Rounding Calculator

Rounding calculator at a glance#

How do you round a number?#

To round a number, identify the digit at the place you are rounding to and examine the digit immediately to its right. If this digit is 5 or greater, add 1 to the rounding place. If it is 4 or lower, leave the rounding place unchanged. Subsequent digits after a decimal point should be dropped. If rounding a whole number, convert digits following the rounding place into zeros. Input a number and select a place value, ranging from billions to billionths, in the calculator above to receive the rounded result.

How do you round to the nearest tenth or hundredth?#

When rounding to the nearest tenth, preserve one decimal place. For the nearest hundredth, maintain two decimal places. Consider 3,266.528: because the digit after the tenths place is 2, it rounds down to 3,266.5. If rounding to the nearest hundredth, the digit following the hundredths place is 8, meaning it rounds up to 3,266.53.

What is 1.25 rounded to the nearest tenth?#

1.25 becomes 1.3 when rounded to the nearest tenth. The tenths digit here is 2, followed by a 5, with a 5 prompting an upward round. Since 1.25 lies precisely between 1.2 and 1.3, the calculator always rounds halfway numbers up, moving them away from zero.

Place value#

Rounding is a process that happens step by step, so begin with the names. In 3,266.528, when you read from the left, 3 is in the thousands place. Next, 2 is in the hundreds, followed by 6 in the tens, and 6 in the ones. After the decimal point, the sequence continues with the tenths (5), the hundredths (2), and the thousandths (8). Each position has a value ten times greater than the one directly to its right.

This page uses the same number for rounding throughout: 3,266.528, the number already entered in the calculator above.

How to round, step by step#

The method is the same for any place. OpenStax Prealgebra 2e teaches it for whole numbers and again for decimals.

1. Find the place you are rounding to. For the nearest hundredth in 3,266.528, that's the 2 after the 5.
2. Look at the digit to its right. Here it is 8.
3. If that digit is 5 or more, add 1 to the kept digit. If it is 4 or less, leave the kept digit as it is. 8 is more than 5, so the 2 becomes 3. If the kept digit is 9, the 1 carries: a 9 becomes 0 and adds 1 to the digit on its left.
4. Drop the decimal digits after the kept place and turn any whole-number digits there into zeros. The result is 3,266.53.

Rounding finds the nearest value with that many places. 3,266.528 is between 3,266.52 and 3,266.53, and the halfway point is 3,266.525. It is past the halfway point, so it is closer to 3,266.53. The digit-5 rule is a shortcut for that comparison.

Rounding whole numbers#

To round to the nearest 10, 100, or 1,000, you need to look at the digit directly to the right of that place. Once you've identified this digit, replace every digit after the place with a zero. Any decimal part is simply removed.

Consider rounding to different places:

• Nearest 10: The tens digit in 3,266.528 is 6, and since the next digit is 6, it rounds up to 3,270.
• Nearest 100: Here, the hundreds digit is 2, and the next digit being 6 means it rounds up to 3,300.
• Nearest 1,000: With the thousands digit as 3 and the next being 2, it rounds down to 3,000.
• Nearest 10,000: Since 3,266.528 is less than 5,000, rounding brings it down to 0.

If you're dealing with a larger number, 84,250 rounded to the nearest ten thousand is 80,000. This is because the thousands digit, 4, is less than 5.

Rounding decimals#

Decimal places operate similarly, except nothing turns into zeros. You just stop writing digits after the place you retain.

• Nearest whole number: 3,266.528 has 5 in the tenths place, so it rounds up to 3,267. 9.69 rounds to 10, and 0.16 rounds to 0.
• Nearest tenth, or 1 decimal place: 3,266.528 rounds to 3,266.5, and 3.24 rounds to 3.2.
• Nearest hundredth, or 2 decimal places: 3,266.528 rounds to 3,266.53.

The nearest cent refers to the nearest hundredth of a dollar. $11,579.9998 rounds to $11,580.00, as the 9s carry all the way up into the dollars.

Halfway numbers and negative numbers#

When the digit following the kept place is a 5 with nothing succeeding it, the number stands exactly halfway. This calculator consistently rounds it up, away from zero: 2.5 becomes 3 and 1.25 becomes 1.3.

For a negative number, the calculator rounds the size while retaining the minus sign. −2.5 becomes −3 and −3.26 rounded to the nearest tenth becomes −3.3.

Trailing zeros#

If your number has fewer decimal places than requested, the calculator adds zeros, so 3.2 to the nearest hundredth displays as 3.20. It also keeps a zero that rounding creates, so 8.96 to one decimal place shows 9.0 and 3.04 shows 3.0. That zero matters when the number of places is significant, such as in money or measured values.

Rounding vs significant figures#

Rounding to a place means keeping a fixed position, like two decimal places, while rounding to significant figures focuses on maintaining a fixed number of meaningful digits starting from the first nonzero digit. For instance, 3,266.528 to three significant figures becomes 3,270, and 0.0045678 to three significant figures turns into 0.00457. This particular calculator rounds to places only. If you need significant figures, use the significant figures calculator.

Where rounding is used#

Money#

In money matters, prices, taxes, and tips get rounded to the nearest cent. For example, a 15% tip on $43.70 amounts to $6.555, which rounds to $6.56.

Estimating#

Rounding helps make mental math faster. Suppose prices are $3.49, $2.75, and $5.10. They round to $3, $3, and $5, giving a total of about $11. The precise sum is $11.34.

Measurements and roots#

Some answers never end, like square roots, and these get rounded to a practical number of places. For example, √5 is 2.2360679..., which rounds to 2.2 to the nearest tenth. Similarly, √7 is 2.6457513..., which rounds to 2.65 to the nearest hundredth. The square root calculator provides these roots to five decimal places, making them ready to round.

3,266.528 rounded to each place#

This section shows the same number rounded to each place the calculator offers, ranging from ten thousands to thousandths.

Answers to common rounding questions#

Here are some frequently searched rounding questions, each explained using the 5-or-more rule.

Sources#

• OpenStax, Prealgebra 2e, section 1.1: Introduction to Whole Numbers (rounding whole numbers)
• OpenStax, Prealgebra 2e, section 5.1: Decimals (rounding decimals)

Frequently asked questions#

What does rounding to 1 decimal place mean?#

It means you're keeping one digit after the decimal point, which is the tenths place. When you round 3.24 to 1 decimal place, the result is 3.2, and 8.96 becomes 9.0.

Does 5 round up or down?#

In this calculator, a 5 will round up. So 2.5 becomes 3, 1.25 turns into 1.3, and 0.125 becomes 0.13. The digit immediately after the place you're keeping is what determines the rounding, so 2.45 rounded to the nearest whole number results in 2, not 3.

How do you round to the nearest cent?#

You'll need to round to two decimal places, which is the hundredths. For example, $6.555 rounds to $6.56, and $11,579.9998 becomes 11580 in the calculator, which you'd write as $11,580.00. Choose hundredths in the calculator.

Can the calculator always round up?#

It can't always round up. It rounds to the nearest value, so if you have 3.21 and round it to the nearest tenth, you get 3.2. If you were to round up every time (often called the ceiling), you'd get 3.3. To do this, add 1 to the kept digit when any nonzero digit follows it.

Is rounding the same as truncating?#

Rounding and truncating aren't the same. Truncating simply cuts off extra digits without considering them. So 3,266.528 truncated to two decimal places becomes 3,266.52, but rounding gives you 3,266.53.

Why does rounding 3,266.528 to the nearest ten thousand give 0?#

The two nearest ten thousands are 0 and 10,000, and 3,266.528 is significantly closer to 0. Any number below 5,000 will round to 0 at that place.

Is rounding to the nearest whole number the same as rounding to the nearest integer?#

Yes, it is. An integer can be a whole number or its negative, so both terms mean rounding to the ones place. For example, −3.6 rounds to −4 and 2.4 rounds to 2. If you need to perform arithmetic with these rounded results, including negative numbers, the integer calculator will help.