sig figs and accuracy

Objectives Define accuracy Define precision Compare accuracy & precision Use significant figures

Accuracy

Accuracy refers to how closely a measurement matches the true or actual values

To be accurate only requires the true value (bulls eye) & one measurement (for the arrow to hit the target)

Highly accurate data can be costly and difficult to acquire

Precision Precision refers to the reproducibility of the

measurement and exactness of description in a number.

To decide on precision, you need several measurements (notice multiple arrow holes), and you do not need to know the true value (none of the values are close to the target but all the holes are close together.)

Accuracy & Precision In order to be accurate and precise, one

must pay close attention to detail to receive the same results every time as well as “hit the target”.

Comparing Accuracy & Precision Notice the difference in these pictures.

To win the tournament the archers must hit the target the most times. The winner must show accuracy & precision.

The 1st archer has _____ accuracy & ____ precision. The 2nd archer has _____ accuracy & ____ precision. The 3rd archer has _____ accuracy & ____ precision. The 4th archer has _____ accuracy & _____ precision

GOOD

BAD BAD

BAD

BAD

GOODGOOD

GOOD

Example 1 A sample is known to weigh 3.182 g.

Jane weighed the sample five different times with the resulting data. Which measurement was the most accurate?3.200 g 3.180 g3.152 g 3.189 g

More practice (page 8)

Significant Figures Why are significant figures necessary?

True accuracy is no better than the measurement obtained by the least precise method.

We use significant digits so we are not exaggerating our precision.

Rules of Significant Digits1. All digits 1 through 9 are significant.

9.342 mg = 4 Sig. Digits

233,124 = 6 sig. digits

Rules of Significant Digits2. Zero is significant when it is between

two non‐zero digits- 2.06 = 3 SD- 206 = 3 SD- 100,001 = 6 SD

Rules of Significant Digits3. A zero to the right of a decimal point in a

number greater than or equal to one is significant.- 1.000 (4 SD)- 30.00 (4 SD)- 205.0 (4 SD)- 2.00000 (6 SD)- 10.0 (3 SD)

Rules of Significant Digits4. A zero to the right of a decimal point (in

a number less than one) but to the left of nonzero digit is not significant.- 0.001020 (4 SD)- 0.00024200 (5 SD)

Rules of Significant Digits5. Zeros used only to space the decimal

point (placeholders) are not significant.

- 1000 (1 SD)- 1010 (3 SD)-78,000 (2 SD)

WORKBOOKS PAGE 9

SWARTZ’S METHOD DECIMALS (If a number has a decimal)

Count from the 1st digit that’s not zero all the way to the right

NON-DECIMALS Count from the 1st digit that’s not zero to the

last digit that’s not zero

Counting SDs How many significant digits are in the following

numbers?A. 1235B. 2020C. 235.0D. 0.0270E. 235F. 0.00010900G. 65,100H. 19,620,000,000I. 102, 800

Operations with Sig Figs (p.10)

Operations with Sig Figs Find the perimeter of a sandbox if it has

a width of 3.5 ft and length of 3.45 ft. (Use the correct number of sig. figs.)

You are given the measurements of a picture to be 7.1 cm by 10.5 cm. Find the area that the picture takes on a wall. (Use the correct number of sig. figs.)