Concept explainers
Perform these calculations and express the result with the proper number of significant figures.
(a)
(b)
(c)
(d) 0.003400/65.2
(a)
To perform:
The calculations of
Explanation of Solution
First, set the rules for “significant numbers”
- zeroes to the left are not significant.
- zeroes to the right are not significant if not specified as “exact” zeroes.
- all other digits other than zero are significant.
- zeroes between non-zero numbers are significant.
Second, define the addition/subtraction and multiplication/division rules for significant numbers.
- Addition/Subtraction ( Always keep the least significant number after the decimal point.
- Multiplication/Division ( Always keep the least significant number of the whole number.
- If addition/subtraction and Multiplication/division are included, separate the operation to simple operations and keep following the rules.
Now, for the given operation.
Perform subtraction.
Since there are only two significant digits after the decimal, keep only 2 significant figures in the product.
Now, for multiplication, perform total operation.
According to sig. fig. rules, we must keep only 2 sig. fig. since that is the least amount of sig. fig. for 1.3 mL. Round if required.
Rounding is required. Report:
(b)
To perform:
The calculations of
Explanation of Solution
First, set the rules for “significant numbers”
- zeroes to the left are not significant.
- zeroes to the right are not significant if not specified as “exact” zeroes.
- all other digits other than zero are significant.
- zeroes between non-zero numbers are significant.
Second, define the addition/subtraction and multiplication/division rules for significant numbers.
- Addition/Subtraction ( Always keep the least significant number after the decimal point.
- Multiplication/Division ( Always keep the least significant number of the whole number.
- If addition/subtraction and Multiplication/division are included, separate the operation to simple operations and keep following the rules.
Now, for the given operation. Substitute
Assume that pi is actually an exact number, i.e. has infinite amount of significant figures.
According to sig. fig. rules, we must keep only 4 sig. fig. since that is the least amount of significant figures for
(c)
To perform:
The calculations of
Explanation of Solution
First, set the rules for “significant numbers”
- zeroes to the left are not significant.
- zeroes to the right are not significant if not specified as “exact” zeroes.
- all other digits other than zero are significant.
- zeroes between non-zero numbers are significant
Second, define the addition/subtraction and multiplication/division rules for significant numbers.
- Addition/Subtraction ( Always keep the least significant number after the decimal point.
- Multiplication/Division ( Always keep the least significant number of the whole number.
- If addition/subtraction and Multiplication/division are included, separate the operation to simple operations and keep following the rules.
Now, for the given operation. Perform calculation
Total sig. fig. reported are 3, for 4.66.
Round if required
It can also be reported in scientific notation.
(d)
To perform:
The calculations of
Explanation of Solution
First, set the rules for “significant numbers”.
- zeroes to the left are not significant.
- zeroes to the right are not significant if not specified as “exact” zeroes.
- all other digits other than zero are significant.
- zeroes between non-zero numbers are significant.
Second, define the addition/subtraction and multiplication/division rules for significant numbers.
- Addition/Subtraction ( Always keep the least significant number after the decimal point.
- Multiplication/Division ( Always keep the least significant number of the whole number.
- If addition/subtraction and Multiplication/division are included, separate the operation to simple operations and keep following the rules.
Now, for the given operation. Perform calculation
Total sig. fig. are 4 for
Round if required
Always ensure to keep the correct significant numbers when performing addition, subtraction, multiplication and division. It is relevant to keep track of accuracy in the measurements.
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Chapter 1 Solutions
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