Chapter 1: Measurement

Measurement

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Section 1.2

Scientific Method

( method of observations, and making predictions )

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( English )

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Section 1.4

Systems of Units

Metric Units vs. SI Units

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Metric Prefixes

( Base - 10 System )

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Metric Prefix

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Metric conversions

meter 1

10 deci - meter

centi 100 - meter

milli 1000 - meter

0.1 deca - meter

hecta 0.01 - meter

kelo 0.001 - meter

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Section 1.5

The Kilogram

( the amount of water in a 1L=1000 cm 3 )

Section 1.6

Conversion Factors (Relates one unit to another unit)

How many centimeters are there in 65 inches?

2.54 cm

65 in. × = 165 cm (the inches cancel out!!) 1 in.

Conversion Factors (Relates one unit to another unit)

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Convert 50 km/h into mi/h?

0.621 mi/h

50 km/h 31.05 mi/h

1 km/h

Starting Value Conversion Result

Factor

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Section 1.6

Multi-Step Conversion – No Problem! Convert 22 inches into meters?

2.54 cm 1 m

22 in. 0.56 m

1 in. 100 cm

Starting Value Conv. Factor #1 Conv. Factor #2 Result in. cm cm m

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Conversion Factors (Relates one unit to another unit)

Convert 10 yard into meters?

0. 914 m

10 yd × = 9.14 m

1 yd Starting Value Conversion Result

Factor

Measurement and Significant Figures Exact numbers:

counting numbers like numbers of people, items, etc. have an unlimited number of Significant Figures

Measured numbers:

4.45 cm, 12.345 g, have a specific number of Significant Figures

Significant figures = all certain digits + one estimated digit

30.2 5

(4 significant figures)

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object

certain

4.4

estimated

cm .

5

0.1 cm preci = =0 sio

0

n .01 cm

1

Measurement and Significant Figures

distance between two

adjacent markings = 0.1cm

• All non-zero digits are significant 23.4 has 3 SF

• Zeros to the left of non-zero digits (leading zeros) are not significant

0.0000035 has 2 SF

• Zeros to the right of non-zero digits (trailing zeros) are significant

45.0 has 3 SF

• If a number does not contain decimal point, the trailing zeros may or may not be significant

400 cm (has either 1, 2 or 3 SF)

Significant Figures –

Rules

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Section 1.7

Measurement and Significant Figures

Addition and Subtraction:

Rule: Retain the fewest decimals for the answer

Example:

234.5 0 6 cm 0.1 2 cm +4455.9 cm 4690.5 2 6 cm 4690.5 cm

Measurement and Significant Figures Multiplication and Division:

Rule: Retain the lowest sig fig for the answer

Example: 2.44.52

0.10848 100.0

1 0. 1

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• If the first digit to be dropped is less than 5, leave the preceding digit unchanged.

Round off to 3 SF: 26.142 26.1

• If the first digit to be dropped is 5 or greater, increase the preceding digit by one.

Round off to 3 SF: 10.063 10.1

©

Rounding Off Numbers

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• Many numbers are very large or very small – it is more convenient to express them in ’powers-of-10’ notation

( Scientific Notation )

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• The exponent is increased by one for every place the decimal point is shifted to the left.

• The exponent is decreased by one for every place the decimal point is shifted to the right© .

Examples –

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Rounding/Scientific Notation

• 5.6256×0.0012 = 0.0067507

round to 2 SF: 0.0067507 rounds to 0.0068

change to scientific notation: 0.0068 = 6.8×10–3

• 0.0024/8.05 = 0.0002981

round to 2 SF: 0.0002981 rounds to 0.00030 change to scientific notation: 0.00030 = 3.0×10–4

©

mass density =

volume

Find the density for each cube?

Density (

) :

Typical units used – g/cm3, kg/m3 (Iron, Fe = 7.8 g/cm3)

Chapter 1 Homework:

1

3

12 19

21

22 23 24

25

26