Question

a chemist needs to know the mass of a sample of potassium sulfate to 6 significant digits. she puts the sample on a digital scale. this is what the scale shows. 0 0 4 1. 0 4 g if this measurement is precise enough for the chemist, round it to 6 significant digits. otherwise, press the
o solution\ button.

Explanation:

Step1: Identify the number

The number from the scale is \(0041.04\) g.

Step2: Count significant digits

Leading zeros are not significant, but zeros between non - zero digits and trailing zeros after the decimal are significant. The number \(0041.04\) has 5 significant digits? Wait, no. Wait, \(0041.04\): the leading two zeros are not significant. Then we have 4, 1, 0, 4. Wait, no, let's re - evaluate. The number is \(41.04\) (after removing leading zeros). Wait, no, the original number is \(0041.04\). Let's count significant figures:

• Leading zeros: the two zeros before 4 are not significant.
• The 4 (first non - zero), 1, 0 (between 1 and 4), and 4 are significant. Wait, that's 4? No, wait, \(0041.04\) is equal to \(41.04\). Wait, no, maybe I misread. Wait, the scale shows \(0041.04\) g. So the digits are 0, 0, 4, 1,., 0, 4. So significant figures: non - zero digits (4,1,4) and the zero between 1 and 4. So 4,1,0,4. Wait, that's 4 significant digits? But the problem says to round to 6 significant digits. Wait, maybe the number is \(0041.04\) which is \(41.04\) with leading zeros. But if we consider the number as \(0041.04\), to round to 6 significant digits, we need to express it in a form with 6 significant digits. Wait, \(0041.04\) can be written as \(4.104\times10^{1}\), but to have 6 significant digits, we can add trailing zeros? Wait, no. Wait, maybe the original number is \(0041.04\) which is \(41.04\) (4 significant digits), but we need to round to 6. So we can write it as \(41.0400\) (by adding two trailing zeros after the decimal, since trailing zeros after the decimal are significant). Let's check:
• \(41.0400\): the digits 4,1,0,4,0,0. Now we have 6 significant digits. Because:
• 4 (significant), 1 (significant), 0 (between 1 and 4, significant), 4 (significant), 0 (trailing after decimal, significant), 0 (trailing after decimal, significant).

Answer:

\(41.0400\)