Rounding

Place value (as discussed in the previous lesson) is necessary for rounding. When a problem asks us to round, it will always tell us what place we need to round to. For example, it will say "round your answer to the nearest tenth" or "round your answer to the nearest whole number."


 * What information do we need in order to round?** We only need two digits to round - the digit in the place value that the problem asks us to round to AND the digit in the place after the one we're rounding to. For example, if a problem asks us to round 123.3456 to the nearest tenth, we only need to look at the number in the tenths place, the 3, and the number after that (in the hundreths place), the 4.


 * What are we looking for when rounding?** We are looking to see if the number after the place value we're rounding to is 5 or greater. **If the digit is 5 or greater, then we round up**. **If the digit is less than 5, then we leave the number** in the place we're rounding to the same. All numbers after the place we rounded to become zeroes.

For example, if we're asked to round 123.3456 to the nearest tenth, we look at the 3 and the 4. Since the 4 is less than 5, the 3 stays the same and all the digits after it become 0. We get: 123.3000 BUT, we don't need to put all the zeroes at the end of a decimal, so our final answer is: 123.3


 * We do not need to include the zeroes at the end of a rounded number if they are AFTER the decimal point. We DO need to include them if they are BEFORE the decimal point.


 * Examples:**


 * Round -19.246 to the nearest hundreth: -19.25 because 4 is in the hundreths place and the digit after it is greater than 5, so we round the 4 up to 5 and everything after it becomes 0 (but we don't have to write them because they're after the decimal point). **


 * Round 1298.12387 to the nearest whole number: 1298 because a whole number does not have any decimal places. The number after the decimal point is less than 5, so we leave the number the same and everything after the decimal becomes 0 and we don't need to write them because they're after the decimal point. **


 * Round 78634.34568 to the nearest thousand: 79000 because 8 is in the thousands place and the number after it (6) is greater than 5. Therefore, we round the 8 up to a 9 and all the digits after it become zeroes. We do need to include the zeroes before the decimal point. **

**TASK: Describe the rules for rounding in your own words.**

**TASK: Round each of the following numbers to the nearest: a) whole number b) tenth c) hundreth**

1) 34850.34789 2) -9.8426 3) 6046.7926 4) 2.50963 5) 0.234