Question

Perform the following calculations. In each case, first estimate the solution without using a calculator and then do the calculation, paying attention to significant figures.

(a) (2.7)(8.632)
(b) (3.600 x 10^-4) / 45
(c) 2.365 + 125.2
(d) (4.753 x 10^4) - (9 x 10^2)

Answer 1

For a: The answer is
`2.3* 10^1`

For b: The answer is
`8.0* 10^(-6)`

For c: The answer is 127.6

For d: The answer is
`4.66* 10^4`

Explanation:

Significant figures are defined as the figures in a number which express the value -the magnitude of a quantity to a specific degree of accuracy is known as significant digits.

Rules for significant figures:

• Digits from 1 to 9 are always significant and have infinite number of significant figures.
• All non-zero numbers are always significant. For example: 654, 6.54 and 65.4 all have three significant figures.
• All zero’s between integers are always significant. For example: 5005, 5.005 and 50.05 all have four significant figures.
• All zero’s preceding the first integers are never significant. For example: 0.0078 has two significant figures.
• All zero’s after the decimal point are always significant. For example: 4.500, 45.00 and 450.0 all have four significant figures.
• All zeroes used solely for spacing the decimal point are not significant. For example : 8000 has one significant figure.

Rule applied for the addition and subtraction is:

The least precise number present after the decimal point determines the number of significant figures in the answer.

Rule applied for the multiplication and division is:

The number of significant digits is taken from the value which has least precise significant digits.

For the given options:

• Option a: (2.7)(8.632)

The given problem is a multiplication one.

`\Rightarrow (2.7* 8.632)=23.3`

Here, the least precise significant digits are 2. So, the answer is
`2.3* 10^1`

• Option b: (3.600 x 10^-4) / 45

The given problem is a division one.

`\Rightarrow ((3.600* 10^(-4)))/(45)=0.08* 10^(-4)`

Here, the least precise significant digits are 2. So, the answer is
`8.0* 10^(-6)`

• Option c: 2.365 + 125.2

The given problem is an addition one.

`\Rightarrow (2.365+125.2)=127.565`

Here, the least precise significant digits after decimal is 1. So, the answer is 127.6

• Option d: (4.753 x 10^4) - (9 x 10^2)

The given problem is a subtraction one.

`\Rightarrow (4.753* 10^4)-(9* 10^2)=(4.753* 10^4)-(0.09* 10^4)=4.663* 10^4`

Here, the least precise significant digits after decimal are 2. So, the answer is
`4.66* 10^4`