Multiply 1.24 by 0.2, leaving your answer in standard form.
The correct answer and explanation is:
To multiply 1.24 by 0.2 and express the result in standard form, follow these steps:
- Multiply the numbers: 1.24×0.2=0.2481.24 \times 0.2 = 0.248
- Convert the result to standard form:
Standard form is a way of expressing numbers that are too large or too small to be conveniently written in decimal form. It is written as a number between 1 and 10, multiplied by a power of 10. In this case, the result is 0.248, which is less than 1. To convert 0.248 to standard form, move the decimal point two places to the right, making the number between 1 and 10. This gives: 0.248=2.48×10−10.248 = 2.48 \times 10^{-1}
Thus, the result of multiplying 1.24 by 0.2 is 2.48×10−12.48 \times 10^{-1} in standard form.
Explanation:
Multiplying numbers in decimal form works like regular multiplication, but with careful attention to the position of the decimal point. After performing the multiplication, the next step is to convert the result to standard form, which is a mathematical convention used to simplify the representation of numbers. In standard form, the first part of the number is a coefficient between 1 and 10, while the second part is a power of 10 that adjusts the magnitude of the number accordingly. For 0.248, moving the decimal point two places to the right and adjusting the power of 10 to reflect that shift gives us the final result: 2.48×10−12.48 \times 10^{-1}. This is a simple application of the rules of scientific notation, which is used to handle both very large and very small numbers efficiently.