Question

a cake is baked at 400. °f.
part: 0/2
part 1 of 2
convert this temperature to °c. be sure your answer has the correct number of significant figures.

Explanation:

Step1: Recall the formula for converting Fahrenheit to Celsius.

The formula to convert temperature from Fahrenheit ($^\circ\text{F}$) to Celsius ($^\circ\text{C}$) is $^\circ\text{C} = \frac{5}{9}(^\circ\text{F} - 32)$.

Step2: Substitute the given Fahrenheit temperature into the formula.

We are given $^\circ\text{F} = 400$. Substitute this into the formula:
$$^\circ\text{C} = \frac{5}{9}(400 - 32)$$
First, calculate the value inside the parentheses: $400 - 32 = 368$.
Then, multiply by $\frac{5}{9}$: $^\circ\text{C} = \frac{5}{9} \times 368$.
Calculate $\frac{5\times368}{9} = \frac{1840}{9} \approx 204.444\ldots$

Step3: Determine the number of significant figures.

The given temperature in Fahrenheit, 400, has one significant figure? Wait, no—if 400 is considered to have three significant figures (if the trailing zeros are significant) or one (if they are not). But in the context of baking, 400 $^\circ\text{F}$ is likely intended to have one significant figure? Wait, no, maybe it's three. Wait, the problem says "Be sure your answer has the correct number of significant figures." Let's check: 400 $^\circ\text{F}$—if it's written as 400 without a decimal, the trailing zeros may be ambiguous, but sometimes in such problems, 400 is taken as having one significant figure? Wait, no, maybe the problem expects us to consider 400 as having three significant figures (assuming the zeros are significant). Wait, but let's see: when we calculate $\frac{5}{9}(400 - 32) = \frac{5}{9}(368)$. 368 has three significant figures, 5 and 9 are exact (from the conversion formula), so the result should have three significant figures. Wait, but 400: if 400 is three significant figures, then 400 - 32 = 368 (three significant figures, since 400 is three, 32 is two, but when subtracting, the number of decimal places matters; here, both are whole numbers, so 400 - 32 = 368, which is three significant figures). Then $\frac{5}{9} \times 368$: 5 and 9 are exact, so 368 $\times$ 5 = 1840, divided by 9 is approximately 204.444... So with three significant figures, that would be 204 $^\circ\text{C}$? Wait, no, 204.444... rounded to three significant figures is 204? Wait, 204.444... the first three significant figures are 2, 0, 4? Wait, no, 204.444...: the first significant figure is 2, second 0? Wait, no, leading zeros are not significant, but zeros between non-zero digits are. So 204 has three significant figures (2, 0, 4). Wait, but maybe the original 400 has one significant figure. Let's re-examine: if 400 has one significant figure, then the result should have one. But 400 $^\circ\text{F}$ in baking is a common temperature, and maybe it's intended to have three significant figures (4.00 $\times$ 10$^2$). Alternatively, maybe the problem expects us to not worry about significant figures and just give the approximate value. Wait, maybe the problem has a typo, or maybe we should just calculate it as is. Let's do the calculation:

$\frac{5}{9}(400 - 32) = \frac{5}{9}(368) = \frac{1840}{9} \approx 204.44^\circ\text{C}$. If we take 400 as having three significant figures, then 204 $^\circ\text{C}$ (three significant figures) or 200 $^\circ\text{C}$ (one significant figure). But maybe the problem expects the approximate value, so we can write it as approximately 204 $^\circ\text{C}$ or 200 $^\circ\text{C}$. Wait, let's check with the formula again.

Wait, 400 - 32 = 368. Then 368 * 5 = 1840. 1840 / 9 ≈ 204.44. So if we round to a reasonable number, maybe 204 $^\circ\text{C}$ or 200 $^\circ\text{C}$. But let's see, the problem says "Be sure your answer has the correct number of significant figures." Let's assume 400 has one significant figure (since it's written as 400 without a decimal), so the answer should have one significant figure. Then 204.44... rounded to one significant figure is 200 $^\circ\text{C}$. But that seems too vague. Alternatively, maybe 400 is considered to have three significant figures (if the zeros are significant), so 204 $^\circ\text{C}$ (three significant figures).

But maybe the problem just wants the numerical value, so we can calculate it as:

$^\circ\text{C} = \frac{5}{9}(400 - 32) = \frac{5}{9} \times 368 \approx 204.44^\circ\text{C}$.

Answer:

$\approx 204^\circ\text{C}$ (or $200^\circ\text{C}$ depending on significant figures; but more accurately, approximately 204 $^\circ\text{C}$)