MATHEMATICS FORM 1 – APPROXIMATIONS msomimaktaba, November 11, 2018August 17, 2024 APPROXIMATIONSIs the process of rounding off a number in the given places in rounding makes numbers easier to deal with but at the same time reduces their accuracy.The methods used for approximation or rounding off numbers are decimal places and significant figures.ROUNDING OFF PROCEDURESi) If the first neglected digit is greater or equal to 5 the digit occupying the place value will increase by 1 unitii) If the first neglected number is less than five, then the number occupying the required place value will remain unchanged. ROUNDING OFF NUMBERSExamples1. Round off the following numbers to the nearest whole number. a) 3425 b) 7.283 c) 6.674 d) 0.625 e) 36.12 f) 5446 Solutions a) 3425≈ 3000 b) 7.283≈7c) 6.674≈7d) 0.625≈1 e) 36.12≈36 f) 5446≈5000 2. Round off the following toa) 1 decimal place. b) 2 decimal places. c) 3 decimal places. i) 23.7016 ii) 0.0094 Solutioni) 23.701623.7016≈23.7 to 1 decimal place.23.7016≈23.70 to 2 decimal place.23.7016≈23.702 to 3 decimal places. b) 0.0094 a) 0.0094≈0.0 to 1 decimal place.b) 0.0094≈0.001 to 2 decimal place.c) 0.0094≈0.009 to 3 decimal places. 3. Round off the following number to the nearesta) Whole numberb) Tenthc) Hundredth i. 0.625ii. 8.385 Solutioni. 0.625 a) 0.625≈1 to whole numbersb) 0.625≈0.6 to tenthc) 0.625≈0.63 to hundredths ii. 8.385 a) 8.385≈8 to whole numbersb) 8.385≈8.4 to tenth c) 8.385≈ 8.39 to hundredths Example: Round off 84678 toi) TensSolution84678 = 84700ii) HundredsSolution84678 = 85000iii) ThousandsSolution84678 = 80000Example: Round off 179999 correct to i) hundreds ii) Thousand iii) Tens iv )Ten thousandsSolutioni) 179999180000ii) 180000iii) 180000iv) 180000Significant Figures The are the total number of digits in the given number including zero’s which are in between non-zero digits. Notei) Zero is a significant figure when is in between two non – zero digitsii) When zero is an outcome of approximation (rounding off) where a 9 receives l and becomes ten, then zero of ten is a significant figure.Examples: determine the number of significant figures in the followingi) 20896100= There are six significant figuresii) 0.00025060= There are four significant figuresiii) 2.00008453= There are nine significant figuresExamples: Re write following numbers correcting to the required of significant figures.a. 0.23678 to 3 significant figuresSolution0.23678∴= 0.24b. 2.09478 to 3 significant figuresSolution2.09478∴= 2.09c. 0.009994 to 2 significant figuresSolution0.009994∴= 0.010d. 0.00931225697 to 7significant figuresSolutions0.00931225697∴= 0.0093123ExerciseRe write the following numbers correctly toa. 10.999009 to three significant figuresSolution10.999009∴= 11.0b. 705.4005 to six significant figuresSolution705.4005= 705.401C. 847910 to three significant figuresSolution847910∴= 848000Approximations in operationsWhen you want to check approximation whether a calculation is correct or not. Round each number in the calculation to 1 significant figure. Do the calculation mentally. Example: A group of 42 people go to the cinema, which cost 680/- each. What is the approximation total cost? Solution Round 42 to 40 and 680 to 700 Therefore 40 x 700 = 28,000/= Note: The exact cost is 28,560 The approximation is 28,000 which is close. ALL NOTES FOR ALL SUBJECTS QUICK LINKS:AGRICULTURE O LEVEL PURE MATHEMATICS A LEVELBAM NOTES A LEVELBASIC MATH O LEVELBIOLOGY O/A LEVELBOOK KEEPING O LEVELCHEMISTRY O/A LEVELCIVICS O LEVELCOMPUTER(ICT) O/A LEVELECONOMICS A LEVELENGLISH O/A LEVELCOMMERCE O/A LEVELACCOUNTING A LEVELGENERAL STUDIES NOTESGEOGRAPGY O/A LEVELHISTORY O/A LEVELKISWAHILI O/A LEVELPHYSICS O/A LEVELMOCK EXAMINATION PAPERSNECTA PAST PAPERS Basic Mathematics Study Notes Form 1 Basic Mathematics Study Notes Msomi Maktaba All Notes FORM 1MATHEMATICSPost navigationPrevious postNext postRelated Posts Book Keeping Study Notes BOOK KEEPING FORM ONE – INTRODUCTION OF BOOK KEEPING November 11, 2018May 7, 2020SUBJECT MATTER OF BOOK KEEPING Subject Matter of Book Keeping The Meaning of Book Keeping Define book keeping Book-keeping is an art of recording financial business transaction in a set of books in terms of money or money worth. 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