Physics 11: Skills Review Significant Digits (and measuring, scientific notation, conversions……)

Precision: to describe how well a group of measurements made of the same object or event under the same conditions actually do agree with one another. These points on the bulls eye are precise with one another but not accurate.

Accuracy: represents the closeness of a measurement to the true value. Ex: the bulls eye would be the true value, so these points are accurate.

Let’s use a golf analogy

Accurate?No Precise?Yes

Accurate?Yes Precise?Yes

Precise?No Accurate?No

Scientific Notation Scientists have developed a shorter method to express very large or very small numbers. Scientific Notation is based on powers of the base number 10. Ex: The mass of an electron is: kg. This can easily be expressed as: 9.11 X kg

123,000,000,000 in s.n. is 1.23 x The first number 1.23 is called the coefficient. It must be between The second number is called the base. The base number 10 is always written in exponent form. In the number 1.23 x the number 11 is referred to as the exponent or power of ten.

Using Scientific notation in calculations: When using scientific notation in calculations it is important to be able to enter the these measurements into your calculator. expe Use the exp or the e button on your calculator. Ex: divide 3.4 x 10 3 m by 1.7s = 2000 m/s

When determining the # of sig figs in a number written scientific notation in use the same rules for sig figs. Do not include the 10 to the power in the sig figs. Ex x 10 6 has 4 sig figs x has 5 sig figs

Practice converting to scientific notation and back: A) m B) km C) s D) 3.6 x E) x 10 5 F) 5 x 10 4

x 10 6 m 6.7 x km 8.9 x 10 5 s

Rules on determining significant digits: 1. Nonzero digits are always significant. 2. All final zeros after the decimal point are significant. 3. Zeros between two other significant digits are always significant. 4. Do not count leading zeros as significant. 5. Zeros at the end of a number which has no decimal point are NOT significant.

Determine the correct number of significant digits: A) _____ B) _____ C) _____ D) _____ E) _____ F) 1999 _____ G) ____ H) _____ I) 555 _____ J) _____ K) 20 _____ L) ____ M) 56.0 ____ N) ____

ANSWERS A) (5) B) (5) C) (2) D) (2) E) (5) F) 1999 (4) G) (6) H) (4) I) 555 (3) J) (1) K) 20 (1) L) (4) M) 56.0 (3) N) (5)

Addition/Subtraction using Significant Digits: The number of significant digits is equal to the value having the fewest decimal places. Ex: 2.03 mm mm = 5.1 mm not 5.13.

Multiplication/Division using significant Digits: The number of significant digits is equal to the value with the fewest significant digits. Ex: 3.2 s x = 9.6 s not s

Measurement: Why we actually care about sig figs! When taking measurements, it is important to note that no measurement can be taken exactly Therefore, each measurement has an estimate contained in the measurement as the final digit When taking a measurement, the final digit is an estimate and an error estimate should be included

Significant Digits for measuring When using a measuring device, use all the given lines to measure, then estimate the last number The accuracy of the sig figs depends upon the measuring device. Ex: a ruler

Read the ruler

Answers cm42.15

Significant Figures Because all numbers in science are based upon a measurement, the estimates contained in the numbers must be accounted for: 1+1 = 3 While we know think this is not true, from a science standpoint, the measurements could have been: = 2.8

Significant Figures: the Why! Since the final digit in each measurement is an estimate, we refer to it as an uncertain digit or the least significant digit This means that any mathematical operation involving this digit in introduces uncertainty to the answer

Significant Figures: the Why! In the result of this calculation, there are two uncertain digits As this does not make sense, the second uncertain digit would be discarded, making the answer

SI (System International ) Units This system is used for scientific work around the world It is based on the metric system

SI: Base Units Length - meter - m Mass - grams – (about a raisin) - g Time - second - s Temperature - Kelvin orºCelsius K orºC Energy - Joules- J Volume - Litre - L The number of particles of a substance - mole - mol

Conversions The metric system uses prefixes added the base unit (SI unit). We often have to convert from a prefixed unit to the base unit Refer to hand out for conversion chart Conversions are made by moving the decimal place to the left or right the appropriate number of times

Examples: mL = ? L  move the decimal 3 times left  L kg = ? g  move the decimal 3 times right  g