Which number, rounded to the nearest hundred thousand, is 800,000?
The correct answer and explanation is:
Correct answer:
Any number from 750,000 up to 849,999 rounds to 800,000 when rounded to the nearest hundred thousand.
Explanation (300 words):
Rounding a number to the nearest hundred thousand means you look at the digit in the ten-thousands place to decide whether to round up or down.
- The place values for the first six digits are (from left to right): hundred thousands, ten thousands, thousands, hundreds, tens, and ones.
- When rounding to the nearest hundred thousand, you focus on the digit immediately to the right of the hundred thousand place — that is the ten-thousands digit.
Rules for rounding:
- If the ten-thousands digit is less than 5, you round down (keep the hundred thousands digit the same, and change everything after it to zero).
- If the ten-thousands digit is 5 or greater, you round up (increase the hundred thousands digit by 1, and change everything after it to zero).
Step-by-step example:
- Suppose we want to find the range of numbers that round to 800,000.
- The hundred thousands digit for 800,000 is 8.
- Numbers from 750,000 up to 849,999 will round to 800,000:
- For example, 749,999 rounds down to 700,000 because the ten-thousands digit is 4 (less than 5).
- 750,000 rounds up to 800,000 because the ten-thousands digit is 5.
- 849,999 rounds down to 800,000 because the ten-thousands digit is 4 (less than 5) when you consider rounding at that level.
- 850,000 rounds up to 900,000 because the ten-thousands digit is 5.
So the range of numbers rounding to 800,000 is 750,000 to 849,999.
Summary:
- Numbers between 750,000 and 849,999 round to 800,000.
- Numbers below 750,000 round to 700,000.
- Numbers at 850,000 and above round to 900,000.
This rule applies because rounding depends on the digit immediately right of the place you are rounding to, and all digits to the right become zero after rounding.