Round to the Left Most Digit
It’s probably unusual for me to write anything about Math. I hated math and I failed the subject all the time. But I got pretty excited when I knew this trick from my colleague. I also asked this question at stackoverflow.
The problem
Let’s say you have a number 423
and you want to round the number to the nearest leftmost digit which in this case it’s 4
. If you want to round to the leftmost digit it’s going to be 400
.
The solution
The solution is quiet simple. You just need to get the place value of the number, take the number in question divided by the place value and floor
the number then multiply the result with the place value again. That’s it! Simple right?
So, the place value of 423
is 100
.
\begin{align} \frac{423}{100} \end{align}
which you will get 4.23
. The you floor
the number
1


And then you multiple 4
with 100
to get the rounded number.
\begin{align} {400}\cdot{100} = {400} \end{align}
The problem is how are we going to get the place value
of the number?
You want logarithm.
The idea of this is to reverse the operation of exponentiation. For example, the log10
of 423
is 2.62634036738
then 10^2.62634036738
equals 423
. But you want the place value. You would need to round the 2.62634036738
which is going to be 2
then 10^2
is 100
. There! you get the place value of the 4
.
\begin{align} d = \lfloor\frac{n}{10^{\lfloor\log_{10} n \rfloor}} \rfloor \cdot 10^{\lfloor\log_{10} n\rfloor} \end{align}
Show me the code
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