Q. 2.81 - An Introduction to General, Organic, and Biological Chemistry

Question

In which of the following pairs do both numbers contain the same number of significant figures? $(2.2)$

a. $2.0500 \mathrm{m} and 0.0205 \mathrm{m}$

b. $600.0 \mathrm{K} \mathrm{and} 60 \mathrm{K}$

c. $0.00075 \mathrm{s} \mathrm{and} 75000 \mathrm{s}$

d. $6.240 \mathrm{L} \mathrm{and} 6.240\times {10}^{-2} \mathrm{L}$

Step-by-Step Solution

Answer

Part (a) As a result, $2.0500 \mathrm{m}$ and $0.0205 \mathrm{m}$ have different numbers of significant figures.

Part (b) As a result, $600.0 \mathrm{K}$ and $60 \mathrm{K}$ have different numbers of significant figures.

Part (c) There are the same number of significant figures in the integers  $75,000 \mathrm{s}$ and $0.00075 \mathrm{s}$.

Part (d) There are the same number of significant figures in the integers  $6.240 \mathrm{x} {10}^{-2}$ and $6.240 \mathrm{L}$.

Part (a) Step 1: Given Information

The numbers that are given are : $2.0500 \mathrm{m} and 0.0205 \mathrm{m}$.    

We have to find whether the significant numbers are the same or different. 

Part (a) Step 2: Explanation

• The zeros between the nonzero digits, as well as the zeros at the conclusion of a number with a decimal point, are always important. 
• The zeros at the start of a number are never relevant, but the zeros between the nonzero digits are.
• There are 5 significant figures in the number $2.0500 \mathrm{m}$, and $3$ significant figures in the number $0.0205 \mathrm{m}$.
• As a result, $2.0500 \mathrm{m}$ and $0.0205 \mathrm{m}$ have different numbers of significant figures.

Part (b) Step 3: Given information

The numbers that are given are :  $600.0 \mathrm{K} \mathrm{and} 60 \mathrm{K}$

We have to find the whether the significant numbers are same or different. 

Part (b) Step 4 : Explanation

• A significant figure is one that appears at the end of a decimal number. 
• As a result, all of the zeros in $600.0 K$ are meaningful.
•  A significant figure is never considered to be a zero used as a placeholder in a number without a decimal point. 
• As a result, in $60 K$, just the $6$ is relevant.
• The number $600.0 K$ has four significant figures, but $60 k$ only has one.
• As a result, $600.0 K$ and $60 K$ have different numbers of significant figures.

Part (c) Step 4: Given Information

The numbers that are given are :  $0.00075 \mathrm{s} \mathrm{and} 75000 \mathrm{s}$ 

We have to find the whether the significant numbers are same or different. 

Part (c) Step 5: Explanation

• The zeros at the start of a number are never taken into consideration. As a result, only $0.00075 s$ believe $7$ and $5$ to be important.
• A significant figure is never considered a zero used as a placeholder in a number without a decimal point.
• As a result, in $75,000 s$, only $5$and $7$are deemed important.
• $0.00075 s$ has two significant figures, while $75,000 s$ also has two significant figures.
• There are the same number of significant figures in the integers $0.00075 s$ and $75,000 s$.

Part (d) Step 7: Given information

The numbers given are : $6.240 \mathrm{L} \mathrm{and} 6.240\times {10}^{-2} \mathrm{L}$ 

We have to find the whether the significant numbers are same or different. 

Part (d) Step 8: Explanation

• A important figure is one that appears at the end of a decimal number. 
• As a result, all of the zeros in $6.240 L$are meaningful.
• A number expressed in scientific notation with a zero in the coefficient is regarded significant.
• As a result, all of the numbers in $6.240 \times {10}^{-2 }L$ are meaningful. $6.240 L$has four significant figures, and $6.240 \times {10}^{-2 }L$ has four significant figures as well.
• There are the same number of significant figures in the integers $6.240 L$and $6.240 \times {10}^{-2} L$.