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Why 6.35.toFixed(1) == 6.3?

importance: 4

According to the documentation Math.round and toFixed both round to the nearest number: 0..4 lead down while 5..9 lead up.

For instance:

alert( 1.35.toFixed(1) ); // 1.4

In the similar example below, why is 6.35 rounded to 6.3, not 6.4?

alert( 6.35.toFixed(1) ); // 6.3

How to round 6.35 the right way?

Internally the decimal fraction 6.35 is an endless binary. As always in such cases, it is stored with a precision loss.

Let’s see:

alert( 6.35.toFixed(20) ); // 6.34999999999999964473

The precision loss can cause both increase and decrease of a number. In this particular case the number becomes a tiny bit less, that’s why it rounded down.

And what’s for 1.35?

alert( 1.35.toFixed(20) ); // 1.35000000000000008882

Here the precision loss made the number a little bit greater, so it rounded up.

How can we fix the problem with 6.35 if we want it to be rounded the right way?

We should bring it closer to an integer prior to rounding:

alert( (6.35 * 10).toFixed(20) ); // 63.50000000000000000000

Note that 63.5 has no precision loss at all. That’s because the decimal part 0.5 is actually 1/2. Fractions divided by powers of 2 are exactly represented in the binary system, now we can round it:

alert( Math.round(6.35 * 10) / 10); // 6.35 -> 63.5 -> 63(rounded) -> 6.3