Question

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

a. $2.0500\mathrm{m}and0.0205\mathrm{m}$

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

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

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

Short 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$6.240\mathrm{L}$.

Step-by-step solution

Part (a) Step 1: Given Information 

The numbers that are given are : $2.0500\mathrm{m}and0.0205\mathrm{m}$.

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 $600.0K$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 $60K$, just the $6$is relevant.
• The number $600.0K$has four significant figures, but $60k$only has one.
• As a result, $600.0K$and $60K$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 $0.00075s$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 $75,000s$, only $5$and $7$are deemed important.
• $0.00075s$has two significant figures, while $75,000s$also has two significant figures.
• There are the same number of significant figures in the integers $0.00075s$and $75,000s$.

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