Question

which sign makes the statement true? 4.55? 4\frac{17}{20} > < =

Explanation:

Step1: Convert mixed number to decimal

First, convert the fraction part of \(4\frac{17}{20}\) to a decimal. The fraction is \(\frac{17}{20}\), and \(\frac{17}{20}=17\div20 = 0.85\). Then add the whole number part: \(4 + 0.85=4.85\)? Wait, no, wait, 17 divided by 20: 20 times 0.8 is 16, 17 - 16 = 1, so 1/20 = 0.05, so 0.8 + 0.05 = 0.85? Wait, no, 17 ÷ 20: 20 × 0.85 = 17, so \(\frac{17}{20}=0.85\). Then \(4\frac{17}{20}=4 + 0.85 = 4.85\)? Wait, no, wait the original number is 4.55 and \(4\frac{17}{20}\). Wait, no, I made a mistake. Wait, 17 divided by 20: 20 × 0.8 = 16, 17 - 16 = 1, so 1/20 = 0.05, so 0.8 + 0.05 = 0.85? Wait, no, 20 × 0.85 = 17, so yes, 0.85. So \(4\frac{17}{20}=4.85\)? Wait, but 4.55 and 4.85? Wait, no, wait the problem is 4.55 and \(4\frac{17}{20}\). Wait, maybe I miscalculated. Wait, 17/20: let's do 17 ÷ 20. 20 goes into 17 zero times. Add decimal point, 20 goes into 170 eight times (20×8=160), remainder 10. 20 goes into 100 five times (20×5=100), so 0.85. So \(4\frac{17}{20}=4.85\)? But 4.55 is less than 4.85? Wait, no, wait the problem is 4.55 and \(4\frac{17}{20}\). Wait, maybe I messed up. Wait, no, wait 17/20: 20×0.85=17, so 4 + 0.85=4.85. But 4.55 is 4.55, so 4.55 < 4.85? Wait, but that contradicts. Wait, no, wait maybe I made a mistake in the fraction. Wait, 17/20: 20×0.8=16, 17-16=1, so 1/20=0.05, so 0.8+0.05=0.85, so 4.85. But 4.55 is 4.55, so 4.55 < 4.85? Wait, but the options are >, <, =. Wait, maybe I made a mistake. Wait, wait the original number is 4.55 and \(4\frac{17}{20}\). Wait, no, wait 17/20 is 0.85, so 4 + 0.85 is 4.85. But 4.55 is 4.55, so 4.55 < 4.85? Wait, but that seems off. Wait, maybe I misread the fraction. Is it \(4\frac{17}{20}\) or \(4\frac{7}{20}\)? Wait, the problem says \(4\frac{17}{20}\). