How to round numbers: a guide with examples

2024 Author: Malcolm Clapton | [email protected]. Last modified: 2023-12-17 03:44

We recall a useful rule from the school curriculum.

What is number rounding

Rounding is the replacement of a number with a close value, which has a zero at the end. Then the original number will become round. For example, the round numbers are 10, 20, 100, 730, 1 420, 15 000.

The rounding result is called the approximate value of this number and is indicated after the ≈ sign (“approximately equal to”).

How to round numbers

Integers

All numbers with more than one sign have digits. This is the place where this or that number is in the number. For example, 342 has three digits: hundreds (three hundred), tens (four tens), and ones (two ones). Accordingly, numbers can be rounded to tens, hundreds, thousands, and so on.

When rounding, the digits in the digits we do not need are replaced with zeros (in fact, they are discarded), and the digit in the necessary digit either changes up or remains unchanged. It depends on what number is behind it. If it is from 0 to 4, then nothing happens. If from 5 to 9, then one is added to the category.

Let's take the number 21 769. It can be rounded as follows:

• Up to dozens. Find the number of tens in the number 21 7 69 - there are six of them. The number 9 is behind the six, which means that when rounding, the tens place will increase by one. That is, the answer is 21 7 70.
• Up to hundreds. Find the number of hundreds in the number 21 769 - there are seven of them. Now we check the number by seven - this is 6, respectively, we add one to the place of hundreds. Result - 21 800.
• Up to thousands. We find the number of thousands - there are 21 of them. There is a seven behind the unit, which means that when rounding off the number, we increase the number of thousands by one and get 22 000.

Fractional numbers

When rounding fractions, exactly the same rules apply as when rounding natural numbers. You just need to be more careful, because there are more digits in fractions - they are in the whole part (units, tens, hundreds, thousands, etc.), and in the fractional part (tenths, hundredths, thousandths, etc.).

For example, let's take the decimal number 45, 836. It can be rounded like this:

• to hundredths → 45, 84;
• up to tenths → 45, 8;
• to integer → 46;
• up to tens → 50.

When rounding numbers comes in handy

Rounding helps in a wide variety of cases. For example, when you need to estimate the result of multiplying large numbers. Let's say you want to imagine how much 738 × 46 will be. According to the rounding rules, this is approximately equal to 700 × 50. It turns out: 738 × 46 ≈ 700 × 50 ≈ 35,000. And the exact multiplication result is 33,948.

Rounding rules are useful not only when solving problems, but also when you need to roughly calculate the cost of something in order to understand whether it fits into your budget or not.

Rounding is also used when absolute precision is simply not important. For example, if acquaintances from another city ask you how many people live in yours, you are unlikely to name a number up to tens and ones, even if you know it. Rather, you would say that it is home to "about four hundred thousand" or "about a million" people.