How many significant figures are in 1.001? a) 4.008 b) 1000.0 C) 26.7800 d) 5.0000
The number 1.001 has four significant figures.
a) 4.008 has four significant figures.
b) 1000.0 has five significant figures.
c) 26.7800 has six significant figures.
d) 5.0000 has five significant figures.
To determine the number of significant figures in a number, follow these rules:
1. Non-zero digits are always significant.
2. Zeros between non-zero digits are always significant.
3. Leading zeros (zeros to the left of the first non-zero digit) are not significant.
4. Trailing zeros (zeros to the right of the last non-zero digit) are only significant if there is a decimal point present.
Let's apply these rules to the given options:
a) 4.008: There are four non-zero digits (4, 0, 0, and 8), so there are four significant figures.
b) 1000.0: There are five non-zero digits (1, 0, 0, 0, and 0), so there are five significant figures.
c) 26.7800: There are six non-zero digits (2, 6, 7, 8, 0, and 0), so there are six significant figures.
d) 5.0000: There are five non-zero digits (5, 0, 0, 0, and 0), so there are five significant figures.
Therefore, the answer is:
a) 4.008 has 4 significant figures.
To determine the number of significant figures in a given number, you need to follow a few rules:
1. Non-zero digits are always significant. For example, the number 1.001 has four significant figures because all the digits (1, 0, 0, and 1) are non-zero.
2. Zeros between non-zero digits are always significant. For example, 1.001 contains four significant figures because the zeros between the non-zero digits (1 and 1) are considered significant.
3. Leading zeros (zeros before the first non-zero digit) are not significant. For example, the number 1000.0 contains five significant figures because the leading zero is not significant.
4. Trailing zeros (zeros after the last non-zero digit) are significant only if there is a decimal point present. For example, 26.7800 contains six significant figures because the trailing zeros after the non-zero digits (8 and 0) are considered significant due to the presence of the decimal point.
Based on these rules, let's analyze the options:
a) 4.008: The decimal point suggests that the trailing zero is significant. Therefore, this number has four significant figures.
b) 1000.0: The leading zero is not significant, and the decimal point indicates that the trailing zero is significant. Hence, this number has five significant figures.
c) 26.7800: The decimal point indicates that all trailing zeros are significant. Therefore, this number has six significant figures.
d) 5.0000: All the digits in this number are non-zero, and the decimal point indicates that the trailing zeros are significant. Hence, this number has six significant figures.
Therefore, the correct answer is d) 5.0000, which has six significant figures.