# If 0 999 1 what is 0

## Rounding Numbers

Rounding - how to do it in math - is covered in this article. First of all, we explain why you round at all. Then we will show you how to round to 10, 100, 1000 digits after the decimal point. As always, we also provide exercises or written exams with solutions.

As soon as the topic of laps comes up in school, many students ask themselves: What do I even need this for? After all, this makes my number less precise, which means I am actually making a small "mistake" in my calculation. The main reasons for this are:

• Rounding brings a space advantage, the number becomes shorter
• A rounded number is often easier to remember
• A system cannot be too accurate
• Without rounding, the result would simulate incorrect accuracy

The first two points mentioned are initially of interest to schools. Points 3 and 4 are things that you - if at all - only fall over during your studies.

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### Rounds on 10s, 100s, 1000s

After we have explained the reasons for rounding, the next step is practical work: How do I actually round a number? To do this, you have to know which digit is rounded to (this is what the teacher tells you at the beginning and later you get an idea of ​​it yourself). For rounding it is important: A 0-4 is rounded down, a 5-9 rounded up. The following examples of rounding to certain places illustrate this.

Rounds to the 10th place:

• 72 -> Rounded: 70
• 74 -> Rounded: 70
• 75 -> Rounded: 80
• 77 -> Rounded: 80
• 79 -> Rounded: 80
• 80 -> Rounded: 80
• 84 -> rounded: 80
• 85 -> rounded: 90
• 111 -> rounded: 110
• 115 -> rounded: 120
• 119 -> Rounded: 120
• 1234 -> rounded: 1230
• 1235 -> rounded: 1240

We hang on to: To round a natural number to the 10th place, look at the last digit: If this is a 1-4 is rounded down, this is a 5-9 is rounded up. Look through all of the examples again, they illustrate the principle.

Rounds to 100's:

• 230 -> rounded: 200
• 249 -> rounded: 200
• 250 -> Rounded: 300
• 299 -> Rounded: 300
• 320 -> Rounded: 300
• 349 -> rounded: 300
• 350 -> Rounded: 400
• 950 -> rounded: 1000
• 999 -> rounded: 1000
• 1000 -> Rounded: 1000
• 1456 -> rounded: 1500
• 1934 -> rounded: 1900
• 34321 -> rounded: 34300
• 87351 -> rounded: 87400

We hang on to: To round a natural number to the hundred, look at the last two digits: 1-49 is rounded down and 50-99 is rounded up. Here, too, it is best to go through the examples again thoroughly, they clarify the principle.

Rounds to the 1000th place:

• 1012 -> rounded: 1000
• 1499 -> rounded: 1000
• 1500 -> rounded: 2000
• 1999 -> rounded: 2000
• 2499 -> rounded: 2000
• 2500 -> rounded: 3000
• 7897 -> rounded: 8000
• 9523 -> rounded: 10000
• 81232 -> rounded: 81000
• 88888 -> rounded: 89000
• 99999 -> rounded: 100000

We hang on to: To round a natural number to the thousand digit, look at the last three digits: 0-499 leads to rounding down, 500-999 to rounding up. Here, too, it makes sense to thoroughly understand the examples. Especially since larger numbers quickly lose track of things.

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### Rounding of point numbers / decimal numbers

In the section Calculating with Floating Numbers / Decimal Numbers, we saw that divisions can result in decimal numbers. These may have a large number of places after the decimal point or they never end (e.g. because they are periodic or, like the number Pi, never end). It is also very ugly to write out numbers like 2.34321232332114 or the like. That is why you usually round these decimal numbers as well. Here, too, you have to think about (or be told) to which point you round off. We'll show you some examples again and then explain the process.

Round to whole numbers:

• 0.6 -> rounded: 1
• 1.2 -> Rounded: 1
• 1.4 -> Rounded: 1
• 1.5 -> rounded: 2
• 7.7 -> Rounded: 8
• 10.0 -> Rounded: 10
• 10.42 -> Rounded: 10
• 10.49 -> Rounded: 10
• 10.50 -> Rounded: 11
• 23.42 -> Rounded: 23
• 55.66 -> rounded: 56

Explanation: To round to a whole number, look at the place after the decimal point: A 1-4 leads to rounding down, a 5-9 to rounding up.

Round to the place after the comma:

• 4.04 -> Rounded: 4.0
• 4.05 -> rounded: 4.1
• 4.44 -> Rounded: 4.4
• 4.45 -> Rounded: 4.5
• 9.12 -> Rounded: 9.1
• 9.95 -> Rounded: 10.0
• 12.23 -> Rounded: 12.2
• 12.29 -> Rounded: 12.3
• 99.89 -> Rounded: 99.9

Explanation: To round to the place after the decimal point, look at the second place after the decimal point: A 1-4 is rounded down, a 5-9 rounded up.

Round to two places after the comma:

• 3.231 -> Rounded: 3.23
• 3.234 -> Rounded: 3.23
• 3.235 -> Rounded: 3.24
• 5.786 -> Rounded: 5.79
• 2.342 -> rounded: 2.34
• 1.2345 -> Rounded: 1.23
• 8.2345 -> Rounded: 8.23
• 8.2350 -> Rounded: 8.24

Explanation: To round to the second place after the decimal point, look at the third place after the decimal point: A 1-4 is rounded down, a 5-9 is rounded up.

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