Scientific Notation, Conversions and Significant Digits Learning Goals … … convert numbers to scientific notation … convert measurements using the metric system … identify the number of significant digits in a measurement

Try working on Practice Questions … Scientific Notation Ex) Convert the following to scientific notation: (a) 0.000053 = ______________________ (b) 40 000 000 = ____________________ (c) (2.63 x 10-9)(5.06 x 103) = ______________ Note: use the exponent button on your calculator EXP, E, EE 5.3 x 10-5 4.0 x 107 1.33 x 10-5 Try working on Practice Questions …

Practice Questions: Express the following numbers in scientific notation: 1003000000000 = _________________________ 0.0000000003998 = _________________________ 58.23 = _________________________ 0.2038 = _________________________ 12452 = _________________________ Express the following numbers to decimal notation: 1.77 x 107 = ________________________ 2.552 x 10-9 = _________________________ 1.18 x 103 = _________________________ 4.44 x 10-1 = _________________________ 1.399 x 100 = _________________________ Express the results of the following operations in scientific notation: 1.39 x 10-2 + 3.11 x 10-4 = _________________________ 1.17 x 104 - 3.57 x 102 = _________________________ (1.81 x 10-3) (1.06 x 1020) = _________________________ (5.77 x 10-4)  (1.71 x 10-11) = _________________________ 1.003 x 1012 3.998 x 10-10 5.823 x 101 2.038 x 10-1 1.2452 x 104 17700000 0.000000002552 1180 0.444 1.399 1.42 x 10-2 1.13 x 104 1.92 x 1017 3.37 x 107

Cubic units (m3, cm3, mm3) Vs. Capacity units (mL, L, kL) Volume Cubic units (m3, cm3, mm3) Vs. Capacity units (mL, L, kL) Cubic units can be converted to capacity units (and vice versa) using the following conversions: 1 cm3 = 1mL 1000 cm3 = 1000 mL = 1 L 1 m3 = 1000 L 1 m3 = (100cm)(100cm)(100cm) 1 m3 = 1000000 cm3 = 1000000mL 1 m3 = 1000 L

The Metric System: Convert the following: 3.15 m = __________ cm g) 15.5 mg = ____________ g 955 g = ___________ kg h) 1620 km = ___________ dm 1630 mL = _________ L i) 144 kg = _____________ mg 20.0 hg = __________ mg j) 0.0117 mm = __________ cm 178 mm = _________ cm k) 3450 cm3 = ____________ L 2000 L = ______ m3 l) 126 m3 = ____________ cm3 x 10 x 10 move decimal to the right  k (kilo) h (hecta) da (deca) unit d (deci) c (centi) m (milli) ÷10 ÷10  move decimal to the left 315 0.0155 0.955 16 200 000 1.630 144 000 000 2 000 000 0.00117 17.8 3.450 2 126 000 000

Significant Digits Non-zero digits are always significant. (eg) 22 ______ significant digits 22.3 ______ significant digits With zeros, the situation is more complicated: Zeros placed before other digits are not significant (place holders) (eg) 0.046 ______ significant digits (eg) 0.005487 g ______ significant digits Zeros placed between other digits are always significant. (eg) 20.64 L ______ significant digits (eg) 4009 kg ______ significant digits 2 3 2 4 4 4

Zeros that exist after the decimal place to demonstrate Zeros that exist after the decimal place to demonstrate accuracy are significant. (eg) 46.20 ______ significant digits (eg) 3.000 ______ significant digits Zeros that exist at the end of a number are significant only if they are behind a decimal point. If the zeros at the end of a number do not follow a decimal point, they are not significant (place holders) (eg) 382 000 ______ significant digits (eg) 382 000.0 ______ significant digits 4 4 3 7

Ex. 5 cats 10 chairs 60 min/h 1000m/km Measurement Certainty 522.3 cm sig digs 0.0250 cm 12 m/s 3.10 x 105 m/s 0.005 km 0.06070 m 4 3 3 2 1 4 If you have an exact value or defined value, the significant digits are infinite Ex. 5 cats 10 chairs 60 min/h 1000m/km

ROUNDING If the digit after the digit to be retained as significant is a greater than 5, round up If the digit after the digit to be retained as significant is a 4 or less, round down If the digit after the digit to be retained as significant is exactly 5: if the digit to be retained is odd, round up if the digit to be retained is even, round down Round the following to a whole number: 91.8  _______ d) 78.58  _______ 52.3  _______ e) 42.5  _______ 37.53  _______ f) 37.5  _______ 92 79 52 42 38 38

CALCULATIONS INVOLVING SIGNIFICANT DIGITS ADDITION AND SUBTRATION Precision Rule – Precision is defined as the place value of the last digit obtained from a measurement or calculation When adding or subtracting, the final answer has the same number of decimal places as the number with the least number of decimal places. The least number of decimal places is ____ (eg) 6.6 m + 18.74 m + 0.766 m = __________________ 1 26.1

Multiplication and Division When multiplying or dividing, the final answer must have the same number of significant figures as the original number with the fewest significant figures (we can’t be any more certain than we were to begin with) (eg) Calculate the volume of a box with sides measuring 5.05 cm, 3.87 cm and 4.7 cm V = (5.05 cm x 3.87 cm x 4.7 cm) = 91.85445 cm3 = 92 cm3

WS “Significant Digits” Complete any Practice Questions CAN I … … convert numbers to scientific notation … convert measurements using the metric system … identify the number of significant digits in a measurement HOMEWORK WS “Significant Digits” Complete any Practice Questions