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Using Math in Science

Each measurement has two parts:. Metric or SI (System Internationale) units are standard. Metric Prefixes: change the size of the basic unit. What quantities do we measure?. Unit conversion changing size of a unit\ or switching between English and metric units. Accuracy and Precision:ACCURACY: how close measurements are to the correct answer PRECISION: how close measurements are to each other .

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Using Math in Science

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    5. Figure: 02-02 Title: The relationship between metric units Caption: A cubic meter is the volume of a cube that is 1m on each edge. Each cubic meter contains 1000 cubic decimeters (liters), and each cubic decimeter contains 1000 cubic centimeters (milliliters). Thus, there are 1000 mL in a liter and 1000 L in a cubic meter. Notes: The metric system of measurement is used by all industrialized nations of the world, except the United States. The relationships between metric units are based on powers of 10. This makes the conversion between metric units easier to calculate than conversions between the English units more familiar to Americans. Conversion from millimeters to meters is therefore as simple as dividing the number of millimeters by 1000. To contrast, converting inches to yards requires dividing the number of inches by 36. Keywords: metric, volume, length, unitFigure: 02-02 Title: The relationship between metric units Caption: A cubic meter is the volume of a cube that is 1m on each edge. Each cubic meter contains 1000 cubic decimeters (liters), and each cubic decimeter contains 1000 cubic centimeters (milliliters). Thus, there are 1000 mL in a liter and 1000 L in a cubic meter. Notes: The metric system of measurement is used by all industrialized nations of the world, except the United States. The relationships between metric units are based on powers of 10. This makes the conversion between metric units easier to calculate than conversions between the English units more familiar to Americans. Conversion from millimeters to meters is therefore as simple as dividing the number of millimeters by 1000. To contrast, converting inches to yards requires dividing the number of inches by 36. Keywords: metric, volume, length, unit

    6. Figure: 02-01UN01T04 Title: Units of length Caption: Units of length and their conversion factors. Notes: Units of length and their conversion factors. Keywords: unit conversions, lengthFigure: 02-01UN01T04 Title: Units of length Caption: Units of length and their conversion factors. Notes: Units of length and their conversion factors. Keywords: unit conversions, length

    7. Figure: 02-02UN00T05 Title: Units of volume Caption: Units of volume and their conversion factors. Notes: Units of volume and their conversion factors. Keywords: unit conversions, volumeFigure: 02-02UN00T05 Title: Units of volume Caption: Units of volume and their conversion factors. Notes: Units of volume and their conversion factors. Keywords: unit conversions, volume

    8. Figure: 02-03 Title: Significant figures in measurement Caption: How would you report the volume in this graduated cylinder? Notes: The reported measurement should always include every certain digit plus one uncertain digit. This digit can be referred to as the “first uncertain digit.” It can be difficult to accept that it is better to report one uncertain value than to not report any uncertain value. However, loss of precision from dropping off a digit is always greater than the loss of precision from being off by 1 or 2 in an estimation. Keywords: significant figures, measurementFigure: 02-03 Title: Significant figures in measurement Caption: How would you report the volume in this graduated cylinder? Notes: The reported measurement should always include every certain digit plus one uncertain digit. This digit can be referred to as the “first uncertain digit.” It can be difficult to accept that it is better to report one uncertain value than to not report any uncertain value. However, loss of precision from dropping off a digit is always greater than the loss of precision from being off by 1 or 2 in an estimation. Keywords: significant figures, measurement

    10. Figure: 02-03UN20 Title: Converting concentration to mass Caption: A patient requires an injection of 0.012 g of a painkiller available as a 15 mg/mL solution. How many milliliters should be administered? Notes: Knowing the amount of painkiller in 1 mL allows us to use the concentration as a conversion factor to determine the volume of solution that would contain the desired amount. Keywords: calculations, conversionsFigure: 02-03UN20 Title: Converting concentration to mass Caption: A patient requires an injection of 0.012 g of a painkiller available as a 15 mg/mL solution. How many milliliters should be administered? Notes: Knowing the amount of painkiller in 1 mL allows us to use the concentration as a conversion factor to determine the volume of solution that would contain the desired amount. Keywords: calculations, conversions

    13. Figure: 02-03UN12 Title: Significant figures in calculation Caption: When multiplying or dividing numbers, the answer reported cannot have more significant figures than either of the original numbers. Notes: When multiplying or dividing numbers, the answer reported cannot have more significant figures than either of the original numbers. Keywords: significant figures, calculationFigure: 02-03UN12 Title: Significant figures in calculation Caption: When multiplying or dividing numbers, the answer reported cannot have more significant figures than either of the original numbers. Notes: When multiplying or dividing numbers, the answer reported cannot have more significant figures than either of the original numbers. Keywords: significant figures, calculation

    14. Figure: 02-03UN14 Title: Significant figures in calculations Caption: When adding or subtracting numbers, the reported answer cannot have more digits after the decimal point than any of the added numbers. Notes: When adding or subtracting numbers, the reported answer cannot have more digits after the decimal point than any of the added numbers. Keywords: significant figures, calculationFigure: 02-03UN14 Title: Significant figures in calculations Caption: When adding or subtracting numbers, the reported answer cannot have more digits after the decimal point than any of the added numbers. Notes: When adding or subtracting numbers, the reported answer cannot have more digits after the decimal point than any of the added numbers. Keywords: significant figures, calculation

