Question

How many significant figures are in each of the following numbers? a) 4.01 c) 4 e) 0.00001 g) \(7.01 \cdot 3.1415\) b) 4.010 d) 2.00001 f) \(2.1-1.10042\)

Short answer

a) 4.01 b) 4.010 c) 4 d) 2.00001 e) 0.00001 f) 2.1 - 1.10042 g) 7.01 * 3.1415 Answer: a) 3 significant figures b) 4 significant figures c) 1 significant figure d) 5 significant figures e) 1 significant figure f) The result will have 1 decimal place g) The result will have 3 significant figures

Step-by-step solution

Rule for counting significant figures

: 1. Any non-zero digit is considered a significant figure. 2. Any zeros between non-zero digits are significant. 3. Leading zeros (zeros that precede non-zero digits) are not significant. 4. Trailing zeros in a decimal number (zeros that follow the decimal point and non-zero digits) are significant. 5. Trailing zeros in a whole number without a decimal may or may not be significant depending on the context.

Rule for arithmetic operations

: 1. For multiplication and division, the result should have the same number of significant figures as the measurement with the least number of significant figures. 2. For addition and subtraction, the result should have the same number of decimal places as the measurement with the least number of decimal places. Now, we will apply these rules to find the number of significant figures for each number.

a) 4.01

: There are no leading zeros. There are three non-zero digits, and they are all considered significant. Therefore, this number has 3 significant figures.

b) 4.010

: There are no leading zeros. There are three non-zero digits and one trailing zero, which is significant since it follows a decimal point. Therefore, this number has 4 significant figures.

c) 4

: There are no leading or trailing zeros in this whole number without a decimal point. It has one non-zero digit, which is considered significant. Therefore, this number has 1 significant figure.

d) 2.00001

: There are no leading zeros. There are two non-zero digits and three trailing zeros, which are all significant since they follow a decimal point. Therefore, this number has 5 significant figures.

e) 0.00001

: There are four leading zeros, which are not significant. There is one non-zero digit, which is considered significant. Therefore, this number has 1 significant figure.

g) \(7.01 \cdot 3.1415\)

: There are 3 significant figures in 7.01 and 5 significant figures in 3.1415. According to the rule for multiplication, we should use the measurement with the least number of significant figures to determine the number of significant figures in the result. So, the result will have 3 significant figures.

f) \(2.1 - 1.10042\)

: There is 1 decimal place in 2.1 and 5 decimal places in 1.10042. According to the rule for subtraction, we should use the measurement with the least number of decimal places to determine the number of decimal places in the result. So, the result will have 1 decimal place.