// Numbas version: exam_results_page_options {"name": "Rounding and estimating calculations", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"name": "Rounding and estimating calculations", "type": "question", "tags": ["estimation", "rounding", "taxonomy"], "variablesTest": {"condition": "", "maxRuns": 100}, "variables": {"int": {"templateType": "anything", "name": "int", "description": "

6 random integers.

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Integers from 1 to 100.

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Small integer.

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Multiples of ten.

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Integer (if rounded to 1 s.f. either 20 or 40).

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Integer (if rounded to 1 s.f. either 10 or 20).

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A decimal number.

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It is often appropriate to estimate calculations. The sign ≈ denotes \"approximately equal to\".

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In this question, approximate calculations by rounding the numbers in the question to 1 significant figure before calculating answers.

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Estimate $\\var{int[0]} \\times \\var{int[1]}$.

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[[0]]  $\\times$    [[1]]  $=$  [[2]]

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Therefore, $\\var{int[0]} \\times \\var{int[1]} ≈$  [[2]].

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Estimate $\\var{sint} \\times \\var{int[2]}$.

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[[0]]  $\\times$    [[1]]  $=$  [[2]]

\n

Therefore, $\\var{sint} \\times \\var{int[2]} ≈$  [[2]].

Estimate $\\displaystyle \\frac{\\var{int[3]} - \\var{int[4]}}{\\var{b}}$.

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[[0]] $-$  [[1]] [[2]]   $=$ [[3]]

\n

Therefore, $\\displaystyle \\frac{\\var{int[3]} - \\var{int[4]}}{\\var{b}} ≈$  [[3]].

Estimate $\\displaystyle \\frac{\\var{int[5]*10 + ran}}{\\var{c}} - \\var{a}$.

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[[0]] [[1]]   $-$  [[2]]  $=$  [[3]]

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Therefore, $\\displaystyle \\frac{\\var{int[5]*10 + ran}}{\\var{c}} - \\var{a} ≈$  [[3]].

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Estimate the result of an arithmetic operation by first rounding numbers to given significant figures

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To round to 1 significant figure, we look at the first non-zero digit, increasing this digit by one if the following digit is 5 or more and keeping the digit the same if the following digit is below 5. We replace the rest of the digits by 0.

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#### a)

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\$\\var{int[0]} \\times \\var{int[1]} ≈ \\text{ ?}\$

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Rounding to 1 significant figure gives:

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\\\begin{align} \\var{siground(int[0], 1)} \\times \\var{siground(int[1], 1)} = \\var{siground(int[0], 1)*siground(int[1], 1)} \\text{.} \\end{align} \

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#### b)

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\$\\var{sint} \\times \\var{int[2]} ≈ \\text{ ?}\$

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Rounding to 1 significant figure:

\n

\\\begin{align} \\var{siground(sint, 1)} \\times \\var{siground(int[2], 1)} = \\var{siground(sint, 1)*siground(int[2], 1)} \\text{.} \\end{align} \

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A common mistake may be rounding $\\var{sint}$ to the nearest 10 instead of 1 significant figure (in this case the number itself already consists of 1 s.f. only).

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#### c)

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\$\\displaystyle \\frac{\\var{int[3]} - \\var{int[4]}}{\\var{b}} ≈ \\text{ ?}\$

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Rounding to 1 significant figure:

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\\\begin{align} \\displaystyle \\frac{\\var{siground(int[3], 1)} - \\var{siground(int[4], 1)}}{\\var{siground(b, 1)}} &=\\frac{\\var{siground(int[3], 1) - siground(int[4], 1)}}{\\var{siground(b, 1)}} \\\\&= \\var{(siground(int[3], 1) - siground(int[4], 1)) / siground(b,1)} \\text{.} \\end{align} \

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#### d)

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\$\\displaystyle \\frac{\\var{int[5]*10 + ran}}{\\var{c}} - \\var{a} ≈ \\text{ ?}\$

\n

Rounding to 1 significant figure:

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\\\begin{align} \\displaystyle \\frac{\\var{siground(int[5]*10, 1)}}{\\var{siground(c, 1)}} - \\var{siground(a, 1)} &= \\frac{\\var{siground(int[5]*10, 1)/10}}{\\var{siground(c, 1)/10}} - \\var{siground(a, 1)} \\\\&= \\var{(siground(int[5]*10, 1))/siground(c, 1)} - \\var{siground(a, 1)} \\\\&= \\var{siground(int[5]*10, 1)/siground(c, 1) - siground(a, 1)} \\text{.} \\end{align} \

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