Question

in a recent survey of 188 nurses, 123 were unhappy with their jobs due to the difficult working hours and work - related stresses. find the percent unhappy with their jobs.
% of the nurses were unhappy with their jobs.
(round to the nearest tenth of a percent as needed.)

Explanation:

Step1: Calculate the ratio of unhappy nurses

To find the percentage, first find the ratio of unhappy nurses to total nurses. The formula for the ratio is $\frac{\text{Number of unhappy nurses}}{\text{Total number of nurses}}$. So we have $\frac{123}{188}$.

Step2: Convert the ratio to a percentage

Multiply the ratio by 100 to get the percentage. So we calculate $\frac{123}{188} \times 100$. Let's compute that: $\frac{123\times100}{188}=\frac{12300}{188}\approx 65.4255$. Rounding to the nearest tenth of a percent, we look at the hundredth place, which is 2, so we keep the tenth place as is. Wait, no, wait: 65.4255, the tenth place is 4, the hundredth is 2, so when rounding to the nearest tenth, we see that 0.4255 is closer to 0.4 than 0.5? Wait, no, 65.4255: let's do the division more accurately. 123 divided by 188: 188 goes into 1230 six times (1886=1128), 1230 - 1128 = 102. Bring down a 0: 1020. 188 goes into 1020 five times (1885=940), 1020 - 940 = 80. Bring down a 0: 800. 188 goes into 800 four times (1884=752), 800 - 752 = 48. Bring down a 0: 480. 188 goes into 480 two times (1882=376), 480 - 376 = 104. Bring down a 0: 1040. 188 goes into 1040 five times (188*5=940), 1040 - 940 = 100. So now we have 65.4255... So the number is approximately 65.4% when rounded to the nearest tenth? Wait, no, 65.4255, the tenths place is 4, hundredths is 2, so since 2 < 5, we round down, so 65.4? Wait, but wait, 123/188 = 0.654255... Multiply by 100 is 65.4255..., so to the nearest tenth of a percent, it's 65.4%? Wait, no, wait, 65.4255, the tenths digit is 4, the hundredths is 2, so when rounding to the nearest tenth, we look at the hundredths digit. If the hundredths digit is less than 5, we round down, so 65.4. But wait, let me check with a calculator: 123 divided by 188. Let's do 123 ÷ 188. 188 × 0.6 = 112.8, 123 - 112.8 = 10.2. 10.2 ÷ 188 = 0.054255. So total is 0.6 + 0.054255 = 0.654255, times 100 is 65.4255%, so rounding to the nearest tenth is 65.4%? Wait, no, 65.4255, the tenth is 4, hundredth is 2, so yes, 65.4. Wait, but maybe I made a mistake. Wait, 123/188: let's compute 123 ÷ 188. Let's use a calculator approach. 188 × 65 = 188×60 + 188×5 = 11280 + 940 = 12220. 12300 - 12220 = 80. So 65 + 80/188 = 65 + 0.4255 = 65.4255, so 65.4% when rounded to the nearest tenth. Yes, that's correct.

Answer:

65.4%