How do you write 310 in scientific notation?
The Correct Answer and Explanation is:
To write the number 310 in scientific notation, you need to express it in the form of:
[
a \times 10^n
]
where ( a ) is a number greater than or equal to 1 but less than 10, and ( n ) is an integer.
Steps to Convert 310 into Scientific Notation:
- Identify the Decimal Point:
Start by recognizing that the number 310 can be written as:
[
310.0
]
The decimal point is assumed to be at the right end of the number. - Move the Decimal Point:
To convert 310 into scientific notation, we need to move the decimal point so that it is located between the first and second digits. In this case, you would move the decimal point two places to the left:
[
310.0 \rightarrow 3.10
] Now, the number is in the form of ( 3.10 ), which is a number between 1 and 10, as required in scientific notation. - Determine the Exponent of 10:
The decimal point was moved two places to the left, so the exponent on 10 will be +2. This indicates that you multiplied the number by ( 10^2 ) to shift the decimal point. Thus, the exponent is positive because the original number was greater than 1. - Write the Final Answer:
Combining the coefficient ( 3.10 ) and the exponent ( 2 ), the number 310 in scientific notation is:
[
3.10 \times 10^2
]
Explanation of Scientific Notation:
Scientific notation is a way to express large or small numbers in a compact form. The main purpose of scientific notation is to simplify the representation of very large or very small numbers, especially when dealing with measurements in fields like science and engineering.
In scientific notation, the coefficient ( a ) is always a number between 1 and 10, and the exponent ( n ) shows how many places the decimal point was moved to convert the original number into the form ( a \times 10^n ). For numbers greater than 1, the exponent is positive, and for numbers less than 1, the exponent is negative.