1/27/09

Post date: Jan 26, 2009 9:29:54 PM

Bell Ringer: Why do we use significant digits in science?

    • Arithmetic with scientific notation

      • In order to add or subtract, we must first have common exponents for the x 10^n .

        • If n's are the same for each, add or subtract the M values and keep the "x 10^n" at the end

        • If n's are different, move the decimal in the M value until you have a common n for each, then add or subtract the M's.

      • To multiply

        • Multiply the M values to get the M for your product

        • Add the n values to the get the n for your product

      • To divide

        • Divide your M values to get the M for your quotient

        • Subtract your n values to get the n for your quotient

      • Pages 18-19: 7-10 in your notebook for practice

    • Significant Digits

      • Related to precision of the measuring tool

      • Page 23 - picture describing need for significant digits

      • Rules

        1. Non-zero digits are ALWAYS significant

        2. All final zeroes after the decimal are significant

        3. Zeroes between other significant digits are significant

        4. Zeroes used only for spacing the decimal are NOT significant

      • Example problems

        1. 251.38 --> All are non-zeroes, so 5 sig digs

        2. 1001 --> Two zeroes are between sig digs, so 4 sig digs

        3. 0.00240 --> 2 and 4 are sig., final zero after decimal is sig, other zeroes are only spacing the decimal, so 3 sig digs

    • Do page 24: 12-13 (only a-c for each)

      • Scientific notation ONLY shows sig digs (eliminates 0 confusion)

        • e.g. 251.30 --> 2.5130 x 10^2

        • e.g. 1001 --> 1.001 x 10^3

        • e.g. 0.00240 --> 2.4 x 10^-3

    • For the problems you did earlier, write each number in scientific notation

    • Operations with significant digits

      • Addition or subtraction

        • Round to the same decimal as the least precise measurement

        • e.g. 1.2 + 3.41 + 12.02 = ?

          • 1.2 is rounded to the tenths place, so answer must be rounded to tenths place

          • 1.2+3.41+12.02=16.63, but rounded to the tenths is 16.6

      • Multiplication or Division

        • Answer has same number of sig digs as the measurement with the fewest sig digs

        • e.g. 3.0 x 14.125

          • 3.0 has 2 sig digs, 14.125 has 5 sig digs, so answer must have 2 sig digs

          • 3.0 x 14.125 = 42.375

          • round to 2 sig digs, so answer is 42

    • Do page 25: 14-17

        • Add to previous problems

        • Due Wednesday, 1/28/09