Practice• A B C• 7 7.9 6.5• 8 8.2 7.3• 9 8.3 8• 10 8.0 8.5

• Temperature conversions

• 270 K _____ C• 345 K _____ C• 50 C _____ K• -30C _____ KKnown value is 7.5ml

Describe each regarding precision and accuracy

Calculate the percentage error for data set A

Chapter 2Significant Digits

Taking Measurements

•All measurements involve one estimation.

•If the measuring device is digital it will take the estimation for you.

•If the measuring device is scaled you must take the estimation yourself.

Electronic Measuring Devices

• Digital readout measuring diameter of 1.0420 inches.

• The last zero is the estimated digit.

Scaled Measuring Devices

Scaled Measuring Devices

•Bottom ruler gives a measurement of 8.? cm.

Scaled Measuring Devices

•Measure the length of the metal using the top ruler.

How to read a meniscus.

Read the Volume in mL

Significant Digits

Rules for Significant Digits

Rules for Significant Digits

• All non-zero digits are significant.

Rules for Significant Digits

• All non-zero digits are significant.

• “Trailing” zeros after the decimal point ARE significant.

Rules for Significant Digits

• All non-zero digits are significant.

• “Trailing” zeros after the decimal point ARE significant.

• Zeros between significant digits are significant.

Rules for Significant Digits

• All non-zero digits are significant.

• “Trailing” zeros after the decimal point ARE significant.

• Zeros between significant digits are significant.

• All other zeros are NOT significant unless indicated to be so by having a bar placed over them.

How to Determine Significant Digits

How to Determine Significant Digits

•Underline the leftmost nonzero digit.

How to Determine Significant Digits

•Underline the leftmost nonzero digit.

•Use the rules for significant digits to determine the rightmost significant digit.

How to Determine Significant Digits

•Underline the leftmost nonzero digit.

•Use the rules for significant digits to determine the rightmost significant digit.

•Every digit in between the leftmost and rightmost significant digits are significant as well.

Counting or Exact Numbers

Counting numbers: If there are 10 people in a room there are not 9.5 or 10.76 people in the room. Counting numbers are exact.

Ones in Conversion Factors: 1 kilometer = 1000 meters.  Exactly 1 km is equal to exactly 1000m. The 1 is considered to be an exact number and so is the 1000.

Since Counting numbers are exact they have an infinite number of significant digits.

Determine the Significant Digits(Examples in Notebook)

• 70.12 L • 0.000800 mg • 82.003 µm • 27.0 km • 50 people • 1.002 cm • _ • 200 kg

• -270.8 ºC • 1000 mL • 42,729.00 cm • 225 beans • 99.294 dm • 0.06900 m • _• 3,200,000 µL

Determine the Significant Digits (Examples in Notebook)

• 70.12 L 4• 0.000800 mg 3• 82.003 µm 5• 27.0 km 3• 50 people infinite• 1.002 cm 4• _ • 200 kg 2

• -270.8 ºC 4• 1000 mL 1• 42,729.00 cm 7• 225 beans infinite• 99.294 dm 5• 0.06900 m 4• _• 3,200,000 µL 5

Math Operations with Significant Digits

• When multiplying and/or dividing your answer must reflect the smallest number of significant digits.

Math Operations with Significant Digits

• When multiplying and/or dividing your answer must reflect the smallest number of significant digits.

• (17.3 cm)(28 cm) = 484.4 cm2

Math Operations with Significant Digits

• When multiplying and/or dividing your answer must reflect the smallest number of significant digits.

• (17.3 cm)(28 cm) = 484.4 cm2 = 480 cm2

Math Operations with Significant Digits

• When multiplying and/or dividing your answer must reflect the smallest number of significant digits.

• (17.3 cm)(28 cm) = 484.4 cm2 = 480 cm2

• 708g ÷ 4.700ml = 150.63829 g/ml =

Math Operations with Significant Digits

• When multiplying and/or dividing your answer must reflect the smallest number of significant digits.

• (17.3 cm)(28 cm) = 484.4 cm2 = 480 cm2

• 708g ÷ 4.700ml = 150.63829 g/ml = 151g/ml

Addition and/or Subtraction reflects the fewest decimal places

decimal places.

• 24.6 cm − 17.01 cm = 7.59 cm

Addition and/or Subtraction reflects the fewest decimal places

decimal places.

• 24.6 cm − 17.01 cm = 7.59 cm = 7.6 cm

Addition and/or Subtraction reflects the fewest decimal places

decimal places.

• 24.6 cm − 17.01 cm = 7.59 cm = 7.6 cm

• 8.5g + 1.32g + 0.18g =

Addition and/or Subtraction reflects the fewest decimal places

decimal places.

• 24.6 cm − 17.01 cm = 7.59 cm = 7.6 cm

• 8.5g + 1.32g + 0.18g = 10g

Addition and/or Subtraction reflects the fewest decimal places

decimal places.

• 24.6 cm − 17.01 cm = 7.59 cm = 7.6 cm

• 8.5g + 1.32g + 0.18g = 10g = 10.0g

Homework

Worksheet – Significant Digits & Rounding.