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Q A
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Multiply, using the shortcuts of scientific notation: (14 102) (20 10 5) 28 10 3 First, multiply the coefficients: 14 20 = 28 Next, add the exponents of the powers of 10: 102 10 5 = 102 + ( 5) = 10 3 Finally, join your new coefficient to your new power of 10: 28 10 3
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Q A
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Divide, using the shortcuts of scientific notation: (36 10 3) / (18 104) 20 10 7 First, divide the coefficients: 36 / 18 = 20 Next, subtract the exponent of the denominator from the exponent of the numerator: 10 3 / 104 = 10 3 4 = 10 7 Then, join your new coefficient to your new power of 10: 20 10 7
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Multiply (22 109) (50 10 4)
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Divide (93 10 5) / (31 102)
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Part I: Getting Cozy with Numbers, Atoms, and Elements
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Using scientific notation, multiply 52 0035
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Using scientific notation, divide 000809 / 203
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Using Exponential Notation to Add and Subtract
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Addition or subtraction gets easier when your numbers are expressed as coefficients of identical powers of 10 To wrestle your numbers into this form, you might need to use coefficients less than 1 or greater than 10 So, scientific notation is a bit too strict for addition and subtraction, but exponential notation still serves us well To add two numbers easily by using exponential notation, first express each number as a coefficient and a power of 10, making sure that 10 is raised to the same exponent in each number Then add the coefficients To subtract numbers in exponential notation, follow the same steps, but subtract the coefficients
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Q A
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Use exponential notation to add these numbers: 3,710 + 24 102 395 10 First, convert both numbers to the same power of 10:
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Next, add the coefficients: 371 + 24 = 395 Finally, join your new coefficient to the shared power of 10: 395 102
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371 102 and 24 102
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1: Noting Numbers Scientifically
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Q A
Use exponential notation to do this subtraction: 00743 00022 721 10 First, convert both numbers to the same power of 10:
743 022 = 721 Then join your new coefficient to the shared power of 10: 721 10 2
743 10 2 and 022 10 2 Next, subtract the coefficients:
Add 398 10 6 + 147 10 6
Subtract 7685 105 1283 105
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Using exponential notation, add 000206 + 00381
Using exponential notation, subtract 9,352 431
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Part I: Getting Cozy with Numbers, Atoms, and Elements
Distinguishing between Accuracy and Precision
Accuracy and precision precision and accuracy same thing, right Chemists everywhere gasp in horror, reflexively clutching their pocket protectors accuracy and precision are different! Accuracy describes how closely a measurement approaches an actual, true value Precision, which we discuss more in the next section, describes how close repeated measurements are to one another, regardless of how close those measurements are to the actual value The bigger the difference between the largest and smallest values of a repeated measurement, the less precision you have The two most common measurements related to accuracy are error and percent error Error measures accuracy, the difference between a measured value and the actual value: Actual value Measured value = Error Percent error compares error to the size of the thing being measured: |Error| / Actual value = Fraction error Fraction error 100 = Percent error Being off by 1 meter isn t such a big deal when measuring the altitude of a mountain, but it s a shameful amount of error when measuring the height of an individual mountain climber
A police officer uses a radar gun to clock a passing Ferrari at 131 miles per hour (mph) The Ferrari was really speeding at 127 mph Calculate the error in the officer s measurement 4 mph First, determine which value is the actual value and which is the measured value: Actual value = 127 mph; measured value = 131 mph Then calculate the error by subtracting the measured value from the actual value: Error = 127 mph 131 mph = 4 mph