State the uncertainty like this: 4. 2 cm ± 0. 1 cm. You can also rewrite this as 4. 2 cm ± 1 mm, since 0. 1 cm = 1 mm.
If your experimental measurement is 60 cm, then your uncertainty calculation should be rounded to a whole number as well. For example, the uncertainty for this measurement can be 60 cm ± 2 cm, but not 60 cm ± 2. 2 cm. If your experimental measurement is 3. 4 cm, then your uncertainty calculation should be rounded to . 1 cm. For example, the uncertainty for this measurement can be 3. 4 cm ± . 1 cm, but not 3. 4 cm ± 1 cm.
Study the edges of the ball and the ruler to get a sense of how reliably you can measure its diameter. In a standard ruler, the markings at . 5 cm show up clearly – but let’s say you can get a little bit closer than that. If it looks like you can get about within . 3 cm of an accurate measurement, then your uncertainty is . 3 cm. Now, measure the diameter of the ball. Let’s say you get about 7. 6 cm. Just state the estimated measurement along with the uncertainty. The diameter of the ball is 7. 6 cm ± . 3 cm.
Let’s say that you can’t get much closer than to . 2 cm of measurements by using a ruler. So, your uncertainty is ± . 2 cm. Let’s say you measured that all of the CD cases stacked together are of a thickness of 22 cm. Now, just divide the measurement and uncertainty by 10, the number of CD cases. 22 cm/10 = 2. 2 cm and . 2 cm/10 = . 02 cm. This means that the thickness of one CD case is 2. 20 cm ± . 02 cm.
Let’s say you measured the five following times: 0. 43 s, 0. 52 s, 0. 35 s, 0. 29 s, and 0. 49 s.
0. 43 s - . 42 s = 0. 01 s 0. 52 s - 0. 42 s = 0. 1 s 0. 35 s - 0. 42 s = -0. 07 s 0. 29 s - 0. 42 s = -0. 13 s 0. 49 s - 0. 42 s = 0. 07 s Now, add up the squares of these differences: (0. 01 s)2 + (0. 1 s)2 + (-0. 07 s)2 + (-0. 13 s)2 + (0. 07 s)2 = 0. 037 s. Find the average of these added squares by dividing the result by 5. 0. 037 s/5 = 0. 0074 s.
(5 cm ± . 2 cm) + (3 cm ± . 1 cm) = (5 cm + 3 cm) ± (. 2 cm +. 1 cm) = 8 cm ± . 3 cm
(10 cm ± . 4 cm) - (3 cm ± . 2 cm) = (10 cm - 3 cm) ± (. 4 cm +. 2 cm) = 7 cm ± . 6 cm
(6 cm ± . 2 cm) = (. 2 / 6) x 100 and add a % sign. That is 3. 3 % Therefore: (6 cm ± . 2 cm) x (4 cm ± . 3 cm) = (6 cm ± 3. 3% ) x (4 cm ± 7. 5%) (6 cm x 4 cm) ± (3. 3 + 7. 5) = 24 cm ± 10. 8 % = 24 cm ± 2. 6 cm
(10 cm ± . 6 cm) ÷ (5 cm ± . 2 cm) = (10 cm ± 6%) ÷ (5 cm ± 4%) (10 cm ÷ 5 cm) ± (6% + 4%) = 2 cm ± 10% = 2 cm ± 0. 2 cm
(2. 0 cm ± 1. 0 cm)3 = (2. 0 cm)3 ± (50%) x 3 = 8. 0 cm3 ± 150 % or 8. 0 cm3 ±12 cm3
