0.3 SIGNIFICANT FIGURES – PART 1

AKA – Sig Figs

AKA – Significant Digits

AKA – The most annoying concept ever (but, sadly it is important)

BY THE END OF THIS LESSON, STUDENTS WILL BE ABLE TO…

MEASUREMENT UNCERTAINTY

• In measurement, there are always uncertainties such as meter sticks with rounded off ends, air movement around balances, etc.
• Parallax: Reading an instrument at an angle can also give inaccurate readings. If you are driving a car and are looking at the speedometer dead on you will see one reading (eg. 95 km/h). If your mother is in the passengers seat, she views the speedometer at an angle and might see 91 km/h. This is known as parallax.

MEASUREMENT UNCERTAINTY

• Parallax is the apparent shift in the position of an object when viewed from different angles.
• Measurements must be made at eye level and straight on (no angle).

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PRECISION

• Precision: If you were measuring a piece of metal with a ruler (like below), you would get a more exact measurement by using the side graduated in mm (the bottom of the ruler).
• Precision is the degree of exactness that measurement can be reproduced. The precision of a measuring tool is limited by the graduations or divisions on its scale. In other words, you will have a more precise measurement of the metal strip above by using the graduations on the bottom of the ruler (mm) rather than the top (cm).

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PRECISION

• The precision of an instrument is indicated by the number of decimal places used. For example, 5.14 cm is more precise than 5.1 cm.

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ACCURACY

• Accuracy: Accuracy is to the extent that a measurement agrees or compares with an accepted value or standard. A very accurate measure of boiling water might be 99.8°C, because it would be compared to the standard of 100°C. 
• The difference between an observed or measured value and a standard is known as error, and is sometimes written as a percentage.
• The accuracy of a measuring instrument depends on how well it compares to an accepted standard, and it should be checked regularly. A known 500.0 g mass should show that same reading on a balance. If it doesn't, the balance should be re-calibrated.

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PRECISION VS. ACCURACY

• Precision:
• The more precise our measurement is, the more significant digits we will have.

• Accuracy
• The more accurate our measurement is, the closer we are to the exact value. Or, the more ‘right’ we are.

PRECISION VS. ACCURACY

• Precise & Accurate
• * This is where we want to be when we measure, both precise and accurate*

SIGNIFICANT DIGITS

• When measuring, the precision is limited by the device
• the number of digits is also limited.
• Valid digits are called significant digits or significant figures.
• Significant digits consist of all digits known with a certainty plus the first digit that is uncertain.

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SIGNIFICANT DIGITS

• The strip below is somewhere between 5.1 and 5.2 cm. We would state that the length is 5.14 cm. The last digit is an estimate (uncertain), but it is still valid and considered to be significant.
• There are 3 significant digits in this measurement; the 5 and 1 are known and the 4 is an estimate.
• If the strip was dead on the 5.1 graduation, we should record this as 5.10 cm and we would have 3 significant digits.

SIGNIFICANT DIGITS

• *When recording measurements on an instrument (i.e.: ruler, balance, cylinder:
• Record the numbers you are sure of using the smallest division of the scale
• i.e.: We are sure of the “5” and the “0.1”
• Add an estimate digit to the tenth of the smallest division
• i.e.: We estimate the 0.04

RULES FOR SIGNIFICANT DIGITS

• All non-zero digits in a measurement are considered significant. It's the zeros that sometime create problems.
• 1) Non-zero digits are always significant.
• i.e.: 127.34 grams = 5 significant digits (s.d.)
• 2) All zeros between nonzero digits are significant.
• i.e.: 1205 m = 4 s.d.
• 3) All final zeros to the right of a decimal point are significant.
• i.e.: 21.50 grams = 4 s.d.

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RULES FOR SIGNIFICANT DIGITS

• 4) Zeros used only for spacing the decimal are not significant.
• i.e.: 0.0025 = 2 s.d.
• 5) Zeros to the right of a whole number are ambiguous. A bar placed over a zero makes all numbers up to and including the barred zero, significant.
• i.e.: 5OŌ = 3 s.d.

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RULES FOR SIGNIFICANT DIGITS

• 6) a) A decimal point makes zeroes before significant (if they are not place holders)
• i.e.: 1200. = 4 s.d. i.e.: 0.05 = 1 s.d.
• 6) b) Zeroes to the right of a decimal may be significant
• i.e.: 10.00 = 4 s.d. i.e.: 105.0 = 4 s.d.

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SIGNIFICANT FIGURES RULES