Step by step
The question
Question: round 0.03846 to 3 significant figures.
1 Find the first significant figure
In 0.03846, the first significant figure is 3.
The first significant figure is the first digit that is not 0.
The zeros in front only hold the place.
They are not counted.
2 Count the figures
We count 3 figures from there: 3, 8, 4.
The 3rd figure, 4, is in the ten-thousandths place.
So we round to the nearest ten-thousandth.
3 Look at the next digit
Now we look at the next digit to the right.
It is 6.
5 or more: we round up, the ten-thousandths digit goes up by 1.
4 or less: we round down, it stays.
6 is 5 or more, so we round up.
4 Keep the size
We stop after the 3rd figure.
So 0.03846 is about 0.0385.
Careful!
The zeros in front are not counted.
But they stay in the answer.
They hold the place.
So 0.03846 to 3 significant figures is 0.0385.
5 Check
Let's check.
0.0385 has 3 significant figures: 3, 8, 5.
And it is close to 0.03846.
So the answer is right!
Let's look back.
First: find the first significant figure.
Then: count the figures.
Then: look at the next digit.
Then: keep the size.
Last: check.