SIGNIFICANT DIGITS MEASUREMENTS AND UNITS WHAT ARE SIGNIFICANT

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SIGNIFICANT DIGITS, MEASUREMENTS AND UNITS

SIGNIFICANT DIGITS, MEASUREMENTS AND UNITS

WHAT ARE SIGNIFICANT DIGITS? ? Number of digits in a figure that express the

WHAT ARE SIGNIFICANT DIGITS? ? Number of digits in a figure that express the precision of a measurement. Today we will learn when digits are significant.

EXAMPLES: How many significant digits are in the following numbers? ? 34. 876 0.

EXAMPLES: How many significant digits are in the following numbers? ? 34. 876 0. 009845 7. 01 4. 0

Scientific Notation: Do you know this number, 300, 000 m/sec. ? It's the Speed

Scientific Notation: Do you know this number, 300, 000 m/sec. ? It's the Speed of light! Do you recognize this number, 0. 000 000 753 kg. ? This is the mass of a dust particle! Scientists have developed a shorter method to express very large numbers. This method is called scientific notation. Scientific Notation is based on powers of the base number 10.

Scientific Notation (continued) The number 123, 000, 000 in scientific notation is written as

Scientific Notation (continued) The number 123, 000, 000 in scientific notation is written as : 1. 23 x 1011 The first number 1. 23 is called the coefficient. It must be greater than or equal to 1 and less than 10. The second number is called the base. It must always be 10 in scientific notation. The base number 10 is always written in exponent form. In the number 1. 23 x 1011 the number 11 is referred to as the exponent or power of ten.

To write a number in Scientific Notation: Put the decimal after the first digit

To write a number in Scientific Notation: Put the decimal after the first digit and drop the zeroes. In the number 123, 000, 000 The coefficient will be 1. 23 To find the exponent count the number of places from the decimal to the end of the number. In 123, 000, 000 there are 11 places. Therefore we write 123, 000, 000 as: 1. 23 x 1011

For tiny numbers: For small numbers we use a similar approach. Numbers smaller than

For tiny numbers: For small numbers we use a similar approach. Numbers smaller than 1 will have a negative exponent. A millionth of a second is: 1. 0 x 10 -6

Sample Questions: a) 5. 3 x 10 -3 0. 0053 b) 6. 34 x

Sample Questions: a) 5. 3 x 10 -3 0. 0053 b) 6. 34 x 105 634 000 c) 5. 56 x 107 55 600 000

MEASUREMENTS Many quantities can be measured like heat, time, temperature, mass and many more!

MEASUREMENTS Many quantities can be measured like heat, time, temperature, mass and many more! For our purposes, we will focus on length, mass and time.

LENGTH A distance between two points Can be measured using a ruler Units can

LENGTH A distance between two points Can be measured using a ruler Units can be millimeters (mm), centimetres (cm), metres (m), etc. What is the length of this pencil? ?

MASS The amount of matter in an object. Can be measured using a scale

MASS The amount of matter in an object. Can be measured using a scale Units can be grams (g), kilograms (kg), pounds (lbs), etc.

TIME An interval between two events Can be measured with a stopwatch Units can

TIME An interval between two events Can be measured with a stopwatch Units can be seconds, minutes, hours etc.

SIGNIFICANT DIGITS AND MEASUREMENTS

SIGNIFICANT DIGITS AND MEASUREMENTS

CONVERTING UNITS Sometimes we need to convert units to be able to solve a

CONVERTING UNITS Sometimes we need to convert units to be able to solve a problem. Units you need to know: 1 km = 1000 m 1 m = 100 cm 1 cm = 10 mm *You should have these memorized* 1 kg = 1000 g 1 min = 60 s 1 hr = 60 min

FOR EXAMPLE: 1100 m = 1. 1 km 78 cm = 780 mm 56.

FOR EXAMPLE: 1100 m = 1. 1 km 78 cm = 780 mm 56. 7 g = 0. 0567 kg 2. 5 min = 150 s

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Significant Digits What are significant digits The significantSignificant Digits What are significant digits The significant
Significant Digits What are significant digits The significantSignificant Digits What are significant digits The significant
Significant Digits Significant Digits l l Significant figuresSignificant Digits Significant Digits l l Significant figures
Significant Digits and Scientific Notation Significant Digits UsingSignificant Digits and Scientific Notation Significant Digits Using
Significant Measured Digits Measuring with Precision Significant DigitsSignificant Measured Digits Measuring with Precision Significant Digits
SIGNIFICANT DIGITS RULES FOR SIGNIFICANT DIGITS 1 NonzeroSIGNIFICANT DIGITS RULES FOR SIGNIFICANT DIGITS 1 Nonzero
Significant Figures or Significant Digits Sig FigsSig DigitsSignificant Figures or Significant Digits Sig FigsSig Digits
Significant Digits Calculations Significant Digits in Calculations NowSignificant Digits Calculations Significant Digits in Calculations Now
Significant Digits Rules 1 All nonzero digits areSignificant Digits Rules 1 All nonzero digits are
Precision Uncertainties Significant Digits How many digits doPrecision Uncertainties Significant Digits How many digits do
Units Dimensional Analysis and Significant Digits Standards ofUnits Dimensional Analysis and Significant Digits Standards of
Determining Significant Digits and Rounding Significant figures areDetermining Significant Digits and Rounding Significant figures are
Measurements SI Units Scientific units that standardize measurementsMeasurements SI Units Scientific units that standardize measurements
Measurements Units Astronomical Measurements the Metric System UnitsMeasurements Units Astronomical Measurements the Metric System Units