Significant digits

Objectives:• State the purpose of significant digits• State and apply the rules for counting and

doing calculations with significant digits

One way engineers use significant digits….

Significant digitsMeasurements that indicate the

precision of the tool used

Important—we want to let other scientists and engineers know how “good” our measurements are!

3.42 cmThis means:

◦My tool had markings to the tenths place (I can COUNT them)

◦ I estimated the hundredths place (the object was between 3.4 and 3.5 but closer to 3.4)

◦ 3 significant digits

3900 cm This means:

◦My tool had markings to the thousands place (I could COUNT them)

◦I estimated the hundreds place (the object was between 3000 and 4000 but much closer to 4000 )

◦ 2 significant digits

3900. cm This means:

◦My tool had markings to the tens place (I could COUNT them)

◦I estimated the ones place (the object appeared to be right at 3900)

◦ 4 significant digits

Clues: How to know when a number is significantIt is a non-zero (1, 2, 3, 4, 5, 6, 7,

8, 9)It is a zero at the END of a

decimal AFTER a decimal point (4.500)

It is a zero between non-zeros (5,005)

It is a zero at the end of a whole number AND there is a decimal (50.)

Examples of Sig zeros

Examples of NON-sig zeros

5,0025600..30

0.0050.033050,000,000

This number has a mix of significant and insignificant zeros:

0.00300

Rules for counting significant digits:23002300Non-zeros are significant2300 zeros are at the end of a number

without a decimal = insignificant2300 = 2 s.f.This means the tool allowed us to

COUNT the thousands place, and estimate the hundreds place (we counted to 2000 and we estimated the value was between 2000 and 3000, but closer to 2000.)

Counting significant digits:230.230. Non-zeros = significant230. zero here is at the end of a

number WITH a decimal = significant

230. = 3 s.f This means the tool allowed us to

COUNT to the ones place 230 and we estimated that the value was exactly at 230.

Counting significant digits:2.300 x 10-3 BIG IDEA: count the digits of the

coefficient only2.300 x 10-3 Non-zeros = significant2.300 x10-3 zeros here are at the end

of a number and AFTER a decimal = significant

2.300 x 10-3 = 4 s.f.This means the tool allowed us to

measure .00230, and we estimated it was exactly at .002300

Counting significant digits - Practice0.004000.00400 Non-zeros = significant!0.00400 zeros here are at the beginning

of a number = insignificant0.00400 zeros here are at the end of a

number and AFTER a decimal = significant

0.00400 = 3 s.f.This means the tool allowed us to

measure 0.0040, and we estimated it was exactly at 0.00400.

PracticeProblems 1-10 on your notes

Compare numbers – which is more precise and how do you know. Game – cc. add this to prac probs

Give practical example – ie 2 diff thermoms to meas the same temp

Practice - AnswersState the number of significant digits.1) 1234   42) 0.023 23) 890 24) 91010 45) 9010.0 5 6) 1090.0010 87) 0.00120 38) 3.4 x 104 29) 9.0 x 10-3 210) 9.010 x 10-2 4

Calculations:Addition and subtraction: USE lowest

number of decimal places as the # of decimal places for your answer. Just do add probs in class maybe 1 subt. Prep to not have add and subt, and have it just in case

Another day multiplying and dividing USE least number of total sig figs as the # of sig figs for your answer.

Example:350.83 kg + 400.0 kg

350.83 2decimal places400.0 1 decimal place

Lowest # of decimal places = 1

750.83 kg I need to round this to only one decimal place

750.8 kg

Example:2.0 x 8000 2.0 2 significant

figures8000 1 significant figure

LEAST? = 116,000 I need to round this to

only one significant digit1

20,000

PracticeProblems 11-20 in your notes

Practice - Answers5.33 + 6.020 = 11.350 11.35 5.0 x 8 = 40.0 4081÷ 9.0 = 9.0 9.03.456 – 2.455= 1.001 1.0015.5 – 2.500 =3.000 3.07.0 x 200 =1400.0 1000300. ÷ 10.0 = 3.0 3 (3.0 x 104)x (2.0 x 101) = 6.0 x 105 6.0 x 105

(9.000 x 10-2)÷ (3.00 x 101) = 3.000 x 10-3 3.00 x 10-3

(3.0 x 104) - (2.0 x 101) = 2.998 x 104 3.0 x 104

Exit Ticket

2300

Counting significant digits:450.0

◦What do we know about the measurement made?

◦ How many significant digits are in the answer?

◦Is this number more less precise than the previous answer?

Counting significant digits:20

◦What do we know about the measurement made?

◦ How many significant digits are in the answer?

◦Is this number more less precise than the previous answer?

Counting significant digits:0.000450

◦What do we know about the measurement made?

◦ How many significant digits are in the answer?

◦Is this number more less precise than the previous answer?

Counting significant digits:3,006

◦What do we know about the measurement made?

◦ How many significant digits are in the answer?

◦Is this number more less precise than the previous answer?

Counting significant digits:23.0023.00 Non-zeros = significant!23.00 zeros here are at the end

of a number and AFTER a decimal = significant

23.00 = 4 s.f.This means the tool allowed us to

measure 23.0, and we estimated it was exactly at 23.0.

Example:10.75 – 0.411 10.75 2 decimal

places0.411 3 decimal places

LEAST? = 210.339 I need to round this to

only two decimal place!

10.34