How do you write 25.4 millimeters in scientific notation
The Correct Answer and Explanation is:
Correct Answer:
25.4 millimeters in scientific notation is 2.54 × 10¹ millimeters.
Explanation
Scientific notation is a way of expressing very large or very small numbers in a more compact and manageable form. This format is especially useful in science and engineering, where such numbers frequently occur. In scientific notation, a number is written as the product of two factors: a decimal number between 1 and 10, and a power of ten. The general form is:
N × 10ⁿ,
where N is a number such that 1 ≤ N < 10, and n is an integer.
To convert a number like 25.4 into scientific notation, the decimal point must be moved so that only one non-zero digit remains to the left of the decimal. In this case, the decimal point in 25.4 is moved one place to the left to become 2.54.
Since the decimal was moved one place to the left, the exponent of 10 becomes positive 1. This is because moving the decimal point to the left increases the value of the exponent in powers of ten. Each movement to the left corresponds to multiplying by 10¹.
Therefore:
25.4 = 2.54 × 10¹
This means that 2.54 should be multiplied by 10 to return to the original value of 25.4.
Scientific notation helps simplify calculations and makes comparisons between numbers more straightforward. It also reduces the risk of error when dealing with many zeros. For example, instead of writing 0.0000000012, it is easier and cleaner to write 1.2 × 10⁻⁹.
In conclusion, the number 25.4 millimeters, when expressed in scientific notation, becomes 2.54 × 10¹ millimeters. This format highlights the precision of the number while efficiently handling its scale.
