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

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: 0.000 000 000 000 000 000 000 000 000 000 911 kg.

This can easily be expressed as: 9.11 X 10-31 kg

• 123,000,000,000 in s.n. is 1.23 x 1011

• The first number 1.23 is called the coefficient. It must be between 1 - 9.99

• The second number is called the base . The base number 10 is always written in exponent form. In the number 1.23 x 1011 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.

• Use the expexp or the e e button on your calculator.

Ex: divide 3.4 x 103m 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. 2.350 x 106 has 4 sig figs

2.0000 x 10-5 has 5 sig figs

Practice converting to scientific notation and back:

• A) 5934587 m

• B) 0.0000067 km

• C) 890000 s

• D) 3.6 x 10-7

• E) 1.324 x 105

• F) 5 x 104

5.934587 x 106 m

6.7 x 10-6 km

8.9 x 105 s

0.00000036

132 400

50 000

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) 1.2345 _____

• B) 4.8900 _____

• C) 22 000 _____

• D) 0.0023 _____

• E) 2567.0 _____

• F) 1999 _____

• G) 10.0001 ____

• H) 120.0 _____

• I) 555 _____

• J) 0.0001 _____

• K) 20 _____

• L) 0.001001 ____

• M) 56.0 ____

• N) 230. 03 ____

ANSWERS• A) 1.2345

(5)• B) 4.8900

(5)• C) 22 000

(2)• D) 0.0023

(2)• E) 2567.0

(5)• F) 1999

(4)• G) 10.0001

(6)

• H) 120.0 (4)

• I) 555 (3)

• J) 0.0001 (1)

• K) 20 (1)

• L) 0.001001 (4)

• M) 56.0 (3)

• N) 230. 03 (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 + 3.1 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 2.991 =

9.6 s not 9.5712 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

40.51 cm 42.15

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:

1.4 + 1.4 = 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!

• 100.21• +22.436• 122.646• 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 122.65

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:

1. 992 mL = ? L

move the decimal 3 times left

0.992 L

2. 28.3 kg = ? g

move the decimal 3 times right

28 300 g