Question

read the elapsed time on the stopwatch and answer the questions. in which digit is there the least amount of confidence? how many significant figures does this measurement have?

Explanation:

First Question: In which digit is there the least amount of confidence?

When reading a stopwatch (or any measurement), the last digit is often an estimate or has the least confidence because it's the most precise (or least certain) digit. The time here is \(0:13_{37}\) (interpreted as \(13.37\) seconds, or looking at the digits: the digits are 1, 3, 3, 7? Wait, no, the display is \(0:13_{37}\) – maybe it's \(13.37\) seconds? Wait, the digits shown: the first digit of the seconds is 1 (tens place of seconds), then 3 (ones place of seconds), then 3 (tenths place), then 7 (hundredths place)? Wait, no, maybe the subscript is the decimal? Wait, the stopwatch shows \(0:13_{37}\) – perhaps it's \(13.37\) seconds, but the last digit (the 7, or the last digit of the decimal? Wait, no, the digits: let's parse the time. The format is minutes:seconds.decimal? Wait, \(0:13_{37}\) – maybe it's \(13.37\) seconds, where the digits are 1 (ten seconds), 3 (one second), 3 (tenth of a second), 7 (hundredth of a second). The last digit (the 7, or the rightmost digit) is the one with the least confidence because it's the estimated digit (the precision is to the hundredth, but the last digit is the least certain). So the rightmost digit, which is the 7 (or the last digit in the measurement). Wait, the digits are 1, 3, 3, 7? Wait, no, the time is 0 minutes, 13 seconds, and then 37 hundredths? Wait, maybe \(13.37\) seconds. So the digits are 1 (10s place), 3 (1s place), 3 (0.1s place), 7 (0.01s place). The last digit (7) is the least confident because it's the most precise (smallest unit) and thus an estimate. So the digit with the least confidence is the last one, which is the 7 (or the fourth digit, but in terms of place: the hundredths place digit, which is 7? Wait, no, maybe the subscript is the decimal: \(0:13.37\) seconds. So the digits are 1 (10s of seconds), 3 (1s of seconds), 3 (tenths of seconds), 7 (hundredths of seconds). The last digit (7) is the least confident.

Significant figures: non-zero digits are significant, and all digits from the first non-zero digit. Let's parse the measurement. The time is \(13.37\) seconds (assuming \(0:13_{37}\) is \(13.37\) seconds). The digits are 1, 3, 3, 7. All non-zero digits are significant, and there are four digits. Wait, let's confirm: significant figures are digits that carry meaning contributing to precision. For \(13.37\), all digits (1, 3, 3, 7) are significant because there's a decimal? Wait, no: significant figures rules: 1. All non-zero digits are significant. 2. Zeros between non-zero digits are significant. 3. Trailing zeros after a decimal are significant. Here, the number is \(13.37\) (assuming), so digits are 1, 3, 3, 7 – four significant figures. Let's check: the first digit is 1 (significant), 3 (significant), 3 (significant), 7 (significant). So four significant figures.

Answer:

7 (or the last digit, the 7 in the hundredths place; or the digit in the hundredths place, which is 7)

Second Question: How many significant figures does this measurement have?