Rounding number nearest 0.05
I have question about rounding and please help me, suppose that question is round given number nearest 0.01 or 0.1 or 0.05 or maybe nearest 0.5, then what could i do? For example we are given some rational value 0.16 or 0.167, how could I round it to nearest 0.05? What is required I could not understand well. My attempt is following if we have data like 2.65, because after point first number is greater then 5(also it could be equal to 5), then nearest to 0.1, this number is equal to 3, but what about number 0.16 rounded to nearest 0.05 or 0.01? Please help me.
$\endgroup$ 43 Answers
$\begingroup$There can be some ambiguities. For example, when we are asked to round $7.5$ to the nearest integer, there is a problem, since there are two nearest integers. That is often, but not always, resolved by rounding to the nearest even integer. A similar convention applies to say $0.145$ rounded to the nearest $0.01$, that is, to $2$ digits after the decimal point. One would often round to $0.14$, since $4$ is even.
But that doesn't seem to be what your question is about. When we are asked to round $0.16$ to the nearest $0.05$, what is meant is that we should find the number which is an integer times $0.05$, and is closest to $0.16$. That number is $0.15$.
Similarly, the number $1.88$, rounded to the nearest $0.05$, is $1.9$. And $1.87$ rounded to the nearest $0.05$ is $1.85$.
Always, when we round to the nearest $0.05$, there should be at most two digits after the decimal point. The second digit after the decimal point should be $5$ or $0$. A $0$ would often be omitted.
If we are rounding to the nearest $0.01$, then $0.16$ rounds to $0.16$, and $0/123$ rounds to $0.12$, while $0.678$ rounds to $0.68$.
Remark: One way to think of it concretely is like this. A bug starts at $0$, and can only take jumps of $0.05$. She wants to land as close as possible to $0.16$. Three jumps take her to $0.15$. Four take her to $0.20$. Three jumps get her closer than four, so $0.16$ rounded to the nearest $0.05$ is $0.15$.
$\endgroup$ 2 $\begingroup$$x$, rounded to the nearest $y$, is $$y\left[ \frac{x}{y}\right]$$
Where $[z]$ is the nearest integer to $z$.
e.g. $0.167$ to the nearest $0.05$ is $$0.05\left[ \frac{0.167}{0.05}\right]=0.05[3.34]=0.05\cdot3=0.15$$
Why it works: Recall the definition of division - $\frac{x}{y}$ is how many copies of $y$ will 'fit' into $x$. You want to know how many whole copies of $y$ fit into $x$, so we take the nearest integer. We must then multiply by $y$ to go from a 'number of copies of $y$' to an actual quantity.
$\endgroup$ 1 $\begingroup$Rounding to the nearest 0.05 corresponds to $f' =\frac 1{20}\operatorname{int}[20f+0.5]$. This rounds values between $x.x25$ and $x.x75$ to $x.x50$, and other values rounded to the nearest tenth, ie $x.w75$ to $x.x25$ round to $x.x00$, where $x.w = x.x - 0.1$.
It should be noted than when one is dealing with exact quarters, like $0.375$, one rounds upwards on even, and downwards on odd numbers, so here $3$ is odd, so $0.375$ rounds to $0.37$.
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