HW answers 1 - 16

1. Precision = reproducibility; repeatability. How close a series of measurements are to each other. If the “range” (difference between highest and lowest measurement) is very small, then the series is precise. Use less than or equal to 0.02 as the criteria for “precise”.

2. Accuracy = How close either a series of measurements, or a single measurement, is to the “true” value (the correct answer. If the difference between the average of the measurements and the correct answer is very small, then the series is accurate. Use an average that is less than or equal to 0.02 (either higher or lower than) the correct answer as the criteria for “accurate”.

3. precision. The word “no” is in precision! So, “no average” is needed for this one.

But, you still need to remember somehow that you should calculate the range when asked about precision. (you need to subtract the lowest number in the series from the highest number in the series, and see how close together they are).

4. product

coefficient

10

power

Coefficient is always… equal to or greater than…1

And

Less than…..10

5.

1.1563 x 10 4

1.1563 x 10 -4

1.035 x 10 -1

1.035 x 10 +1

6.19 x 10 -2

6.19 x 10 +2

6.

0.0892 892

7352.8 0.0073528

80.5 0.805

386.8 0.03868

290 0.029

2900 0.0029

7.

Always estimate exactly 1 digit when measuring with a lined device.

We call this, “the estimated digit”.

The estimate digit is placed one decimal place to the right of the “known” digits.

8. 0 2 1 0(found farthest right)

9. Ely’s measurements are NOT accurate because the average (34.030) falls too far from the correct answer (35.000). His measurements are precise because the range (34.039 – 34.029) of 0.019 is very small.

Ellie’s measurements are accurate because the average (35.000) hits the correct answer exactly. Her measurements are NOT precise because the range (35.020 – 34.980) of 0.040 is not small enough.

0)

9. Eloise’s measurements are accurate because the average of 35.02 is close enough to the correct answer (35.000). Her measurements are also precise because the range (35.010 – 34.995) of 0.015 is very narrow.

Ellen’s measurements are NOT accurate because the average of 34.265 is not close enough to the correct answer (35.000). Her measurements are not precise because the range (34.90 – 34.020) of 0.880 is too large.

9: A. Not accurate: average of the shots are lower down than where they should be. Not precise: shots are not close to each other (large range).

B. Both: on average hits the correct spot, AND all shots are very close to each other (small range).

C. only precise: average doesn’t hit the correct spot; but, all shots very close to each other (small range).

**Accuracy is compared to “being correct”, and an average is calculated; precision is a comparison only within the data, and a range is calculated.

12 (temporarily skip 11)

STEP 1: Interval = 0.1

-The interval is what you use as you “count by” the littlest lines on the device.

-There is only 1 interval on a given device! --For a metric ruler, the interval is 0.1 cm (which is identical to saying, 1 mm)

0.1 cm is probably easier to understand!

.

12 STEP 1: Interval = 0.1STEP 2: “count by” the interval until you get to the last line that the object passes. Write down the measurement….. This is called, “determining the known digits in the measurement”.

A = 0.3 B = 4.6

C = 10.0 D = 13.8

IMPT – Always, the “last” known digit (the digit right-most) MUST be in the same decimal place as the “interval” for THIS step!

12 Step 1: Interval = 0.1

Step 2 Step 3 (estimate 1 digit

to the right of “last” known

0.3 0.34 or 0.35 (choose what u think)

4.6 4.64 or 4.65 (ditto)

10.0 10.00 (looks right on to me)

13.8 13.80 (looks right on to me)

12 Step 3 (the finals answers I would use)

0.34

4.64

10.00

13.80

**Measurements from the same device (as long as they are written with the same unit), will always stop at the same right-most decimal place…

0.34 4.64 10.00 13.80

*The digits generated during the measurement process are all called “significant”!

*All but one of the “0”s above is “significant”.

A “0” found to the left of a decimal point is NEVER significant… It is only a place holder.

0.34 4.64 10.00 13.80 *The digits generated during the measurement process are all called “significant”!

A “0” found to the left of a decimal point is NEVER significant… It is only a place holder.

15. # significant figures in answer 12?

2 3 4 4

11.What is your “final answer” (after measuring using the step 1, step 2, step 3 approach?

A. 75 7.5 70.5 70.50

C. 60 60.0 60.00 60.000

B. 7.5 7.50 7.05 7.050

D. 6.0 6.00 6.000 6.0000

13. See p. 66 “The significant figures in a measurement include all of the digits that are known, plus a last digit that is estimated.

14. How many sig figs are in your 4 measurements from question #11?

70.5 has 3 7.05 has 3

60.0 has 3 6.00 has 3

Every digit generated during measurement is a significant figure, if you did it correctly!

16. Rule 1: All “non-zero” digits are always significant (if you followed the 3 step process correctly).

123456789 has 9 sig figs

Rule 2: All zeros found with non-zero digits somewhere to their left and somewhere to their right always significant (if you followed the 3 step process correctly.

6.000 006 has 7 sig figs

Rule 3: “left-most” zeros are placeholders. Placeholders are NEVER significant.

0.1 has 1 sig fig

0.01 has 1 sig fig

0.00001 has 1 sig fig

But 0.0000101 has 3 sig figs

And 0.00001001 has 4 sig figs

Rule 4: Zeros to the “end” of a measurement (if you used the 3 step process correctly) are significant IF there is a written decimal point in the measurement.

1.0 has 2 sig figs

1.00 has 3 sig figs

1.000 has 4 sig figs

10. Has 2 sig figs

10 has only 1 sig fig

1000 has only 1 sig fig

Rule 5: “Right-most zeros” in whole numbers with “understood decimal points” are NOT significant. [An “understood decimal point” is one that you don’t see written down.

Ex: The whole number, “12”, has an understood decimal point. We know if we put a “.” in, it would be like this: “12.”

“12” and “12.” each have 2 sig figs

While “10.” has 2 sig figs and 10.0 has 3

“10” has 1 sig fig; 100 has 1

Rule 6: counting numbers, metric system exact conversions, other “exact conversions”, and whole numbers found in mathematical formulas all have “unlimited” (or “infinite”) significant figures.

The numbers used below: all have:

12 inches = 1 foot unlimited sig figs

1000 mm = 1 m unlimited sig figs

28 students per class unlimited sig figs

R = D / 2 unlimited sig figs