Download Scientific Notation

SCIENTIFIC NOTATION
SCIENTIFIC NOTATION
Scientific Notation: a short-hand
way of writing large numbers or
small numbers without writing
all of the zeros.
THE DISTANCE FROM THE SUN TO
THE EARTH
93,000,000
STEP 1
• 1) Rewrite the number as a number
less than 10 but at least 1.
9.3 is less than 10, but at least one
Then…..
• Write number without zeros
Step 2
• Count how many
places you moved decimal
• Make that your power of ten
STANDARD V SCIENTIFIC
• 93,000,000 --Standard Form
• 9.3 x 107 --Scientific Notation
EXAMPLE 1
• Convert to Scientific Notation
• Given: 289,800,000
• Use: 2.898
• Answer:
2. 898 x
8
10
Why is the exponent positive?
PRACTICE PROBLEM
Write in scientific notation. Decide the power of 10
1)
0.0985 = 9.85 x 10?
2)
64,100,000,000 = 6.41 x 10?
3)
0.00279 = 2.79 x 10?
4)
4,200,000 = 4.2 x 10?
9.85 x 10-2
6.41 x 1010
2.79 x 10-3
4.2 x 106
MORE PRACTICE PROBLEMS
On these, decide where the decimal will be moved.
1)
734,000,000 = ______ x 108
2)
0.00072 = ______x 10-4
3)
90,000,000,000 = _____ x 1010
1) 7.34 x 108
2) 7.2 x 10-4
3) 9 x 1010
COMPLETE PRACTICE
PROBLEMS
Write in scientific notation.
1)
2)
3)
50,000
0.005
802,000,000,000
1) 5 x 104
2) 5.0 x 10-3
3) 8.02 x 1011
SCIENTIFIC NOTATION TO
STANDARD FORM
Step 1: Determine the sign of the power of 10.
Step 2: Move the decimal point according to
the power of 10.
SCIENTIFIC NOTATION TO
STANDARD FORM
Example 1
3.4 x 105 in scientific notation
3.40000 --- move the decimal
340,000 in standard form
EXAMPLE 2
• Convert to Standard Notation
• Given: 5.093 x 10-6
• Answer: (move 6 places to the right)
0.000005093
WRITE IN STANDARD FORM
1) 6.27 x 106
3) 5.98 x 10-3
2) 9.01 x 104
4) 9.0 x 100