Presentation on theme: "Significant Digits and Scientific Notation"— Presentation transcript:
1 Significant Digits and Scientific Notation SNC 1DY
2 Learning GoalsBy the end of today’s lesson, you will be able to count sig figs and express the appropriate amount of sig figs in a mathematical answerBy the end of today’s lesson, you will be able to convert standard notation to scientific notation, and vice versa
3 Significant Digits (Sig figs) In science, we make quantitative observations – observations that require numbers and measurements.All measurements have a certain amount of uncertainty associated with them
4 1) Significant Digits in Measurement The number of significant digits in measurement is defined as all certain digits plus the first uncertain (or estimated) digit.
5 The measured value has three certain digits (1, 5, and 6) and one uncertain digit (5, or is it 4 or 6?). We say that the measurement has four significant digits.
6 Significant Figure Rules ExampleSignificant Figures1. Nonzero digits are always significant1.2544 sig. fig.2. Leading zeros (zeros before any nonzero digits) are NOT significant3 sig. fig.3. Embedded zeros are significant305.045 sig. fig.4. Zeros’ behind the decimal point are significant124.005 sig fig
7 State the number of significant figures in each of the followings: MeasurementS.F.967ebf. 9.3cgd. 5h. 8.21
8 Rules for Sig Figs In Mathematical Operations Multiplying and Dividing NumbersIn a calculation involving multiplication or division, the number of significant digits in an answer should equal the least number of significant digits in any one of the numbers being multiplied or divided.Ex. 9.0 x 9.0 =8.1 x 101, while 9.0 x 9 and 9 x 9 = 8 x 101
9 Rules for Sig Figs In Mathematical Operations Adding and Subtracting NumbersWhen quantities are being added or subtracted, the number of decimal places (not significant digits) in the answer should be the same as the least number of decimal places in any of the numbers being added or subtracted.e.g = 4.0
10 Sig Fig Practice #2CalculationCalculator says:Answer3.24 m x 7.0 m22.68 m223 m2100.0 g ÷ 23.7 cm3g/cm34.22 g/cm30.02 cm x cmcm20.05 cm2710 m ÷ sm/s237 m/slb x ftlb·ft5873 lb·ft1.030 g ÷ 2.87 mLg/mL2.96 g/mL
11 Sig Fig Practice #3CalculationCalculator says:Answer3.24 m m10.24 m10.2 m100.0 g g76.27 g76.3 g0.02 cm cm2.391 cm2.39 cm713.1 L LL709.2 Llb lblblb2.030 mL mL0.16 mL0.160 mL
12 Scientific NotationA method used to express really big or really small numbers. Consist of two parts:2.34 x 103The first part of the number indicates the number of significant figures in the value.The second part of the number DOES NOT count for significant figures.This number is ALWAYS between and 10The 2nd part is always 10 raised to an integer exponent
13 How its Done1. Place the decimal point between the first and second whole number, and write ‘x 10’ after the number.e.g. For 12345, it becomes 1.2 x 10e.g. For , it also becomes 1.2 x 102. Indicate how many places you moved the decimal by writing an exponent on the number 10.a) A move to the left means a positive move.e.g. For 12345, it becomes 1.2 x 104b) A move to the right means a negative move.e.g. For , it becomes 1.2 x 10-4
14 Success Criteria Answer questions on pg. 74 – 77 of Extensions Package Answer questions on pg. 8 – 10 of Handout