Changing TI-nspire from Fraction to Decimal Mode

I've had a lot of questions about changing the mode from fraction to decimal.  Here are the steps.

From the home screen:  Push the on button again (the house)
1) 5: Settings & Status
2) 2: Settings
3) 1: General
4) Calculation Mode
5) Change from Auto to Approximate
6) Tab to Make Default and press enter

Unit Analysis: Density

You must use unit analysis to solve density problems in chemistry (NOT THE FORMULA & ALGEBRA).  Remember you are learning the process  of unit analysis, not simply finding the correct answer!

Use the technique you have learned in problem solving:  what are you looking for, what are you given, put the units together to cancel and solve.

Example #1

A sample of a known metal is dropped into a graduated cylinder with 25.0 mL of water. The level rises to 31.5 mL. If the given density of the metal is 2.56 kg/L, what is the mass of the sample in grams?

Possible Questions
Where did 6.5 mL come from? A substance displaces its volume when immersed in water.  The water level rose from 25.0 to 31.5 mL.
Why are there only 2 sig dig in the final answer?  When you multiply and divide, you use the least number of sig dig.  2.56 kg/1L has 3, 6.5 mL has 2, and the conversions for L and kg are exact values with an infinite number of sig dig.


Example #2

What is the volume of a sample of aluminum in L that weighs 56.7 g?  The density of aluminum is 2.71 g/mL.

Possible Questions

Why flip the density?  To make sure the units of volume will be in the numerator.

I got a different answer (0.153657), why? Remember that 2.71 is in the denominator.  You must divide, not multiply. You can either input 56.7 first, divided by 2.72, divided by 1000
OR start with 1 divided by 2.71, times 56.7, divided by 1000.

Unit Analysis: Solving Word Problems

Unit Analysis can make solving complex word problems much easier.  First, DON’T BE INTIMIDATED!  The problem is not going to jump off the page and bite you if you get it wrong!  Just TRY!  Follow these basic steps to simplify problem solving.

1. What are your looking for?  Read through the problem and determine the exact units requested.

          WRITE THAT DOWN!

2. What are you given?  Sometimes, there is so much information given it is a good idea to write it all down or underline it in the problem.  It also helps if you will label what type of given information it is.  For instance:  mass, distance, …

3. Is there any other information you need?  Conversions, molar mass, reactions, …

4. Put the units together in such as way that you cancel out the units you don’t want and end up with only the units requested.  If the units are reversed in your final answer, just flip your calculation.

Example #1

A farmer has 2 cows and he decides to change to chickens.  He can barter 4 emu for each cow, 3 emu for 5 pigs, 8 pigs for 3 llama,  a llama for 20 rabbits and 3 rabbits for 2 chickens.  How many chickens can he get for both his cows?

1. What are you looking for?  chickens

2. What are you given?  Many ridiculous ratios with animals.

3. Is there any other information needed?  Not for this problem, just watch out where you step.

4. Use UA to determine the units requested.

When you plug these values into the calculator, the screen reads 66.66666667, but we are looking for WHOLE, LIVE chicken, not parts.

Remember that in science we deal with objects and measurements, NUMBERS HAVE MEANING.  You must evaluate your answer based on what the units are, as well as significant digits.

Example #2

A machine produces 4.5 x 10³ m of spaghetti noodles each minute. A package of noodles contains 128 noodles that are each 12.5 inches long.  The company sells the noodles in cartons containing 20 packages for $75.50.  If the machine runs 12.0 hr a day, 5.00 days a week, 50.0 weeks a year, how much money can the company make each year from that one machine?

Unit Analysis: Both Numerator & Denominator

Changing both the unit in the numerator and the denominator is just like changing only one set of units.  Just remember that all the units except the ones needed must cancel.

Change 3.40 m/sec to km/yr.

Notice that you must put the 60 sec in the numerator to cancel the sec you were given.  All units must cancel except the ones requested in the problem.  In this case, km/year.

