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Chapter 2: Problem 177

Indicate the number of significant zeros in each value: (a) \(2.300\) (b) \(2.3003\) (c) \(0.0023\) (d) 2300 (e) \(23.000\)

Short Answer

Expert verified
(a) 2 significant zeros (b) 1 significant zero (c) 0 significant zeros (d) 0 significant zeros (e) 3 significant zeros

Step by step solution

01

(a) \(2.300\)

Rule: In a number with a decimal point, zeros at the end (trailing zeros) are considered significant. Number: \(2.300\) Significant zeros: 2 (Both zeros at the end are significant)
02

(b) \(2.3003\)

Rule: Zeros between non-zero numbers (called captive zeros) are always significant. Number: \(2.3003\) Significant zeros: 1 (Only the zero between 2 and 3 is significant)
03

(c) \(0.0023\)

Rule: Zeros to the left of the first non-zero digit (leading zeros) are not significant. Number: \(0.0023\) Significant zeros: 0 (The zeros to the left of 2 are not significant)
04

(d) 2300

Rule: In a whole number with no decimal point, zeros at the end (trailing zeros) are not considered significant. Number: 2300 Significant zeros: 0 (The zeros at the end are not significant because there is no decimal point)
05

(e) \(23.000\)

Rule: In a number with a decimal point, zeros at the end (trailing zeros) are considered significant. Number: \(23.000\) Significant zeros: 3 (All three zeros at the end are significant)

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