# Rounding Large and Small Numbers Lesson

Rounding large and small numbers involves approximating a given number to a simpler or more manageable value. This is often done to make calculations easier or to present data in a more concise form. The process of rounding depends on the desired level of precision. Rounding numbers makes the number less precise than the original number, but is sometimes necessary. When rounding large and small numbers it is important for us to remember our place values chart, as seen below.

We round numbers for real world examples often, for example, if we calculate that we need 3.6 gallons of paint, we would round this up to say that we need about 4 gallons of paint. Another example is, Frank walked 4.1 miles yesterday, we would say Frank walked about 4 miles yesterday. These are real world examples of rounding. When rounding it is important to know which place value our final answer needs to be rounded to.

For example if given the number 7,549 and asked to round to the nearest thousands, the answer would be 7,000 however, if we were asked to round the same number to the hundreds place, the answer is 7,500, and so on.

When rounding large and small numbers there is a simple rule that we use; decide which place value that you need to round to, then look at the digit to the right of that place value, if the digit is 5 or more, we round up, otherwise we round down which means the number in the desired place value stays the same.

Steps for Rounding:

1) Identify the place value in which you need to round.

2) Identify the digit to the right of that place value

a) If it is 5 or more, the digit of the place value round ups
b) If it is less than 5, the digit of the place value stays the same.
c) Indicating the original number is being rounded down

3) Replace all the digits to the right of the rounding place with 0’s.

For example, if we are rounding the number 3,452 to the nearest hundreds place, we would notice that the tens place is a 5, therefore we would round the 4 in the hundreds place up to a 5, replace all the digits to the right of 5 with 0’s, and the rounded answer would be 4,500. Another example to consider would be if we had the number 3,432 and we wanted to round this to the nearest hundreds place, we would notice that the tens place is a 3, which is less than 5, therefore we would keep the 4 the same, replace all the digits to the right of the 4 with 0’s, and our rounded down answer would be 3,400.

We can use these rules to round large and small numbers. An example of rounding with small numbers would be, round the number 0.0246 to the nearest hundredth. In this example, we would look at the number in the thousandth place(4 in this case). If the number is 5 or more we round up, otherwise we round down. In this case, the number is less than 5, therefore we will round the number down, meaning that the 2 in the hundredth place will stay the same, and our answer rounded to the nearest hundredth is 0.02.

Remember that the digit to the right of the desired decimal place is always used to determine whether you round up or round down.

Examples

Example 1: Round 7,862 to the Nearest Hundred.

Solution:

1. The digit in the tens place is 6 (which is 5 or greater), so we round up.
2. Replace the digits to the right of 9 with 0’s.
3. Rounded to the nearest hundred: 7,900.

Example 2: Use rounding rules to round the number 4,352 to the nearest tens place

Solution:

• The digit in the ones place is 2 (which is less than 5), so we round down.
• The 5 in the tens place stays the same, replace the digits to the right of 5 with 0’s.
• Rounded to the nearest hundred: 4,350.

Example 3: Round 4.1365 to the thousandths place.

Solution:

• The digit in the ten thousandths place is 5 (5 or greater), so we round up the digit in the thousandths place (6 becomes 7).
• Rounded to the thousandths place: 4.137

1) What does Rounding Numbers mean in Math?

• Rounding numbers is the process of approximating a number to a certain degree of precision. It involves adjusting a number to a simpler or more manageable value.

2) How do I round large numbers?

• Identify the digit in the desired place value and look at the digit to the right. If that digit is 5 or greater, round up; if less than 5, round down. Then fill in the digits to the right of the desired place value with zeros.

3) How do I round small numbers?

• Similar to rounding large numbers, identify the digit in the desired decimal place and look at the digit to the right. If that digit is 5 or greater, round up; if less than 5, round down. Then the digits to the right become zeros. Because it is a decimal we don’t need to keep the zeros to the right of the last decimal.

4) What is the rule for rounding 5?

• The common rule is to round 5 or greater up.

5) Can I round to any decimal place?

• Yes,you can round to any decimal place. Identify the digit to the right of the desired decimal place and round accordingly.

6) Can rounding introduce errors in calculations?

• Yes,rounding can introduce errors, especially in repeated calculations. It’s essential to be mindful of rounding methods to minimize errors in mathematical operations.

7) Is Rounding Numbers used in Real Life?

• Yes, in real life, we usually round numbers when talking about buying products for building. We need to round up to ensure we have enough for the job. We also round when an exact value is not important, when we just need an approximate answer. We round also to make calculations easier.