Question
Perform each of the following computations using the measured quantities below.
Write your final answer with the correct number of significant figures in proper scientific notation (one non-zero number to the left of the decimal point).
a. 917.2 + 45.63 = ___________
b. 3.423 x 10^-4 - 6.42 x 10^-3 =_________
Answer:
(a) 9.6 x 10²
(b) -6.1 x 10⁻³
Explanation:
(a) 917.2 + 45.63
First add the two numbers as follows (ensure that the decimal numbers are well aligned);
9 1 7 . 2
+ 4 5 . 6 3
9 6 2 . 8 3
To write the result in a proper scientific notation (one non-zero number to the left of the decimal point),
i. Express the number is standard form
962.83 = 9.6283 x 10²
Note that;
From the result in (i)
9.6283 = mantissa
10 = base
² = power or exponent.
ii. Express the mantissa of the number in 1 decimal place.
9.6 x 10²
Therefore, the result in the proper scientific notation is 9.6 x 10².
(b) 3.423 x 10⁻⁴ - 6.42 x 10⁻³
Find the difference between the two numbers as follows;
i. Re-write the numbers so that they both have the same exponents:
0.3423 x 10⁻³ - 6.42 x 10⁻³
ii. Factor out 10⁻³
10⁻³(0.3423 - 6.42)
iii. Solve the bracket
10⁻³(-6.0777)
iv. Rewrite the result in (iii)
-6.0777 x 10⁻³
To write the result in a proper scientific notation (one non-zero number to the left of the decimal point),
i. Express the number is standard form
-6.0777 x 10⁻³ [already in standard form]
Note that;
From the result in (i)
-6.0777 = mantissa
10 = base
⁻³ = power or exponent.
ii. Express the mantissa of the number in 1 decimal place.
-6.1 x 10⁻³
Therefore, the result in the proper scientific notation is -6.1 x 10⁻³.