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49. EXPLAIN IN POWER NOTATION. EXPLAIN STEP BY STEP.
Answers
Answer:
Step-by-step explanation:
What is it? Scientific notation is used to represent very large and very small
numbers. In scientific notation, a number is written as a number between 1 and
10 multiplied by a power of 10. Here is a table of the powers of 10 to help you
see how to select your exponent for writing a number in scientific notation.
Powers of Ten
101
= 10 106
= 1,000,000 100
= 1 10-5
= 0.00001
102
= 100 107
= 10,000,000 10-1
= 0.1 10-6
= 0.000001
103
= 1,000 108
= 100,000,000 10-2
= 0.01 10-7
= 0.0000001
104
= 10,000 109
= 1,000,000,000 10-3
= 0.001 10-8
= 0.00000001
105
= 100,000 1010 = 10,000,000,000 10-4
= 0.0001 10-9
= 0.000000001
How to do it (Part 1). Follow these steps to change a number from standard
form to scientific notation.
For a large number.
Step 1: Move the decimal point to the left until you have a number greater than or
equal to 1 and less than 10.
Step 2: Count the number of decimal places you moved the decimal point to the
left and use that number as the positive power of 10.
Step 3: Multiply the decimal (in Step 1) by the power of 10 (in Step 2).
For a small number.
Step 1: Move the decimal point to the right until you have a number greater than
or equal to 1 and less than 10.
Step 2: Count the number of decimal places you moved the decimal point to the
right and use that number as the negative power of 10.
Step 3: Multiply the decimal (in Step 1) by the power of 10 (in Step 2).
Examples
Write 782,000 in scientific notation.
Move the decimal point 5 places to the left.
7.82000
Since the decimal point is moved 5 places to the left, multiply by 105
.
7.82 x 105
So, 782,000 = 7.82 x 105
Write 0.0000006534 in scientific notation.
Move the decimal point 7 places to the right.
6.534
Since the decimal point is moved 7 places to the right, multiply by 10-7
.
6.534 x 10-7
So, 0.0000006534 = 6.534 x 10-7