Using Significant Digits Science 1206-Physics Using Significant Digits

Rules for Determining the Number of Significant Digits : Any non-zero number Ex. 517, 51.7 and 5.17 all have 3 sig figs Any zero between non-zero numbers Ex. 0.05057 , 5057 and 56.50 all have 4 sig figs Any trailing zeros after a decimal Ex. 0.050570 , 5057.0 and 56.500 all have 5 sig figs Any trailing zeros before a decimal if the value is a known measurement Ex. 100 has 1 sig fig while 100. has 3

EXAMPLES Example: Number of Significant Figures: 0.0070 2 50 1 6200. 4 0.0006003 60093 5 5.30 3 5500

Using Significant Digits Addition/Subtraction When adding and subtracting, the answer must have the same number of decimal places as the measured value with the fewest decimal places Ex: 1.2 mm + 3.05 mm + 7.60 mm 2.01 - 3.4 Find the sum (or difference), then round to the correct number of sig figs.

Continued… Multiplication/Division Don’t forget the rules for rounding! Multiplication/Division When multiplying or dividing, the answer must have the same number of sig figs as the factor with the fewest sig figs Ex: Area of a triangle 3.2 cm 10.1 cm

Examples 75 - 3.5 + 4.7 = 13.63 h - 0.5 h = 465 km = 72.5 x 35.24 5.21 h 105

Sometimes have both: 1. 20.2 + 53.4 ÷ 10.0 2. (3.245)(2.05 – 13.6)

Scientific Notation: Numbers greater than 10 Numbers less than 1 Have a positive exponent the exponent is equal to the number of places that the decimal point has been moved to the left. Ex: 1340 Numbers less than 1 Have a negative exponent The exponent is equal to the number of places that the decimal point is moved to the right. Ex: 0.000 72

Many calculators enter it differently

Homework Pg 349 # 2, 3 (List # of sig figs), 4, 6 Will be checked and corrected tomorrow!!

Homework Check Pg 349 # 2, 3 (List # of sig figs), 4, 6

Continued… At times, we need to convert from small units to large units, and vice versa Convert 2000 km into m Convert 45 min into hours Convert 45346 s into hours Sometimes we can do them in our heads, but it is easy to make mistakes

Continued… Conversion Factors: To convert units, multiply the current number by a conversion factor (equality) Example: Change 19.5 min into hours. Step 1: Find the equality  60 min : 1 h Step 2: Convert the equality into a fraction  Step 3: Multiply it to convert the units 19.5 min x = Conversion Factor

Practice (Find the conversion factor first) 5.00 km to m 265 m to mm 4.7h to min 23.6h to s