Scientific Notation and Significant Figures Accuracy and Precision

Scientific Notation and Significant Figures

Accuracy and Precision • Accuracy is the agreement between experimental data and a known value. • Basically how close it is to what it’s supposed to be (the bullseye) • Precision is how well experimental values agree with each other. • How often you can get a similar result

Accuracy vs Precision Data can be very precise, meaning each data point is close to the others, but have lots of error in its results

Scientific Notation • Makes it easier for us to write both large and small values

The number is written in two parts: • Just the digits (with the decimal point placed after the first digit), followed by • × 10 to a power that puts the decimal point where it should be (it shows how many places to move the decimal point). • Decimals can move in a positive OR negative direction • 533. 67 = 5. 3367 x 10^2 • 0. 0000053367 = 5. 3367 x 10^-6

Example: Suns, Moons and Planets • The Sun has a Mass of 1. 988 × 1030 kg. • Easier than writing: 1, 988, 000, 000, 000 kg (and that number gives a false sense of many digits of accuracy. )

Example: 700 • Why is 700 written as 7 × 102 in Scientific Notation ? • 700 = 7 × 100 • and 100 = 102 • so 700 = 7 × 102 • Both 700 and 7 × 102 have the same value, just shown in different ways.

Example: 4, 900, 000 1, 000, 000 = 109 , so 4, 900, 000 = 4. 9 × 109 in Scientific Notation

Learning Check: Scientific Notation Convert into scientific notation: 0. 00056 23900000

Learning Check: Scientific Notation Convert into standard form: 3. 56 x 105 3. 56 x 10 -5

Can also be used in calculations • Example: a tiny space inside a computer chip has been measured to be 0. 00000256 m wide, 0. 00000014 m long and 0. 000275 m high. • What is its volume? • Let's first convert the three lengths into scientific notation: • width: 0. 000 002 56 m = 2. 56× 10 -6 • length: 0. 000 14 m = 1. 4× 10 -7 • height: 0. 000 275 m = 2. 75× 10 -4

Calculations Continued • Multiply the digits together (ignoring the × 10 s): • 2. 56 × 1. 4 × 2. 75 = 9. 856 • Last, multiply the × 10 s: • 10 -6 × 10 -7 × 10 -4 = 10 -17 (just add -6, -4 and -7 together) • The result is 9. 856× 10 -17 m 3

Learning Check: Scientific Notation 3. 61 x 104 mm + 5. 88 x 103 mm + 8. 1 x 102 mm 2. 34 x 10 -2 mm + 3. 44 x 10 -5 mm + 7. 21 x 10 -4 mm

Learning Check: Scientific Notation (7. 20 x 103 cm) x (8. 08 x 103 cm)

Learning Check: Scientific Notation 2. 290 x 107 cm / 4. 33 x 103 s

Sig Fig Rules 1. All non zero digits are significant 2. 0 s are significant if they are sandwiched between two non-zero numbers ex. 409 3. 0 s are significant if they are at the end of the number and there is a decimal ex. 3. 00 4. 0 s are NOT significant at the end of the number if there is NO decimal (placeholders) ex. 250 5. 0 s are NOT significant if they are at the beginning of the number ex. 0. 000065 6. EXACT NUMBERS HAVE INFINITE SIG FIGS ex: 1 day

Learning Check: Sig Figs How many sig figs do each of the following have? 302. 00 ____ 2000 ____ 0. 0056 ___ 1003 ___ 350, 000 ___ 1. 002 ____

Learning Check: Adding and Subtracting with SIG FIGS 22. 0 m + 5. 28 m + 15. 5 m = 0. 003 cm + 0. 0048 cm +0. 100 cm = 202 m + 102. 0 m + 320. 02 m =

Learning Check: Multiplying and Dividing with SIG FIGS 47. 0 ft / 2. 2 min 140 cm x 35 cm 25. 23 cm x 250 cm 200 m x 53 m 30, 000 m / 63. 0 s