Topic Approximations Estimated reading: 4 minutes 123 views Summary: Measurements can be rounded to a certain number of significant figures. Approximation- is a process of rounding numbers to a certain degree of accuracy. A number can be rounded to a certain required place value such as to the nearest ten, hundred, and thousandRounding Off NumbersRounding off Whole Numbers to Given Place ValuesRound off whole numbers to given place valuesSTEPSWhen rounding a number, stand at the digit of the required place value, then look at the next digit to the right; if it is or more, round up (i.e, increase the digit of the required place value by 1) and if it is or less, do not change the digit of the required place valueReplace all the remaining digits to the right of the required place value with the zerosExample 1The population of Tanzania in a census of 2002 was 42,850,671. Round this to the nearestmillionten millionSolutionThe million digit is 2, since the next digit to the right is greater than 5, then we can increase 2 by 1 and put the remaining digits to the right of 2 zeros. There fore;42,850,671 ≈ 43,000,000The ten million digit is 4, since the next digit to the right is less than 5, then we do not change 4 but we put the remaining digits to the right of 4 zeros. There fore;42,850,671 ≈ 40,000,000Decimals to a Given Number of Decimal PlaceRound off decimals to a given number of decimal placeSTEPSWhen rounding a decimal, stand at the digit of the required decimal place, then look at the next digit to the right; if it is or more, round up (i.e increase the digit of the required decimal by 1) and if it is or less, do not change the digit of the required decimal placeReplace all the remaining digits to the right of the required decimal place with the zerosNOTEThe first digit after the decimal point is the first decimal place, the second digit after the decimal point is the second decimal place e.t.cExample 0.568 is the first decimal place and is the second decimal placeExample 2Round 0.24736 to the nearest1 decimal place2 decimal places3 decimal placesSolution0.24736≈ 0.02 (1 d.p)0.24736≈ 0.025 (2 d.p)0.24736≈ 0.0247 (1 d.p)Significant FiguresSignificant figures of a number – are the significant digits, counted from left of the number.The first significant figure must be non-zero; following significant figures may take any value.A Number to a Given Number of Significant FiguresWrite a number to a given number of significant figuresIs the number of significant digits including 0 if it is between the first and the lastExamples13 – has two significant figures709.43 – has five significant figures0.0004001 – has four significant figuresSTEPSWhen rounding a number to a certain significant figure, stand at the digit of the required significant figure, then look at the next digit to the right; if it is or more, round up (i.e increase the digit of the required significant figure by 1) and if it is or less, do not change the digit of the required significant figureReplace all the remaining digits to the right of the required significant figure with the zerosExample 3Given the number 45.274 round to1 first significant figure2 significant figuresignificant figureSolution504545.3Example 4Round 146 400 to2 first significant figure4 significant figure3 significant figureSolution150 000146 400146 000Approximations in CalculationsThe Knowledge of Rounding Off of Numbers in Computations Involving Large Numbers and Small NumbersUse the knowledge of rounding off of numbers in computations involving large numbers and small numbersApproximation can be used in operation to check whether a calculation is correct or not, i.e in addition, subtraction, multiplication and divisione.g 446 x 45 = 20 070The above calculation can be checked quickly whether it is correct or not by rounding each number to 1 significant figure and then multiply i.e 400 x 50 = 20 000Therefore, the approximation of 20 000 is close to 20 0070 is correct.Before carrying an operation, each number in a calculation is rounded to 1 significant figureExample 5Find the approximate value ofExample 6A school trip of 32 people went to a tour, which costs a transport fee of 580/- each people. What was the approximate total transport cost?Solution32 × 580 ≈30×600 = 18 000The approximate transport cost was 18 000/-Tagged:ApproximationsForm 1MathematicsNotes Topic - Previous Units Next - Topic Geometry