Rounding to an arbitrary number of significant digits

algorithmroundingsignificant-digits

How can you round any number (not just integers > 0) to N significant digits?

For example, if I want to round to three significant digits, I'm looking for a formula that could take:

1,239,451 and return 1,240,000

12.1257 and return 12.1

.0681 and return .0681

5 and return 5

Naturally the algorithm should not be hard-coded to only handle N of 3, although that would be a start.

Best Answer

Here's the same code in Java without the 12.100000000000001 bug other answers have

I also removed repeated code, changed power to a type integer to prevent floating issues when n - d is done, and made the long intermediate more clear

The bug was caused by multiplying a large number with a small number. Instead I divide two numbers of similar size.

EDIT
Fixed more bugs. Added check for 0 as it would result in NaN. Made the function actually work with negative numbers (The original code doesn't handle negative numbers because a log of a negative number is a complex number)

public static double roundToSignificantFigures(double num, int n) {
    if(num == 0) {
        return 0;
    }

    final double d = Math.ceil(Math.log10(num < 0 ? -num: num));
    final int power = n - (int) d;

    final double magnitude = Math.pow(10, power);
    final long shifted = Math.round(num*magnitude);
    return shifted/magnitude;
}

Related Solutions

Java – How to round a number to n decimal places in Java

Use setRoundingMode, set the RoundingMode explicitly to handle your issue with the half-even round, then use the format pattern for your required output.

Example:

DecimalFormat df = new DecimalFormat("#.####");
df.setRoundingMode(RoundingMode.CEILING);
for (Number n : Arrays.asList(12, 123.12345, 0.23, 0.1, 2341234.212431324)) {
    Double d = n.doubleValue();
    System.out.println(df.format(d));
}

gives the output:

12
123.1235
0.23
0.1
2341234.2125

EDIT: The original answer does not address the accuracy of the double values. That is fine if you don't care much whether it rounds up or down. But if you want accurate rounding, then you need to take the expected accuracy of the values into account. Floating point values have a binary representation internally. That means that a value like 2.7735 does not actually have that exact value internally. It can be slightly larger or slightly smaller. If the internal value is slightly smaller, then it will not round up to 2.7740. To remedy that situation, you need to be aware of the accuracy of the values that you are working with, and add or subtract that value before rounding. For example, when you know that your values are accurate up to 6 digits, then to round half-way values up, add that accuracy to the value:

Double d = n.doubleValue() + 1e-6;

To round down, subtract the accuracy.

R – Formatting Decimal places in R

Background: Some answers suggested on this page (e.g., signif, options(digits=...)) do not guarantee that a certain number of decimals are displayed for an arbitrary number. I presume this is a design feature in R whereby good scientific practice involves showing a certain number of digits based on principles of "significant figures". However, in many domains (e.g., APA style, business reports) formatting requirements dictate that a certain number of decimal places are displayed. This is often done for consistency and standardisation purposes rather than being concerned with significant figures.

Solution:

The following code shows exactly two decimal places for the number x.

format(round(x, 2), nsmall = 2)

For example:

format(round(1.20, 2), nsmall = 2)
# [1] "1.20"
format(round(1, 2), nsmall = 2)
# [1] "1.00"
format(round(1.1234, 2), nsmall = 2)
# [1] "1.12"

A more general function is as follows where x is the number and k is the number of decimals to show. trimws removes any leading white space which can be useful if you have a vector of numbers.

specify_decimal <- function(x, k) trimws(format(round(x, k), nsmall=k))

E.g.,

specify_decimal(1234, 5)
# [1] "1234.00000"
specify_decimal(0.1234, 5)
# [1] "0.12340"

Best Answer

Related Solutions

Java – How to round a number to n decimal places in Java

R – Formatting Decimal places in R

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