To find the best estimate of [tex]\(\sqrt{47}\)[/tex] to the nearest tenth, we follow these steps:
1. Determine the exact value of [tex]\(\sqrt{47}\)[/tex]:
- The exact value of [tex]\(\sqrt{47}\)[/tex] is approximately [tex]\(6.855654600401044\)[/tex].
2. Round this value to the nearest tenth:
- The digit in the tenths place is the first digit after the decimal point. For [tex]\(6.855654600401044\)[/tex], the tenths place is occupied by the digit [tex]\(8\)[/tex].
- The digit in the hundredths place is the second digit after the decimal point. For [tex]\(6.855654600401044\)[/tex], the hundredths place is occupied by the digit [tex]\(5\)[/tex].
3. Apply the rounding rules:
- If the digit in the hundredths place (which is [tex]\(5\)[/tex]) is 5 or greater, we round up the tenths place digit by 1.
So, rounding [tex]\(6.855654600401044\)[/tex] to the nearest tenth gives us [tex]\(6.9\)[/tex].
Therefore, the best estimate of [tex]\(\sqrt{47}\)[/tex] to the nearest tenth is [tex]\(6.9\)[/tex].
