Question

question
in one month, the median home price in the west fell from $203,400 to $192,300. find the percent decrease. (round to the nearest tenth of a percent.)

provide your answer below:

□%

Explanation:

Step1: Find the amount of decrease

Subtract the new price from the original price.
$203400 - 192300 = 11100$

Step2: Calculate the percent decrease

Use the formula for percent decrease: $\frac{\text{Decrease}}{\text{Original Amount}} \times 100\%$.
$\frac{11100}{203400} \times 100\% \approx 5.457\%$

Step3: Round to the nearest tenth of a percent

Round $5.457\%$ to one decimal place.
$5.5\%$ (Wait, no, 5.457 rounded to the nearest tenth: look at the hundredth place, which is 5, so we round up the tenth place. So 5.4 + 0.1 = 5.5? Wait, no, 5.457: tenth is 4, hundredth is 5, so round up the tenth: 5.5? Wait, no, 5.457 is approximately 5.5 when rounded to the nearest tenth? Wait, no, 5.457: the tenths place is 4, hundredths is 5, so we add 1 to the tenths place: 4 + 1 = 5, so 5.5? Wait, no, 5.457 is 5.4 (tenths) and 57 hundredths. Wait, no, 5.457: the first decimal is tenth (4), second is hundredth (5), third is thousandth (7). To round to the nearest tenth, we look at the hundredth digit. Since 5 is equal to or greater than 5, we round up the tenth digit: 4 becomes 5. So 5.5? Wait, but let's recalculate the percent decrease.

Wait, original calculation: 11100 / 203400 = let's compute that. 11100 ÷ 203400. Let's divide numerator and denominator by 100: 111 / 2034. Let's divide 111 by 2034. 2034 ÷ 111 ≈ 18.324, so 1/18.324 ≈ 0.05457, so 5.457%, which is approximately 5.5% when rounded to the nearest tenth? Wait, no, 5.457: the tenths place is 4, hundredths is 5, so we round up the tenths place to 5, so 5.5? Wait, but maybe I made a mistake. Wait, 5.457 rounded to the nearest tenth: the rule is, if the digit in the hundredths place is 5 or more, we round up the tenths place. So 5.457: hundredths digit is 5, so we round up the tenths digit (4) to 5, so 5.5. Wait, but let's check the calculation again.

Wait, 203400 - 192300 = 11100. Then 11100 / 203400 = 0.05457... Multiply by 100: 5.457... So to the nearest tenth of a percent, that's 5.5%? Wait, no, 5.457 is 5.4 when rounded to the nearest tenth? Wait, no, 5.457: the first decimal is 4 (tenth), second is 5 (hundredth), third is 7 (thousandth). So when rounding to the nearest tenth, we look at the hundredth digit. Since 5 is ≥5, we round up the tenth digit: 4 becomes 5, so 5.5. Yes, that's correct. So the percent decrease is approximately 5.5%. Wait, but let me check with a calculator. 11100 divided by 203400: 11100 ÷ 203400 = 0.0545722714... Multiply by 100: 5.45722714... So rounding to the nearest tenth: look at the first decimal after the decimal point in the percentage, which is 4, and the next digit is 5, so we round up 4 to 5, so 5.5%.

Wait, but maybe I made a mistake in the subtraction. 203400 - 192300: 203400 - 192300 = 11100. That's correct. Then 11100 / 203400 = 0.05457... So yes, 5.5% when rounded to the nearest tenth.

Answer:

5.5%