To convert the number [tex]\(0.031 \times 10^5\)[/tex] into correct scientific notation, follow these steps:
1. Identify the Coefficient:
- The coefficient here is [tex]\(0.031\)[/tex].
2. Convert the Coefficient to a Number Between 1 and 10:
- Move the decimal point two places to the right in [tex]\(0.031\)[/tex] to get [tex]\(3.1\)[/tex].
3. Adjust the Exponent:
- When you move the decimal point to the right, each place you move it, you effectively multiply the number by [tex]\(10\)[/tex]. Since you moved the decimal point two places to the right, you multiply by [tex]\(10^2\)[/tex].
- The original exponent given is [tex]\(5\)[/tex].
- Since you multiplied by [tex]\(10^2\)[/tex], you must compensate this by decreasing the original exponent by 2. Thus, the new exponent is:
[tex]\[
5 - 2 = 3
\][/tex]
4. Write the Result in Scientific Notation:
- The final number is [tex]\(3.1\)[/tex] and the adjusted exponent is [tex]\(3\)[/tex].
- Therefore, the number [tex]\(0.031 \times 10^5\)[/tex] in scientific notation is:
[tex]\[
3.1 \times 10^3
\][/tex]
So the correct scientific notation for [tex]\(0.031 \times 10^5\)[/tex] is [tex]\(3.1 \times 10^3\)[/tex].
