific Notation to express large numbers (especially those with large amounts of zeroes) in smaller, more manageable forms, but its cool to know it anyway!