Answer :
Question:
Solve each calculation. Be sure to report your answer with the correct number of significant figures.
5.61000 dg × 1.1010 dg
12.0 m ÷ 3.1415 m
Answer:
1. [tex]5.61000dg * 1.1010dg[/tex] = [tex]6.177 dg^2[/tex]
2. [tex]\frac{12}{3.1415} = 3.8198[/tex]
Step-by-step explanation:
1. 5.61000 dg × 1.1010 dg
We start by representing each digit using scientific notation
[tex]5.61000 = 561000 * 10^{-5}[/tex]
[tex]1.1010 = 11010 * 10^{-4}[/tex]
Then, Multiply both numbers
[tex]561000 * 10^{-5} * 11010 * 10^{-4}[/tex]
First, rearrange
[tex]561000 * 11010 * 10^{-5} * 10^{-4}[/tex]
[tex]6176610000 * 10^{-5} * 10^{-4}[/tex]
From law of indices, [tex]10^{-5} * 10^{-4} = 10^{-9}[/tex];
So, we have
[tex]6176610000 * 10^{-9}[/tex]
[tex]6.176610000[/tex]
Because 5.61000 is given in 3 significant figures and 1.1010 is given in 4 significant figures, we approximate the result to 4 significant figures
This gives [tex]6.177[/tex]
Hence, [tex]5.61000dg * 1.1010dg[/tex] = [tex]6.177 dg^2[/tex]
2.
12.0 m ÷ 3.1415 m
Using proper notation
12.0 m ÷ 3.1415 m = [tex]\frac{12}{3.1415}[/tex]
We start by representing 3.1415 using scientific notation
[tex]3.1415 = 31415 * 10^{-4}[/tex]
By substitution;
[tex]\frac{12}{3.1415} = \frac{12}{31415 * 10^-4}[/tex]
Take [tex]10^{-4}[/tex] to the numerator
[tex]\frac{12}{3.1415} = \frac{12 * 10^4}{31415}[/tex]
From law of indices, [tex]10^{4}[/tex] = 10000
[tex]\frac{12}{3.1415} = \frac{12 * 10000}{31415}[/tex]
Multiply
[tex]\frac{12}{3.1415} = \frac{120000}{31415}[/tex]
Divide
[tex]\frac{12}{3.1415} = 3.81983129078[/tex]
Because 12.0 is given in 2 significant figures and 3.1415 is given in 5 significant figures, we approximate the result to 5 significant figures
[tex]\frac{12}{3.1415} = 3.8198[/tex]
