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 Form 2 Physics Notes PHYSICS FORM TWO TOPIC 1: STATIC ELECTRICITY November 6, 2018February 13, 2019Concept of Static Electricity The Concept of Static Electricity Explain the concept of static electricity Static electricity refers to the electric charges stored on a conductor. The Orign of Charges Explain the origin of charges When a plastic pen is rubbed with a cloth, it acquires the property of attracting… Read More Form 5 General Studies (GS) Study Notes Form 5 General Studies (GS) – INTRODUCTION TO GENERAL STUDIES November 7, 2018February 13, 2019INTRODUCTION TO GENERAL STUDIES What is general study? General study can be defined as a multi disciplinary Course drawing up and discussing content from different field of studies. It generally touches the contents from arts and science courses in disciplines like Biology, Geography, Sociology, Physics, Chemistry, Religions, Civics, Psychology, Philosophy… Read More Matokeo ya darasa la saba 2023 Mara – PSLE Results for Mara region in a Few Simple Steps February 2, 2024Now that the PSLE exam is over and for all regions in the country including Mara region and its districts such as Mara RS, Musoma MC, Bunda DC, Bunda Mji, Butiama DC, Rorya DC, Tarime DC, Tarime TC, Serengeti DC, Musoma DC, you might be wondering what your results are…. Read More Leave a Reply Cancel replyYour email address will not be published. Required fields are marked *Comment *Name * Email * Website Save my name, email, and website in this browser for the next time I comment. Δ
Form 2 Physics Notes PHYSICS FORM TWO TOPIC 1: STATIC ELECTRICITY November 6, 2018February 13, 2019Concept of Static Electricity The Concept of Static Electricity Explain the concept of static electricity Static electricity refers to the electric charges stored on a conductor. The Orign of Charges Explain the origin of charges When a plastic pen is rubbed with a cloth, it acquires the property of attracting… Read More
Form 5 General Studies (GS) Study Notes Form 5 General Studies (GS) – INTRODUCTION TO GENERAL STUDIES November 7, 2018February 13, 2019INTRODUCTION TO GENERAL STUDIES What is general study? General study can be defined as a multi disciplinary Course drawing up and discussing content from different field of studies. It generally touches the contents from arts and science courses in disciplines like Biology, Geography, Sociology, Physics, Chemistry, Religions, Civics, Psychology, Philosophy… Read More
Matokeo ya darasa la saba 2023 Mara – PSLE Results for Mara region in a Few Simple Steps February 2, 2024Now that the PSLE exam is over and for all regions in the country including Mara region and its districts such as Mara RS, Musoma MC, Bunda DC, Bunda Mji, Butiama DC, Rorya DC, Tarime DC, Tarime TC, Serengeti DC, Musoma DC, you might be wondering what your results are…. Read More