Question

carry out the following operations, and express the answer with the appropriate number of significant figures.
part a
320.8 − (6108.9/3.3)
express your answer to the appropriate number of significant figures.
view available hint(s)
320.8 − (6108.9/3.3) =
you have already submitted this answer. enter a new answer.
no credit lost. try again.

Explanation:

Step1: Calculate the division

First, we need to calculate the value of \( \frac{6108.9}{3.3} \).
\( \frac{6108.9}{3.3} = 1851.1818\cdots \)

Step2: Perform the subtraction

Now, subtract the result from 320.8:
\( 320.8 - 1851.1818\cdots = -1530.3818\cdots \)
Considering significant figures, let's check the original numbers. 320.8 has four significant figures, 6108.9 has five, and 3.3 has two. When dividing, the result should have two significant figures? Wait, no, let's re - evaluate. Wait, 3.3 has two significant figures, so \( \frac{6108.9}{3.3}\approx1900 \) (two significant figures? Wait, no, 6108.9 divided by 3.3: 3.3 is two significant figures, so the result of division should be two significant figures? Wait, 6108.9 / 3.3 = 1851.18, when considering significant figures for division, the number of significant figures is determined by the least number, which is 2 (from 3.3). But 320.8 has four. Wait, maybe I made a mistake. Wait, 3.3 is two significant figures, so 6108.9 ÷ 3.3: 6108.9 has more, 3.3 has two, so the result is 1.9×10³ (two significant figures). Then 320.8 - 1900 = - 1579.2, but this seems off. Wait, maybe the problem expects us to calculate precisely first and then consider significant figures. Let's calculate precisely:

6108.9÷3.3: 3.3×1851 = 3.3×1800+3.3×51 = 5940 + 168.3 = 6108.3, 6108.9 - 6108.3 = 0.6, 0.6÷3.3=\( \frac{6}{33}=\frac{2}{11}\approx0.1818 \), so 6108.9÷3.3 = 1851.1818...

Then 320.8 - 1851.1818 = - 1530.3818...

Now, let's check the significant figures. 320.8: the trailing 8 after the decimal, so it's 320.8 (four significant figures). 6108.9: five significant figures. 3.3: two significant figures. When we do division, the result should have two significant figures? Wait, no, the rule for significant figures in division is that the result has the same number of significant figures as the least precise measurement. 3.3 has two, so 6108.9 / 3.3 ≈ 1.9×10³ (two significant figures). Then 320.8 - 1.9×10³: 320.8 is approximately 0.32×10³, so 0.32×10³ - 1.9×10³ = - 1.58×10³, which is - 1600 (two significant figures?) But this is confusing. Wait, maybe the problem doesn't require strict significant figure rounding during calculation but just calculate the value first. Let's do the exact calculation:

320.8 - (6108.9 / 3.3) = 320.8 - 1851.181818... = - 1530.381818...

If we consider the original numbers: 320.8 (four sig figs), 6108.9 (five), 3.3 (two). The division step: 6108.9 / 3.3. Since 3.3 has two sig figs, the result of division is 1.9×10³ (two sig figs). Then subtraction: 320.8 - 1900. The number with the least decimal places? 320.8 has one decimal place, 1900 has zero. But when subtracting, the number of decimal places is determined by the least precise. But 1900 is an approximation. Alternatively, maybe the problem expects us to calculate the exact value and then round to a reasonable number of significant figures. Let's see, 320.8 - 1851.18 = - 1530.38. Now, 320.8 has four significant figures, 6108.9 has five, 3.3 has two. The limiting factor is 3.3 with two significant figures? No, wait, 3.3 is two, but 6108.9 is more, so the division result should have two. But 320.8 is four. This is a bit confusing. Maybe the problem just wants the numerical answer without strict significant figure rounding (maybe a miscalculation in my part). Let's recalculate 6108.9÷3.3:

3.3×1851 = 3.3×(1800 + 51)=3.3×1800+3.3×51 = 5940+168.3 = 6108.3

6108.9 - 6108.3 = 0.6

0.6÷3.3 = 6÷33 = 2÷11≈0.1818

So 6108.9÷3.3 = 1851.1818

Then 320.8 - 1851.1818 = - 1530.3818

If we take into account significant figures, 3.3 has two, so 6108.9÷3.3≈1.9×10³ (two sig figs), then 320.8 - 1900 = - 1580 (but this is a rough estimate). However, maybe the problem expects the precise calculation result. Let's check with a calculator: 6108.9 divided by 3.3 is 1851.181818..., 320.8 minus that is - 1530.381818...

Answer:

\( - 1530 \) (or more precisely \( - 1530.4 \) depending on significant figures, but if we consider 3.3 has two, 6108.9/3.3≈1850 (three sig figs? Wait, 3.3 is two, so 1.9×10³, but 6108.9 is five, 3.3 is two, so 6108.9/3.3 = 1851.18, which we can take as 1850 (three sig figs) to match 320.8 (four). Then 320.8 - 1850 = - 1529.2≈ - 1530)