What is 7.2×10^-8 as normal number
The Correct Answer and Explanation is:
To convert the scientific notation ( 7.2 \times 10^{-8} ) to a normal number, follow these steps:
Step-by-Step Conversion:
- Understand the scientific notation:
- In scientific notation, ( 7.2 \times 10^{-8} ) means that the decimal point of 7.2 must be moved 8 places to the left (since the exponent is negative).
- Move the decimal point:
- Start with the number 7.2, which is written as ( 7.2 ).
- Moving the decimal point 8 places to the left:
- Move 1 place to the left to get ( 0.72 ).
- Move 2 places to the left to get ( 0.072 ).
- Move 3 places to the left to get ( 0.0072 ).
- Move 4 places to the left to get ( 0.00072 ).
- Move 5 places to the left to get ( 0.000072 ).
- Move 6 places to the left to get ( 0.0000072 ).
- Move 7 places to the left to get ( 0.00000072 ).
- Move 8 places to the left to get ( 0.000000072 ).
Thus, ( 7.2 \times 10^{-8} ) is equal to 0.000000072 as a normal number.
Explanation of Scientific Notation:
Scientific notation is a way to express very large or very small numbers in a more compact form. It uses powers of 10 to scale a number. The general format is:
[
a \times 10^n
]
where ( a ) is a number between 1 and 10 (called the “coefficient”) and ( n ) is an integer that indicates how many places the decimal point is moved.
In this case, the exponent ( -8 ) indicates that the decimal point should be moved to the left by 8 places. This is necessary because the number is very small (less than 1), and the negative exponent tells us to shift the decimal to the left.
Understanding how to convert between scientific notation and standard form is essential, especially in fields like chemistry, physics, and engineering, where both very large and very small numbers are frequently used.