Question

significant figures exit slip name: jeremiah o per: directions: find the number of significant figures of the number provided. 1. 17500 how many sig figs? which rule applies? 1870.7 rule 5 2. 7.056 3. 80.50 4. 1870.7 5. 8060.0 6. 0.000470 7. ½ (exact number)

Explanation:

Problem 1: 17500

Step1: Recall sig fig rules for trailing zeros without decimal.

Trailing zeros in a whole number without a decimal are ambiguous, but if we assume the zeros are not significant (common in cases where precision isn't indicated), the non - zero digits are 1,7,5. Wait, but maybe there's a mis - writing, and if we consider the original problem might have a typo (since 1870.7 was written in the answer space), but for 17500: if we follow the rule that trailing zeros in a number without a decimal are not significant (unless marked), the significant figures are 1,7,5? No, wait, maybe the intended number was 17500. with a decimal? No, the number is 17500. The rules: non - zero digits are significant, zeros between non - zeros are significant, trailing zeros in whole numbers are not significant (unless there's a decimal). So 1,7,5 are significant? Wait, no, 17500: 1,7,5 are non - zero, the two zeros at the end are trailing and without a decimal, so significant figures are 3? But the written answer was 1870.7, maybe a mix - up. Let's correct: for 17500, if we consider that maybe it's 17500. (with a decimal), but it's not. So maybe the problem was mis - written, and the intended number was 17500. (but no). Alternatively, maybe the first problem was supposed to be 1870.7, let's check 1870.7:

Step1: Identify non - zero and zero between non - zeros/after decimal.

In 1870.7, the digits are 1,8,7,0,7. Zeros between non - zeros (or after decimal) are significant. So 1,8,7,0,7: all are significant? Wait, 1870.7: the zero is between 7 and 7? No, 1 (thousands), 8 (hundreds), 7 (tens), 0 (units), 7 (tenths). The zero is between non - zero digits (7 and 7? No, 7 (tens) and 7 (tenths)? Wait, 1870.7 is 1 (1000), 8 (100), 7 (10), 0 (1), 7 (0.1). So the zero is a placeholder? No, in a number with a decimal, trailing zeros (but here it's a zero in the middle? Wait, no, 1870.7: the digits are 1,8,7,0,7. All non - zero digits are significant, and zeros between non - zero digits are significant, and zeros after the decimal (but here the zero is before the decimal). Wait, the rule: all non - zero digits are significant, zeros between non - zero digits are significant, zeros after the decimal (to the right of the decimal) are significant, and zeros before the first non - zero digit are not significant. In 1870.7, the zero is between 7 (tens place) and 7 (tenths place)? No, 7 is in the tens place (10^1), 0 is in the ones place (10^0), 7 is in the tenths place (10^- 1). So the zero is between non - zero digits? 7 (tens) and 7 (tenths)? No, the digits are 1 (10^3), 8 (10^2), 7 (10^1), 0 (10^0), 7 (10^- 1). So the zero is a significant figure because it's between non - zero digits? Wait, no, between 7 (10^1) and 7 (10^- 1) there is the ones place (10^0) with zero. So the significant figures are 1,8,7,0,7: 5 significant figures. And the rule: zeros between non - zero digits are significant, and all non - zero digits are significant, and the zero here is between non - zero digits (7 and 7? No, 7 (tens) and 7 (tenths) with zero in between (ones place). So the rule that applies is: all non - zero digits are significant, and zeros between non - zero digits are significant. So for 1870.7, number of sig figs is 5.

Problem 2: 7.056

Step1: Apply sig fig rules.

Non - zero digits (7,5,6) are significant. The zero between 7 and 5 is also significant (zero between non - zero digits). So count all: 7,0,5,6.

Step2: Count the digits.

There are 4 digits, so 4 significant figures. The rule: zeros between non - zero digits are significant, and non - zero digits are significant.

Problem 3: 80.50

Step1: Analyze each digit.

Non - zero digits: 8,5. Zero between 8 and 5: significant (between non - zeros). Zero after the decimal: significant (trailing zero after decimal). So digits: 8,0,5,0.

Step2: Count the digits.

There are 4 significant figures. The rule: zeros between non - zero digits are significant, and trailing zeros after the decimal are significant.

Problem 4: 1870.7

Answer:

s:

1. For 17500 (assuming a typo and intended 1870.7): 5 (Rule: Zeros between non - zero digits and non - zero digits are significant)
2. 7.056: 4 (Rule: Zeros between non - zero digits and non - zero digits are significant)
3. 80.50: 4 (Rule: Zeros between non - zero digits and trailing zeros after decimal are significant)
4. 1870.7: 5 (Rule: Zeros between non - zero digits and non - zero digits are significant)
5. 8060.0: 5 (Rule: Zeros between non - zero digits, trailing zeros after decimal are significant)
6. 0.000470: 3 (Rule: Leading zeros not significant, non - zero and trailing zero after decimal are significant)
7. 1/2: Infinite (exact number, so unlimited sig figs)