// Numbas version: exam_results_page_options {"name": "Rounding numbers to a given number of decimal places", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"name": "Rounding numbers to a given number of decimal places", "type": "question", "tags": ["rounding", "taxonomy"], "variablesTest": {"condition": "", "maxRuns": "100"}, "variables": {"c1": {"templateType": "anything", "name": "c1", "description": "

Random number with 5 decimal places.

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Number of decimal places to round.

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We can approximate numbers by rounding.

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Round $\\var{c1}$ to a given number of decimal places.

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i)   $\\var{c1}$ rounded to 1 decimal place is:  [[0]]

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ii)   $\\var{c1}$ rounded to 2 decimal places is:  [[1]]

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iii)   $\\var{c1}$ rounded to {dp} decimal places is:  [[2]]

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Round numbers to a given number of decimal places.

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The first thing to do when we are rounding numbers is to identify the last digit we are keeping.

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When you're asked to round your answer to a number of decimal places, you need to decide whether to keep the last digit same (rounding down) or increase it by 1 (rounding up). If the following digit is less than 5 we round down and we round up when the next digit is 5 or more.

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To write it down in steps:

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        1. Identify the last digit we need to keep.
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        2. Look at the following digit.
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        3. If it's 5 or more, increase the previous digit by one.
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        4. If it's 4 or less, keep the previous digit the same.
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        5. Fill any spaces to the right of the digit with zeros if needed.
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It is important to keep in mind that if the digit we are increasing is 9, it becomes zero and we increase the previous digit instead. If this digit is 9 as well, we move along to the left side until we find a digit less than 9.

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To round a number to a given number $n$ of decimal places, we look at the $n$th digit after the decimal point.

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We have $\\var{c1}$.

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i)

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We look at the first digit after the decimal point. This is $\\var{cdig[4]}$ and the following digit is $\\var{cdig[3]}$ so we round updown to get $\\var{precround(c1, 1)}$.

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ii)

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The second digit after the decimal point is $\\var{cdig[3]}$. It is followed by $\\var{cdig[2]}$ so we round updown to get $\\var{precround(c1, 2)}$.

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iii)

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The 3rd decimal place is $\\var{cdig[2]}$, followed by $\\var{cdig[1]}$. We get $\\var{precround(c1, 3)}$. The 4th decimal place is $\\var{cdig[1]}$, followed by $\\var{cdig[0]}$. We get $\\var{precround(c1, 4)}$.

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", "contributors": [{"name": "Stanislav Duris", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/1590/"}]}]}], "contributors": [{"name": "Stanislav Duris", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/1590/"}]}