Round 19.8157157654 to the nearest ten-thousandth.
The correct answer and explanation is:
To round the number 19.8157157654 to the nearest ten-thousandth, follow these steps:
- Identify the ten-thousandth place: The ten-thousandth place is the fourth digit to the right of the decimal point. In the number 19.8157157654, the digits to the right of the decimal point are 8, 1, 5, 7, 1, 5, 7, 6, 5, 4. The digit in the ten-thousandth place is 7.
- Look at the digit in the next place: The next place is the hundred-thousandth place, which is the fifth digit to the right of the decimal point. In this case, the digit in the hundred-thousandth place is 1.
- Apply rounding rules:
- If the digit in the hundred-thousandth place is 5 or greater, round the digit in the ten-thousandth place up by 1.
- If the digit in the hundred-thousandth place is less than 5, leave the digit in the ten-thousandth place unchanged.
- Round the number: Since the digit in the hundred-thousandth place is 1 (which is less than 5), the digit in the ten-thousandth place remains unchanged. Therefore, the number 19.8157157654 rounded to the nearest ten-thousandth is 19.8157.
Explanation:
Rounding is a technique used to simplify numbers while maintaining their approximate value. When rounding to a specific place value, it’s important to look at the digit immediately following the place value you’re rounding to. In this case, rounding to the ten-thousandth means focusing on the fourth digit after the decimal point. Rounding allows us to reduce the number’s precision, which can be helpful in various calculations, especially when dealing with large datasets or when less precision is required. The rule of rounding up or leaving the digit unchanged ensures that numbers are rounded in a consistent way across different situations.