Chemistry Math in Chemistry Unit

How wide is our universe? 210,000,000,000,000,000,000,000 miles (22 zeros) How would you use this number in a calculator?

Luckily, we use something called Scientific Notation to help us out.

What is Scientific Notation? Easier way to represent very large and very small numbers.

What does a number in Scientific Notation look like? A number is expressed in scientific notation when it is in the form a x 10 n where a is between 1 and 9.9 and n is an integer

? What are the steps to put a number in scientific notation ? 1.Find the decimal point. Note: The decimal point is on the end of the last digit in a whole number. 1.Move the decimal point to make a number between 1 and 10. Count the number of moves.

Important MORE positive. 1.If the original number is MORE than 1, the exponent will be positive. LESS negative 1.If the original number is LESS than 1, the exponent will be negative.

Write the width of the universe in scientific notation. 210,000,000,000,000,000,000,000 miles Where is the decimal point now? After the last zero. Where would you put the decimal to make this number be between 1 and 10? Between the 2 and the 1

For example: 2. 10,000,000,000,000,000,000,000. How many decimal places did you move the decimal? 23 The answer in scientific notation is 2.1 x 10 23

1) Express in scientific notation. Where would the decimal go to make the number be between 1 and 10? 9.02 The decimal was moved how many places? 8 When the original number is less than 1, the exponent is negative x 10 -8

Practice Problems Put these numbers in scientific notation. 1) ) ) ) 12 5).987 PROBLEMS ANSWERS

How do you convert to general notation? 1.Look at the exponent, is it negative or positive. 2.If the exponent is negative, the original number is less than 1. 3.If the exponent is positive, the original number is more than 1. 4.Move the decimal point as many times as shown in the exponent.

Express 1.8 x in decimal notation Express 4.58 x 10 6 in decimal notation. 4,580,000

Significant Figures

What is a significant figure? A number that has been measured.

Why do we use these? 1.There is no such thing as a perfect/ exact measurement 2.Every number has some degree of error

The last digit in a measurement is always rounded so that we are as accurate as possible.

Why do we do this? Because we try to be as exact as possible in science.

The difference between accuracy and precision?

What is the first rule I use for significant figures? All non zero numbers are significant

What about zeros and sigfigs? Zeros are strange, look at each one to figure them out.

What is the first zero rule? Sandwiched zeros are significant

What is the second sig fig zero rule? Zeros to the right of the number are significant, only if a decimal is present

What is the third zero rule? Placeholder zeros are not significant No decimal, so they are placeholders

Let’s practice… How many sig figs are there in the following?

What about scientific notation and sig figs? The number before the x10 n will tell you how many sig figs you have. 6.02x x x x10 97

What does that mean? 2 more rules!

What about division and multiplication? You use the least number of sig figs used in the calculation.

How do I figure out the number of sig figs in an addition or subtraction problem? You use the least number of DECIMAL places of your input numbers. DO YOUR MATH FIRST, THEN ROUND!

Let’s practice…

Warm Up Use sig fig rules to calculate the following: / x

Dimensional Analysis

Discussion How old are you in days?

What is Dimensional Analysis? Dimensional analysis is used to go from one unit to another without changing its value.

How Does Dimensional Analysis Work? A conversion factor is used along with what you’re given, to determine what the new unit will be.

Examples of Conversion Factors 60 seconds = 1 min 60 minutes = 1 hour 24 hours = 1 day

How are conversion factors written? You can write any conversion as a fraction. For example, you can write 60 seconds = 1 minute as 60s or 1 min 1 min 60 s

How do you use a Conversion factor? The fraction must be written so that ‘ like’ units cancel. 5 inches 1 inches 2.54 cm

Steps 1.Make a 2.Put the given value 3.Choose the appropriate conversion factor. 4.The unit to be cancelled goes at the bottom of the line.

Example: Convert 8 yards to feet.

Let’s try some examples together… 1.Convert 285 liters to gallons.

Let’s try some examples together… 2. Convert 50cm to meters using Dim. Analysis.

Let’s try some examples together… 3. How many inches are in 17.3 cm?

Now, you try… Darren drank 2 liters of water. How many milliliters of water did he drink?

Multiple-Step Problems Ex: How many seconds are there in 2 hours?

Let’s practice together… 1.Convert 22.5 hours into seconds. 2.Convert 6.9 gallons into milliliters.

Temperature Conversions We use: K = Kelvin ̊ C= Celsius Formula: K= ̊ C+ 273

What is Density? The amount of matter in an object.

For example A rock is denser than a crumpled piece of paper. A styrofoam cup is less dense than a ceramic cup.

What is the formula for density? Density is equal to the mass divided by the volume of an object.

What is the unit for Density? Mass is measured in grams. Volume is measured in ml or cm 3.

What is unit used for Density?

Density of water? The density of water is exactly 1.0 g/ml or 1.0 g/cm 3 As such, many substances are compared to the density of water.

Sink or float? If an object floats on water, it is less dense than water. If an object sinks in water, it is more dense than water.

Lead floats on liquid mercury!

Remember! Density is a physical property. The density of an object does not change if it is cut or broken.

How do I round? A 4 and under, let it rest. A 5 and up, let it soar.

Rounding practice

Let’s practice 1) A chef fills a 50 ml container with 43.5g of cooking oil. What is the density of the oil?

Practice 2) Calculate the mass of a liquid with a density of 2.5g/ml and a volume of 15ml.

3) Calculate the volume of a liquid with a density of 5.45 g/cm 3 and a mass of 65g.