Question

Solve each calculation. Be sure to report your answer with the correct number of significant figures.

Answer 1

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. $5.61000dg * 1.1010dg$ = $6.177 dg^2$

2. $\frac{12}{3.1415} = 3.8198$

Step-by-step explanation:

1. 5.61000 dg  × 1.1010 dg  

We start by representing each digit using scientific notation

$5.61000 = 561000 * 10^{-5}$

$1.1010 = 11010 * 10^{-4}$

Then, Multiply both numbers

$561000 * 10^{-5} * 11010 * 10^{-4}$

First, rearrange

$561000 * 11010 * 10^{-5} * 10^{-4}$

$6176610000 * 10^{-5} * 10^{-4}$

From law of indices, $10^{-5} * 10^{-4} = 10^{-9}$;

So, we have

$6176610000 * 10^{-9}$

$6.176610000$

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 $6.177$

Hence, $5.61000dg * 1.1010dg$ = $6.177 dg^2$

2.

12.0 m  ÷ 3.1415 m

Using proper notation

12.0 m ÷ 3.1415 m = $\frac{12}{3.1415}$

We start by representing 3.1415 using scientific notation

$3.1415 = 31415 * 10^{-4}$

By substitution;

$\frac{12}{3.1415} = \frac{12}{31415 * 10^-4}$

Take $10^{-4}$ to the numerator

$\frac{12}{3.1415} = \frac{12 * 10^4}{31415}$

From law of indices, $10^{4}$ = 10000

$\frac{12}{3.1415} = \frac{12 * 10000}{31415}$

Multiply

$\frac{12}{3.1415} = \frac{120000}{31415}$

Divide

$\frac{12}{3.1415} = 3.81983129078$

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

$\frac{12}{3.1415} = 3.8198$

Answer 2

Answer:

1. 6.1767

2. 3.82

Step-by-step explanation:

Edge