Unit Analysis: The Basics

Unit analysis or dimensional analysis is a method used to calculate values based on the units of each measurement.  We will start by using this method to simply convert one measurement in one unit to another unit. This technique may seem more complicated than necessary at this point, but remember you are learning how to use the units.  Later in the semester you will see that unit analysis will make problem solving so much easier!

Unit analysis is based on two very fundamental mathematical principles.

1. any number multiplied by one is equal to itself
2. a fraction equals one if the value of the numerator equals the value of the denominator

These two properties allow us to let the measurements determine how to do the calculation.  The final answer must have the units desired and all other units must be canceled.

Measurement, Part 3: Accuracy & Precision

Accuracy and precision are terms used to explain the sources of error in a data set.  Accuracy describes how close a measurement is to the correct answer. Precision describes the spread of the data or how close the measurements are to each other.

To determine the accuracy of a measurement, the correct or accepted value must be known.  The most common calculation associated with accuracy is percent error.

percent error = |(accepted value - experimental value)|   x   100

                                   experimental value

The precision of a data set can be determined in a number of ways, including range, standard deviation and percent deviation. Range is determined by subtracting the smallest value from the largest value in a data set.

Deviation literally means difference, so we can calculate it using subtraction.  By finding the difference between an individual measurement and the average of all the measurements in a data set, we can find how "off" that single measurements is from all the others. A very basic way of looking at standard deviation is to think of it as the average of all the deviations of the individual measurements from the average of the data set.  

The problem with simply using standard deviation to determine precision is magnitude (the size of the numbers.) A standard deviation of 1.00 may sound large or small without some idea of the magnitude of the measurements in the data set.  If your measurements range from 1.20 to 3.56, it is huge!  But if the range of the data is 1000.0 to 1002.0, it would be much more acceptable.

Percent compares the part to the whole, so it takes away the uncertainty of magnitude.  Percent deviation allows us to compare the standard deviation to the average of the data set.  The lower the percentage that each individual measurement differs from the average of the data set, the better the precision.

percent deviation = standard deviation  x  100

                                average of the data set

Measurement, Part 2: Measurement & Uncertainty

There are two types of numbers in science: exact (counting) numbers and inexact (measurements and calculated quantities).  Exact or counting numbers represent objects.  For instance, a dozen eggs has exactly 12 eggs.  You can’t have 12.01 eggs.  Measurements and numbers based on calculations will always have some uncertainty. Significant digits are used to represent that uncertainty or the amount of confidence you have in a measurement.

Uncertainty occurs because we use equipment to make measurements.  You can only measure a length as exact as the increments on the ruler you are using.  Significant digits are the numbers we know with certainty plus one more that is estimated.

Basic Rules:

1. All non-zero digits are significant
2. All zeros between non-zero digits are significant
3. Zeros to the right of the decimal and to the right of a non-zero digit are significant
4. Zeros to the right of the decimal, but to the left of all non-zero digits are not significant
5. If there is no decimal, zeros to the right of the last non-zero digit are not significant

Rules for Calculations:

1. In addition and subtraction, use the LEAST number of DECIMALS.
2. In multiplication and division, use the LEAST number of SIGNIFICANT DIGITS.
3. Apply each rule using the order of operations.

Measurement, Part 1: Introduction

All science is based on analyzing data. There are two types of data in chemistry. Qualitative data is based on descriptions such as color, state and luster. Quantitative data is based on numerical measurements.

Chemistry represents its quantitative data using the metric system.  Mass is measured in grams, volume in liters, length in meters, and temperature in Celsius or the Kelvin scale. EVERY QUANTITATIVE MEASUREMENT MUST HAVE BOTH A QUANTITY AND A UNIT.

Numbers mean nothing without a unit!
Volume is the amount of space occupied by a substance.  It can be measured in a derived unit such as liters or gallons, or as a unit of distance^3 such as cm^3 or ft^3.
Mass is the amount of matter present in a substance and is measured in grams.  Weight and mass are not the same thing.  Weight is the pull of gravity on an amount of matter and is dependent on location.  The same object will weigh less on the moon than on Earth, but its mass does not change.