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Scientific Notation and Sig. Figs.

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by

Leanne Hilkowski

on 15 September 2015

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Transcript of Scientific Notation and Sig. Figs.

POSSIBLE
SOLUTIONS

DATE: September 10th, 2013
CREATED BY: Miss Hilkowski
TEAM: Chemistry
GOALS
Write 6,926,300,000 in Scientific Notation
PLAN 1
In order to write in SCIENTIFIC NOTATION, you must start with a number. Let's take these numbers for example:
PLAN 2
For small numbers we use a similar approach
Multiplying and Dividing
123,000,000,000 in scientific notation is written as :

1.23 x 10


EXECUTION
Let's use the same steps we used for large numbers.
Step 1
Put the decimal after the first digit, and drop the zeros.
Step 3
In 0.000001, there are 6 spaces, so we would write it as:
Step 2
To find the exponent count the number of places from the decimal to the end of the number.
RESULTS
Write 0.00361 in SCIENTIFIC NOTATION
EXECUTION
Rules for Multiplication in Scientific Notation
Step 1
Multiply the decimal numbers
Step 3
Put the new decimal number with the new exponent in scientific notation form.
Step 2
Add the exponents
RESULTS
Multiply (2.8 x 10 ) x (1.9 x 10 )
SUCCESS?
6. 9263 x 10
SUCCESS?
0.00361 can be written as:
3.61 x 10
3.61E -3
3.61 x 10^-3
SUCCESS?
YES!
YES!
YES!
NO!
NO!
NO!
WHAT NOW?
Dividing numbers in SCIENTIFIC NOTATION
Step 2
Subtract the exponents of the powers of 10.
Step 3
Place the new power of 10 with the new decimal in scientific notation form.
Step 1
Divide (1.23 x 10 ) by (2.4 x 10 ).
SIGNIFICANT FIGURES
Significant figures are important because they tell us how good the data we are using are. (Incidentally, the word “data” is plural for “datum”, so even though it seems weird saying that “data are [something]”, it’s grammatically correct.) For example, let’s consider the following three numbers:
100 grams

100. grams

100.00 grams
RESULTS
•The first number has only one significant figure (namely, the “1” in the beginning). Because this digit is in the “hundreds” place, this measurement is only accurate to the nearest 100 grams (i.e. the value of what we’re measuring is closer to 100 grams than it is to 200 grams or 0 grams).
Rules
Rule 1: Any number that isn’t zero is significant. Any zero that’s between two numbers that aren’t zeros is significant.

•All this means is that if you have actual numbers written down (or zeros between these numbers), they have actual meaning and give you meaningful information.

•Example: 198, 101, and 987 all have three significant figures.
REMAINING PROBLEMS
When combining measurements with different degrees of accuracy and precision, the accuracy of the final answer can be no greater than the least accurate measurement
NEW CHALLENGES
How many significant figures are in the following numbers?
RESULTS
Write 6,926,300,000 in Scientific Notation
Step one
Put the decimal after the first digit and drop the zeroes
Step three
In 300,000,000 there are 8 zeros so we write it as:
Step two
To find the exponent count the number of places from the decimal to the end of the number.
EXECUTION
The steps for doing SCIENTIFIC NOTATION are simple!
PROBLEM
Sometimes in Chemistry, numbers are too long to write out in complete form.

PROJECT REPORT
Do these look familiar?
300,000,000 m/sec


0.000 000 000 753 kg
That's the speed of light!
That's the mass of a dust particle!
300,000,000
3.00000
0
0
0
3.00000000
8 zeros
3.0 x 10
8
9
Did you know?
Exponents are often expressed using other notations. The number 6,926,300,000 can also be written as:
6.9263E + 9 or 6.9263 x 10^9
How about this?
Write 0.000001 sec (one millionth of a second!) in SCIENTIFIC NOTATION.
0001.0
0
0
000001.0
6 spaces
1.0 x 10
-6
How else?
What is another way we can write 0.000001?
1.0E -6 or 1.0 x 10^-6
-3
11
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 10 the number 11 is referred to as the exponent or power of ten.
Multiply (2.6 x 10 ) by (6.3 x 10 ).
7 4
2.6
x6.3
-------
16.38
(2.6 x 10 ) by (6.3 x 10 ).
7 4
7 + 4 = 11
16.38 x 10
11
Wait a second...
Because the new decimal number is
greater than 10, count the number of places
the decimal moves to put the number
between 1 and 10. Add this number to the
exponent. In this case, the decimal point
moves one place, so add 1 to the exponent.
16.38 x 10 → 1.638 x 10
11 12
8 4
5.32 x 10
12
11
11 4
Divide the decimal numbers
1.23 / 2.4 = 0.5125
11 - 4 = 7
0.5125 x 10
7
Because the decimal number is
not between 1 and 10, move the decimal
point one place to the right and
decrease the exponent by 1.
0.5125 x 10 → 5.125 x 10
7 6
100 grams

100. grams

100.00 grams
•The third number has five significant figures (as we’ll talk about later). Because the last significant figure is in the “hundredths” place, the measurement can be considered to be accurate to the nearest 0.01 grams (i.e. the value of what we’re measuring is closer to 100.00 grams than it is to 100.01 or 99.99 grams)
•The second number has three significant figures (the decimal makes all three digits significant, as we’ll discuss later). Because the last significant figure is in the “ones” place, the measurement is accurate to the nearest gram (i.e. the value of what we’re measuring is closer to 100 grams than it is to 101 grams or 99 grams).
Rule 2
Any zero that’s before all of the nonzero digits is insignificant, NO MATTER WHAT.

•Basically, this applies to numbers that are very small decimals. For example, if you have the number 0.000054, there are only two significant figures (the 5 and the 4), because the zeros in front are insignificant.

Any zero that’s after all of the nonzero digits is significant only if you see a decimal point. If you don’t actually see a little dot somewhere in the number, these digits are not significant.
Rule 3
Consider the numbers “10,000 lbs” and “10,000. lbs”.
The first number is significant only to the nearest ten thousand pounds (only the first “1” is significant) and the second is significant to the nearest pound (all five digits are significant). What the addition of the decimal does is tell us how good our measuring equipment is.
Rule 4
When you write numbers in scientific notation, only the part before the “x” is counted in the significant figures. (Example, 2.39 x 10^4 has three significant figures because we only worry about the “2.39” part).

Let’s go back to Rule #2, in which we said that “0.000054” had two significant figures. The reason for this is that if we convert it into scientific notation, we end up with the number “5.4 x 10^-5”

When measurements are added or subtracted, the answer can contain no more decimal places than the least accurate measurement.
150.0 g H2O
+ 0.507 g salt
-------------------
150.5 g solution

Although 0.507 is accurate to the thousandths place, 150.0 is only accurate to the tenths place. Therefore, the answer cannot be more accurate than the tenths place.
When measurements are multiplied or divided, the answer can contain no more significant figures than the least accurate measurement.
Likewise....
1234

0.023
4

2
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