WRITING A NUMBER IN SCIENTIFIC NOTATION
About "Writing a number in scientific notation"
Writing a number in scientific notation :
To translate between standard notation and scientific notation, you can count the number of places the decimal point moves.
To write a number which is greater than 1 in scientific notation, move the decimal point left and use a positive exponent.
It has been illustrated in the picture given below.
To write a number which is less than 1 in scientific notation, move the decimal point right and use a negative exponent.
It has been illustrated in the picture given below.
Writing a number in scientific notation - Examples
Example 1 :
The distance from Earth to the Sun is about 93,000,000 miles. Write this distance in scientific notation.
Solution :
Step 1 :
Move the decimal point in 93,000,000 to the left until you have a number that is greater than or equal to 1 and less than 10.
Move the decimal point 7 places to the left.
Remove extra zeros.
9.3
Step 2 :
Divide the original number by the result from Step 1.
That is, divide 93,000,000 by 9.3.
10,000,000
Write your answer as a power of 10.
10⁷
Step 3 :
Write the product of the results from Steps 1 and 2.
Write a product to represent 93,000,000 in scientific notation.
93,000,000 = 9.3 × 10⁷ miles
Example 2 :
The average size of an atom is about 0.00000003 centimeter across. Write the average size of an atom in scientific notation.
Solution :
Step 1 :
Move the decimal point as many places as necessary to find a number that is greater than or equal to 1 and less than 10.
Place the decimal point after 3 and put one zero to make the decimal visible.
3.0
Step 2 :
Count the number of places you moved the decimal point.
8
Step 2 :
Multiply 3.0 times a power of 10.
Since 0.00000003 is less than 1, you moved the decimal point to the right and the exponent on 10 is negative.
3.0 × 10⁻⁸
The average size of an atom in scientific notation is 3.0 × 10⁻⁸.
Reflect
When we write a number that is less than 1 in scientific notation, how does the power of 10 differ from when we write a number greater than 1 in scientific notation ?
The exponent is negative instead of positive.
After having gone through the stuff given above, we hope that the students would have understood, how to write a number in scientific notation".
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