Significant Figures and Rounding of Numbers :Significant Figures and Rounding of Numbers


Significant Figures :Significant Figures Units that reflect the accuracy of a number. Integers 1-9 are always significant. If a 0 is a placeholder then it is not a significant figure (ex:5,000- the 5 is the only significant figure) The only way a 0 significant is by it being sandwiched by two other numbers (ex:505) When a 0 is the last digit of an accurate measurement, then it is a significant figure. Zero’s are usually dropped from a decimal place if a number is rounded to 0.


Check your Knowledge*Significant Figures* :Check your Knowledge*Significant Figures* How many significant figures appear in this problem? 8,000,000,000 Answer- There is one significant figure which is the 8. The following zero’s denote unmeasured units. Round this number to two significant figures. 24,765 Answer- 25,000- The second integer is followed by a 7, which is higher than 5 automatically raising the 4 to a 5 and replacing the rest of the integers with 0’s.


Rounding of Numbers :Rounding of Numbers How to Round Numbers Select the numbers to be retained based on the potential for accuracy. Examine the first digit to be dropped. This is the first number to the right of the retained number. If the first digit to be dropped is less than 5, the retained number is unchanged. If the first digit to be dropped is a 5, round down when the retained number is odd. If a decimal place is rounded up to a 0, drop the 0.


Check your KnowledgeRounding Numbers :Check your KnowledgeRounding Numbers Round 9.351 to two significant figures. The answer is 9.4 because the first digit is a 5 and the retained number is odd. The retained number is therefore increased by 1 unit. Round 1.9582 to four significant figures. The answer is 1.958 because the 2 that was dropped is less than 5.


Test Yourself-Rounding Off :Test Yourself-Rounding Off Round the following number to three significant figures… 8.057 Answer: 8. 06


Test Yourself- Significant Figures :Test Yourself- Significant Figures How many significant figures is in the next figure? 505 Answer :three


Signification Figures and Mathematical Operations :Signification Figures and Mathematical Operations


Objectives :Objectives How to eliminate inaccuracies introduced during Mathematical Operations by rounding off figures. How to determine the significant figures in a Product or quotient Sum or difference


Methods :Methods During multiple steps of a long mathematical operations, each intermediate answer should be rounded to retain one more significant figure than the final answer. The product or quotient of an operation should have as many significant figures as the least accurate number in the equation. The sum or difference of an operation should have the same number of significant decimal places as the least accurate number of the operation.


Examples :Examples 1. 2.45 x 251 = 615 Example of resolution : 2.45 x 251 = 614.95 2.45 is the least accurate number and it has three significant figures. Therefore, product of the operation should have three significant figures. The final answer is 615. 2. 35.64 + 74406 = 74,442 Example of resolution 35.64 + 74406 = 74,442.64 74406 is the least accurate number and it has no decimal places, so the answer must be rounded. 3. 27.356 – 5.58 = 21.78 Calculator Enter 2.45 Press x Enter 251 Press = Answer


Conclusion :Conclusion It is important to know how to round off numbers. This will help eliminate errors in doses of radiopharmaceuticals given to patients.


Powers and Exponents :Powers and Exponents


Objective :Objective If a number is multiplied by itself a set number of times , then it can be expressed in terms of powers or exponent. Example: 4 x 4 x 4 This can be expressed in a simpler form: 43 and the input in the calculator without all the tedious repetitive pressing of numbers.


Example :Example 3 x 3 x 3 x 3 x 3 Would be 3 to the number of times it appears which 5…..so it equals 35


Using the calculator :Using the calculator This could be put in the calculator as Press the “3” the original number Press the “ Ʌ” Press the “5” which is the exponent. It looks like 3^5 Press “=“ and the answer is 243.


Example 2 :Example 2 What is 2 x 2 x 2 x 2 x 2 Write as 25 and input as 2^5. Answer is 32.


Conclusion :Conclusion The expressing of numbers in terms of powers and exponents makes it easier to do calculations and to input into a calculator.c


SCIENTIFIC NOTATION :SCIENTIFIC NOTATION


OBJECTIVE :OBJECTIVE The objective of scientific notation is to make the very large or small numbers easy to record and handle. Example: 0.00000034 = 3.4 x 10ˉ 7


Example 1 :Example 1 Example: 0.00000034 = 3.4 x 10ˉ 7 First step is to move the decimal point to the left until there is only one digit in the front of the decimal. Then count the space the decimal was moved. (This number will be the exponent value). Finally, rewrite the number.


Calculator :Calculator Scientific notation can be checked if correct on a calculator. Simply follow these instructions…… Example: 2.9 x 10-5 = 0.000029 1) Enter value 2) Press the EE key or the exponent key 3) Change the sign to negative(if necessary) 4) Finally, press = for the answer


Question #1 :Question #1 Convert 0.00000075 to scientific notation. Answer: The decimal point is moved to the right 7 times, therefore: 7.5 x 10-7


Question #2 :Question #2 Convert 2,456,000,000 in scientific notation. Answer: The decimal point is moved 9 times to the left, therefore: 2.456 x 109


Conclusion :Conclusion By using scientific notation we can do calculations involving large numbers without all the cumbersome imput of digits.


Works Cited :Works Cited Wells, P. (1999). Practical Mathematics in Nuclear Medicine Technology. Reston: Society of Nuclear Medicine. page 6