Download Scientific Notation to Standard Form Worksheet - Sci3

Name: ________________________________
Mr. Art
Sci3
Date: _____________
Period: ___________
Scientific Notation to Standard Form
--------------------------------------------------------------------------------------------------------------------------------Type #1: Scientific Notation (with POSITIVE exponents) to LARGE Numbers in Standard Form
---------------------------------------------------------------------------------------------------------------------------------Example: Convert 1.8  10 to standard form.
---------------------------------------------------------------------------------------------------------------------------------Steps:
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1) Move the decimal point to the RIGHT as many places as the exponent indicates. While moving the
decimal point to the RIGHT, create “waves” under each number. When the numbers end, continue
drawing in “waves” until you have drawn the same number of “waves” as the exponent indicates.
2) Place a zero in each of the “waves” that do not already have a number in them.
3) The number is now in standard form.
4) To finish it off, place commas after every three digits when reading right to left. Start at the decimal
point, go to the left three digits (place a comma), continue to the left three digits (place a comma),
etc.
Type #2: Scientific Notation (with NEGATIVE exponents) to SMALL Numbers in Standard Form
---------------------------------------------------------------------------------------------------------------------------------8
Example: Convert 1.8  10 to standard form.
---------------------------------------------------------------------------------------------------------------------------------Steps:
1)
Move the decimal point to the LEFT as many places as the exponent indicates. While moving the
decimal point to the LEFT, create “waves” under each number. When the numbers end, continue
drawing in “waves” until you have drawn the same number of “waves” as the exponent indicates.
2)
Place a new decimal point at the end of the last “wave”.
3)
Place a zero in each of the “waves” that do not already have a number in them.
4)
The number is now in standard form.
Comparing Numbers in Scientific Notation
Step #1: If they have the same power of 10... compare the COEFFICIENTS
Directions: Use an inequality symbol to state which following numbers in scientific notation is
greater than the other.
Example #1: 5.2 x 108
3.7 x 108
Example #2: 2.10 x 10-3
2.01 x 10-3
Step #2: If they have different powers of 10... compare the EXPONENTS (the greater the exponent, the
greater the number)
Directions: Use an inequality symbol to state which following numbers in scientific notation is
greater than the other.
Example #1: 1.2 x 109
2.85 x 107
Example #2: 6.7 x 10-3
5.7 x 10-4
Practice Examples
Directions: Convert the following numbers from scientific notation to standard form.
1) 4.12 x 10-9 = _________________________
2) 6.3 x 107 = _________________________
3) 9 x 10-5 = _________________________
4) 3.14 x 108 = _________________________
Directions: Use an inequality symbol to state which following numbers in scientific notation is greater than
the other or write an equal sign if they are equivalent.
5) 1.3 x 10-3
1.2 x 10-2
6) 1.2 x 109
0.12 x 108