Write 400+5 in standard form
The Correct Answer and Explanation is:
To write 400 + 5 in standard form, we first need to evaluate the expression and then convert the result into the appropriate format.
Step 1: Evaluate the expression
The expression is:
[
400 + 5 = 405
]
Step 2: Convert 405 into standard form
Standard form, in mathematics, typically refers to writing a number as a product of a number between 1 and 10 and a power of 10. To express 405 in standard form, we need to rewrite it as:
[
405 = 4.05 \times 10^2
]
Explanation:
The standard form (also known as scientific notation) represents numbers in a concise way, particularly useful for very large or very small numbers. The general rule for converting a number into standard form is:
[
N = a \times 10^n
]
Where:
- ( a ) is a number such that ( 1 \leq a < 10 ),
- ( n ) is an integer.
In this case, 405 is a regular number. To express it in standard form, we first move the decimal point so that only one non-zero digit is left to the left of the decimal. In 405, we move the decimal point two places to the left, converting 405 into 4.05.
Then, to account for the movement of the decimal point, we multiply by ( 10^2 ) because the decimal point was moved two places to the left (this means the exponent of 10 is 2). Thus, the standard form of 405 is:
[
4.05 \times 10^2
]
This is the scientific notation or standard form representation of the number. It simplifies writing and comparing numbers, especially when dealing with extremely large or small values, making it easier to perform arithmetic operations like multiplication or division.