Download What is Scientific Notation? Why do we use Scientific Notation

Scientific Notation Worksheet
What is Scientific Notation?
A shortcut used to report numbers that are really small or really large. Makes it easier to enter into
calculators and calculate.
Why do we use Scientific Notation?
Scientific data (measurements) are usually extremely small or extremely large (lots of zeros) numbers.
For example:
602000000000000000000000 is a common number used in chemistry
That many zeros would be impossible to put into the calculator
without making errors.
So, to deal with these types of
numbers we report them in a
different type of notation called
“scientific notation.”
Can we just leave off the zeros?
Well is $25 the same as $25,000. No, they are significantly different numbers. So, the
zeros are really important.
Which one would you rather enter into the calculator?
602000000000000000000000
6.02 x 1023
Do I Understand?
Circle the numbers that are written in scientific notation:
.000057
2.45 x 1045
2.45 x 10-7
1250000000000
Scientific Notation Worksheet
How do I put a number into scientific notation?
6.02 x 1023
_____________________________ should only include the most significant digits. So it should
not include leading or trailing zeros). But it
should include all non-zero numbers and trapped
zeros.
_____________________________ always has a decimal after the first non-zero number.
.000000000000000000542
(leading zeros)
542000000000.0000
(trailing zeros)
500042 (trapped zeros)
_____________________________ on the ten tells you how many places the decimal is moved
to the right or left.
o
o
A _________________ exponent – means the number is really small
A _________________exponent – means the number is really big
Do I Understand?
Circle the number that is the smallest number:
.000057
2.45 x 1045
2.45 x 10-7
1250000000000
Scientific Notation Worksheet
How do I put it into my calculator?
Mastering how to enter a number in scientific notation will help eliminate errors when multiplying,
dividing, adding or subtracting when using scientific notation.
5
The following is how you should enter the following number, 3.45 x 10 into the TI 30XA calculator:
3
.
4
5
EE
5
Notice the “x” or the “10” ARE NOT
to be typed into the calculator.
For those of you with a different calculator I will show you the different steps:
Do I Understand?
Round the coefficient to the second decimal place (the hundredths place). Use your calculator.
1. (1.14 x 103) (3.1 x 1042) =
_________________
2. (2.75 x 10-3) (2.7 x 10-4)=
_________________
3. (1.48 x 107)/(1.4 x 10-5)=
_________________
4. (2.57 x 105)/(1.4 x 1012)=
_________________
Scientific Notation Worksheet
What if my calculator breaks?
Scientific Notation and Mathematical Operations:

Multiplication:
Multiply the numbers and add the exponents
Ex: (9.45 x 1034)(2.58 x 1042)
Step #1 Multiply the coefficients
Step #2 Add the exponents
34 + 42 = 76
The answer is 23.625 x 1076
Is this the correct
answer?_____________________
Why or Why not?
____________________________
If not, what should the answer be?_______________
Step #3 Put into Scientific Notation
Step 3A.
Move the decimal to the proper location ------- 23.625
Step 3B.
How many decimal places did you move ---------1
Step 3C.
Add the number from Step 3B to the exponent in Step 2 ----------- 76 + 1
Answer ---- 2.36 x 1077
Scientific Notation Worksheet

Division:
Multiply the numbers and add the exponents
Ex: (9.45 x 1034)/(2.58 x 1042)
Step #1 Divide the coefficients
Step #2 Subtract the exponents
9.45 ÷ 2.5 = 3.66
34 - 42 = -8
The answer is 3.66 x 10-8
Follow the same steps as listed in Step 3 on the previous page
Do I Understand?
5. (5.87 x 103) (3.1 x 104) =
_________________
6. (1.48 x 1017)/(1.4 x 10-8)=
_________________
I KNEW YOU COULD DO IT…….