    17. Figure: 02-03UN15 Title: Factor-label method for problem solving Caption: Conversion between kilometers and miles using factor-label method. Notes: All conversion factors used in this method need to be numerically equal to 1. Note that the conversion factor here follows this rule: one kilometer equals 0.6214 mile. The conversion factor could just as legitimately be inverted to read 0.6214 mile equals one kilometer. Keywords: conversion factor, factor-label, problem solvingFigure: 02-03UN15 Title: Factor-label method for problem solving Caption: Conversion between kilometers and miles using factor-label method. Notes: All conversion factors used in this method need to be numerically equal to 1. Note that the conversion factor here follows this rule: one kilometer equals 0.6214 mile. The conversion factor could just as legitimately be inverted to read 0.6214 mile equals one kilometer. Keywords: conversion factor, factor-label, problem solving

    18. Figure: 02-03UN18 Title: Factor-label method for problem solving Caption: Factor-label problems need to be set up so the unit labels cancel properly. Notes: If the unit labels do not cancel properly, the numerical answer will be wrong. Conversion factors can be inverted as necessary to make units cancel out. Keywords: factor-label, problem solving, conversion factorFigure: 02-03UN18 Title: Factor-label method for problem solving Caption: Factor-label problems need to be set up so the unit labels cancel properly. Notes: If the unit labels do not cancel properly, the numerical answer will be wrong. Conversion factors can be inverted as necessary to make units cancel out. Keywords: factor-label, problem solving, conversion factor

    20. Figure: 02-04 Title: Temperature scales Caption: Comparison of the Fahrenheit, Celsius, and Kelvin temperature scales. Notes: Fahrenheit degrees are 5/9 the size of a kelvin or Celsius degree. Kelvin and Celsius degrees are the same size, but start at different points--zero degrees Celsius is equal to 273.16 K. Keywords: temperature, Fahrenheit, Celsius, kelvinFigure: 02-04 Title: Temperature scales Caption: Comparison of the Fahrenheit, Celsius, and Kelvin temperature scales. Notes: Fahrenheit degrees are 5/9 the size of a kelvin or Celsius degree. Kelvin and Celsius degrees are the same size, but start at different points--zero degrees Celsius is equal to 273.16 K. Keywords: temperature, Fahrenheit, Celsius, kelvin

    22. Figure: 02-05UN00T06 Title: Specific heats of some common substances Caption: Specific heats of some common substances Notes: Specific heats of some common substances Keywords: specific heatFigure: 02-05UN00T06 Title: Specific heats of some common substances Caption: Specific heats of some common substances Notes: Specific heats of some common substances Keywords: specific heat

    23. DENSITY

    24. Figure: 02-05UN00T07 Title: Densities of some common materials at 25°C Caption: Densities of some common materials at 25°C Notes: Densities of some common materials at 25°C Keywords: densityFigure: 02-05UN00T07 Title: Densities of some common materials at 25°C Caption: Densities of some common materials at 25°C Notes: Densities of some common materials at 25°C Keywords: density

    28. Figure: 02-06 Title: A hydrometer for measuring specific gravity Caption: Hydrometers contain a weighted bulb at the end of a calibrated glass tube. The depth to which the hydrometer sinks in the fluid indicates the fluid’s specific gravity. Notes: Measurements of specific gravity are used in a variety of situations. Fermentation of wine or beer can be tracked by monitoring specific gravity as yeasts metabolize dissolved solids and produce ethanol. Antifreeze solutions are checked by hydrometers to monitor the mix of antifreeze solution and water, which indicates the range over which the antifreeze is effective. Urinometers are used to measure dissolved solids in urine. Keywords: hydrometer, specific gravityFigure: 02-06 Title: A hydrometer for measuring specific gravity Caption: Hydrometers contain a weighted bulb at the end of a calibrated glass tube. The depth to which the hydrometer sinks in the fluid indicates the fluid’s specific gravity. Notes: Measurements of specific gravity are used in a variety of situations. Fermentation of wine or beer can be tracked by monitoring specific gravity as yeasts metabolize dissolved solids and produce ethanol. Antifreeze solutions are checked by hydrometers to monitor the mix of antifreeze solution and water, which indicates the range over which the antifreeze is effective. Urinometers are used to measure dissolved solids in urine. Keywords: hydrometer, specific gravity

    29. Figure: 02-06UN01 Title: Specific gravity Caption: The amount of fermentation that has taken place in the wine can be measured with a hydrometer. Notes: A hydrometer is a device to measure specific gravity. Specific gravity is the density of the substance divided by the density of water at the same temperature. Keywords: specific gravity, hydrometerFigure: 02-06UN01 Title: Specific gravity Caption: The amount of fermentation that has taken place in the wine can be measured with a hydrometer. Notes: A hydrometer is a device to measure specific gravity. Specific gravity is the density of the substance divided by the density of water at the same temperature. Keywords: specific gravity, hydrometer

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