If the square root is 338 and I'm asked to round to the nearest thousandth, how is the answer 18.385? I don't understand how to formulate that answer?
sqrt 338 = 18.384776 on my calculator.
Rounding to the thousandths place is the 3rd place to the right of the decimal which is the 4. The next number to the right is a 7 which is over 5 so 4 is raised to the next number higher and the answer is 18.385
To understand how the square root of 338 rounds to 18.385, let's break down the steps involved in calculating and rounding.
1. Start with the square root of 338. The square root of 338 is an irrational number, which means it cannot be expressed as a terminating decimal or a fraction. Thus, when we calculate the square root of 338, we get a decimal that continues forever without repeating.
2. To round the square root to the nearest thousandth, you need to look at the digit in the fourth decimal place (the thousandth place) and determine how it affects the rounding process.
3. In this case, the digit in the fourth decimal place of the square root of 338 is 5. Since 5 is exactly halfway between 0 and 9, the general rounding rule is to round up if the digit to the right of the rounding position is 5 or greater, and round down if the digit is less than 5.
4. Following the rounding rule, since the digit in the fourth decimal place (5) is exactly halfway, we round up the digit in the third decimal place (8) to the next higher digit (9).
5. This rounding process changes the square root of 338 from approximately 18.38477631 to 18.385.
To summarize, rounding the square root of 338 to the nearest thousandth results in the answer 18.385 because the digit in the fourth decimal place (5) is rounded up according to the general rounding rules.