Estimation & Approximation

Estimation & Approximation

• 1.
  Estimation & approximationBTEOTSSSBAT:Useestimation to check answers
• 2.
  Write numbers to1, 2or 3 significant figuresKey termsApproximationEstimationSignificant figures
• 3.
  Write approximations forthese numbers18.910.2102.417210051779.30.45
• 4.
  Significant figuresThe firstsignificant figure of a number is the first non-zero number from the left.Here the 5 is the first significant figure0.0541054And here the 1 is the first significant figureZeros are only non-significant if they are sandwiched between tow other numbers
• 5.
  0.0740.074Find the firstsignificant figure (7)Look a the next number 4 – if it is 5 or more increase the 7, if it is less than five leave the 7 alone 0.07So 0.074 to 1 sig fig is 0.07
• 6.
  704704Find the firstsignificant figure (7)Look a the next number 0 – if it is 5 or more increase the 7, if it is less than five leave the 7 alone. It’s not a decimal so all the other digits need to be zeros to keep the place value700So 704 to 1 sig fig is 700
• 7.
  0.0760.076Find the firstsignificant figure (7)Look a the next number 6 – if it is 5 or more increase the 7, if it is less than five leave the 7 alone 0.08So 0.076 to 1 sig fig is 0.08
• 8.
  751751Find the firstsignificant figure (7)Look a the next number 5 – if it is 5 or more increase the 7, if it is less than five leave the 7 alone. 800So 751 to 1 sig fig is 800
• 9.
  Write these numbersto 1 significant figure18.92010.210102.41001722001005100020001779.30.50.45
• 10.
  To round to2 significant figures:Ignore all the zeros at the beginning
• 11.
  Find the secondsignificant figure from the left
• 12.
  If the numberto the right is 5 or more, increase the second number by 1
• 13.
  Turn all theother digits to the right to zero.For exampleRound 2684 to 2 significant figuresThere are no zeros at the beginning
• 14.
  Find the secondsignificant figure from the left: The second significant figure is 6 2684The number to its right is 8, which is greater than 5, so increase 6 by 1 to make 7
• 15.
  Turn all theremaining digits to zero Answer2684 to 2 significant figures is 2700.
• 16.
  Another way oflooking at it is to decide if 2684 is nearer to 2700or 26002684260027002650
• 17.
  Writing numbers to1 significant figure can help with checking answers and with estimatingFor exampleCalculate:48 x 10252.4Using a calculator:4896 = 93.43511…. 52.4 Estimating – using 1 sig. fig.:48 x 102 = 52.4 50 x 100 = 50100Check
• 18.
  Writing numbers to1 significant figure can help with checking answers and with estimatingFor exampleCalculate:5.4x 192.4Using a calculator: 102.6 = 42.752.4 Estimating – using 1 sig. fig.:105 x 20= 250Check
• 19.
  Now try theseEstimate:140x 192.1Estimate:540x 1.923.9Estimate:1040x 19248
• 20.
  ExampleRound 0.00854 to2 significant figuresIgnore the zeros at the beginning
• 21.
  The second significantfigure is the 50.00854The number to the left is 4, which is less than 5, so keep the 5 as a 5
• 22.
  The 4 tothe left becomes as zero
• 23.
  So write 0.00854.Answer0.00854to 2 significant figures is 0.0085