General Physics I - Measurement & Unit Conversion

General Physics I - Measurement

Objectives

At the end of this lesson, you should be able to:

  1. Solve measurement problems involving conversion of units.
  2. Express measurements in scientific notation.

Review Questions

  1. What is the equivalent unit of 42.3 centimeters in meters?

    • A. 0.0423 m
    • B. 0.423 m
    • C. 4.23 m
    • D. 42.3 m

  2. Which of the following is equivalent to 76.2 picometers?

    • A. 1.1 \times 10^{-2} m
    • B. 2.1 \times 10^3 m
    • C. 2.278 \times 10^8 km
    • D. 7.62 \times 10^{-8} mm

  3. In writing scientific notation, the exponent is positive if the decimal is moved to the:

    • A. left
    • B. right
    • C. twice to the left
    • D. twice to the right

  4. In multiplying numbers in scientific notation, what do we do to the exponent?

    • A. We add the exponent
    • B. We subtract the exponent
    • C. We multiply the exponent
    • D. We divide the exponent

  5. In Hindu chronology, the longest time measure is a Para. One Para equals 311,040,000,000,000 years. What is the value in nanoseconds?

    • A. 9.81 \times 10^{29} ns
    • B. 98.1 \times 10^{30} ns
    • C. 9.81 \times 10^{30} ns
    • D. 9.81 \times 10^{31} ns

Physical Quantities

  • Physical quantities have a numerical value (a number) and a unit of measurement (e.g., 3 m, 10 kg).
  • Fundamental/Base Quantities: Quantities that can be measured directly without depending on other quantities.
  • Derived Quantities: Quantities that use any combination of fundamental quantities.

Fundamental Quantities

  • Distance: meter (m)
  • Mass: Kilogram (kg)
  • Time: Seconds (s)
  • Electric Current: Ampere (A)
  • Temperature: Kelvin (K)
  • Luminous Intensity: Candela (Cd)
  • Amount of Substance: Mole (N)

Derived Quantities

  • Velocity (v): meter/second (m/s)
  • Acceleration (a): velocity/time = meter/second^2 (m/s^2)
  • Force (F): mass × acceleration
  • Power (P): Joules/second or Watts (W)

Significant Figures

  • All non-zero digits are significant (e.g., 1, 2, 3, 4, 5, 6, 7, 8, & 9).
  • Zeros in between non-zero digits are significant (e.g., 105 – 3 significant figures, 20008 – 5 significant figures).
  • Zeros to the right of a non-zero digit in unexpressed decimal point are not significant (e.g., 200 - 1 significant figure).
  • Zeros at the right of a non-zero digit in an expressed decimal point are significant (e.g., 200.00 = 5 significant figures).
  • Zeros at the left of a non-zero digit but to the right of a decimal point are not significant (e.g., 0.0000001 – 1 significant figure).

Rounding Off

  • When the number to be rounded off is less than 5, change that number to zero “0” to retain the preceding number (e.g., 12.34 – 12).
  • When the number to be rounded off is greater than or equivalent to 5, change that number to zero “0” and add one to the preceding number (e.g., 98.76 – 99).

Conversion

  • Conversion of units is the conversion between different units of measurement for the same quantity, typically through multiplicative conversion factors.

  • Examples:

    • Ana is making a TikTok dance tutorial. The mat she uses is 2.5 meters long. She wants to know its length in centimeters so she can post it in the caption. How long is the mat in centimeters?
    • Jayden plays online games for 2 hours and 45 minutes. He wants to know how many minutes he spent playing. Convert the time to minutes.
    • Sarah runs 5 kilometers every Saturday morning. How many meters does she run?

Unit Prefixes

  • An important feature of the metric system is the use of prefixes to express larger and smaller values of a quantity.
  • Unit prefixes are symbols placed before the symbol of a unit to specify the order of magnitude of the quantity.

Commonly Used Prefixes

PrefixSymbolMultiple of Unit
picop10^{-12}
nanon10^{-9}
microμ, mc10^{-6}
millim10^{-3}
centic10^{-2}
decid10^{-1}
decada10^1
hectoh10^2
kilok10^3
megaM10^6
gigaG10^9
teraT10^{12}
exaE10^{18}
zettaZ10^{21}
attoa10^{-18}
zeptoz10^{-21}
femtof10^{-15}

Conversion Factors

  • 1 m = 100 cm
  • 1 kg = 2.2 lb
  • 1 m = 3.28 ft
  • 1 in = 2.54 cm
  • 1 hr = 60 min
  • 1 min = 60 sec
  • 1 ft = 12 in
  • 1 yd = 3 ft
  • 1 mi = 5280 ft
  • 1 mi = 1.609 km
  • 1 km = 0.62 mi
  • 1 mL = 1 cc
  • 1 L = 1000 ml
  • 1 kips = 1000 lbs

Conversion Factors - Temperature

  • ^{\circ}F = \frac{9}{5} {^{\circ}C} + 32
  • ^{\circ}C = \frac{5}{9} ({^{\circ}F} – 32)
  • K = 273 + {^{\circ}C}
  • R = 460 + {^{\circ}F}

Examples

  • Light travels with the speed of 300,000,000 m/s.
  • The weight of a dust particle is about 0.000000000753 kg.

Scientific Notation

  • Regular Notation: The standard way of writing numbers.
  • Scientific Notation: A convenient and shorthand way of writing really large or really small numbers.
    • Example: 280,000,000 can be written in scientific notation as 2.8 \times 10^8.
  • A number between 1 and 10 multiplied by a power of 10.

Rules in Scientific Notation

  1. Determine “a” – by shifting the decimal point of the original number to the left or right, until one digit is to the left of it.
  2. Determine “b” – by counting the number of decimal places the point has moved. If it has been to the left “b” is positive; if to the right “b” is negative.
    • Ex. 123456 – 1.23 \times 10^5 (left)
    • Ex. 0.0009876 - 9.88 \times 10^{-4} (right)

Examples & Practice Conversions

  1. 40 km/hr → ft/sec
  2. 500g → lbs
  3. 5 ft 5 in → m
  4. 4000 mi → km
  5. 1 metric ton to kilograms

Activity - Scientific Notation

Convert to Scientific Notation:

  1. 2 856 000 000 000
  2. 0.000000456
  3. 14.00125
  4. 125.00

Activity - Conversions

  1. How many inches are there in 6 meters?
  2. How many liters are there in 4 gallons?
  3. 1,000,000 grams is equal to how many kilograms?
  4. A marathon is 26.2 miles long. How many kilometers is it?

Activity Answers - Scientific Notation

  1. 1.56 \times 10^8
  2. 9.6 \times 10^{-8}
  3. 2.45 \times 10^1
  4. 9.60 \times 10^4

Problem Solving

  1. The distance from planet Earth to the Sun is 1.5 \times 10^8 km. Find the distance in megameters (Mm)?
  2. Convert 300 seconds to hours.
  3. An airplane took off from Kuala Lumpur airport at 1400 hours and arrived at New Delhi airport at 1830 hours. Calculate the duration of the journey in minutes and seconds?
  4. The distance from the university to home is 15 km, and it usually takes 20 min to drive this distance. Calculate the average speed in meters per second (m/s).
  5. The density of iron is 7.86 g/cm^3 under standard conditions. Convert this to kg/m^3.