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Physics 11 - Significant Figures and Scientific Notation

When we take measurements, there are two aspects to consider:

PRECISION ( The EXACTNESS of measurement.

ACCURACY ( How CLOSE the measure is to a given value.

The following diagrams illustrate the difference between precision and accuracy. Notice that precision is indicated by how close the marks are = the exactness. On the other hand, accuracy is indicated by how close the marks are to the bullseye = closeness to the given value (in this case, the bullseye).

Which trial indicates the most precision? ____________________________

Which trial indicates the most accuracy? ____________________________

Precision is determined by the device being used to measure the value.

Because we must rely on measuring devices such as metre sticks, scales and spring scales, the data we gather is limited to the precision abilities of the device.

Example: Scale 1 Scale 2 Scale 3

When we take measurements and then use them in our calculations, we can only answer to the precision of the devices we have used, even though our calculators may produce numbers with more decimal places.

To account for this, we round our final answers to the lowest number of significant figures (measured numbers) in our data or problems.

How many significant figures does each of the following have?

4.235 – 6.5 – 9.56 - 2.3045 -

ZEROS:

When determining significant figures (sig. figs.), - zeroes that are sandwiched between numbers are considered significant figures (20053) - zeroes to the left of all numbers are NOT considered significant figures (0.00239) - zeroes to the right of numbers depend on the situation and how it was measured (3400 vs. 23000000000) - if a decimal is placed with a zero after it, all zeroes count (45900.0)

Examples:

1) 3400 2) 3040 3) 3004 4) 3400.0 5) 0.0034

On Your Own: Determine the number of sig figs for the following-

1) 500.23 - ____________ 2) 0.00034 - ____________ 3) 5600 - _____________

4) 3467 - ____________ 5) 78.004 - ____________ 6) 430.00 - _____________

In order to keep to the precision of the measuring devices used to gather data, whether it is for a lab or problem, the rule will be to always round the final answer to the lowest number of significant figures found in the question.

Example:

A racecar travels at 25 meters per second (m/s) for 45.0 seconds. How far did the car travel?

Scientific Notation

← Sometimes we can only answer in the correct number of sig figs if we change the answer into scientific notation.

← Used to represent very large or very small numbers.

← Ex. If the number 52100 is only 3 significant figures, then we need to change the number to scientific notation to indicate this.

Rules: - only ever one digit before decimal point

- exponent indicates movement of decimal place:

Positive exponent (5.21 × 10 4 = 52 100 (moves to the right)

Negative exponent ( 5.21 x 10-4 = 0.000521 (moves to the left)

Write the following numbers correctly in scientific notation to 3 sig figs.-

1) 459800 - _____________ 2) 3450 - ______________ 3) 678.00 - _______________

4) 530.05 - _____________ 5) 34.567 - ______________ 6) 0.00034 - _______________

Use your calculator: (All units must be in the same form when adding or subtracting – if they are not, you must convert)

Ex 1. (4.0 × 103 m) (5.2 × 105 m) = Ex 2. 6.02 × 1023 kg =

2.54 × 1012 m

Ex 3. 5.35 × 103 m + 6.2 × 104 cm =

Practice:

1) (4.56 x 104 m) (5.6 x 102 m) = 2) (4.6 x 103 m) ÷ (5.66 x 102 s) =

3) 2.3 x 105 km + 5.66 x 103 m = 4) 4.66 x 1011 m/s – 3.45 x 107 m/s =

Physics 11: Scientific Notation and Significant Figures -

Write the number in scientific notation. Round you answer to 3 Sig Figs.

1. 0.0064 2. 7,697 3. 0.08

4. 230,000 5. 19,190 6. 76,000

7. 0.06 8. 0.07 9. 8,523

10. 5,764,000 11. 0.015 12. 4,887

13. 0.01 14. 9,858,000 15. 530

Complete using the following directions:

A) In brackets next to the number, write the number of sig figs.

B) Round to 3 sig figs (if possible) and place in proper scientific notation.

.0051678 (5) ____________________ 2134500 (7) ____________________

230000 ____________________ .000003346 ____________________

9855676 ____________________ 22342 ____________________

.0078923 ____________________ 231121 ____________________

956.44 ____________________ 4.5671 ____________________

33.3354 ____________________ 231.56 ____________________

456.88 ____________________ 34444.569 ____________________

450005.1 ____________________ .00033459 ____________________

11.500 ____________________ 1784000 ____________________

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Ability to measure to 4 decimal places. ( 3.0212

Ability to measure to 3 decimal places. ( 3.021

Ability to measure to 2 decimal places. ( 3.02

2.13 x 106

5.16 x 10-3

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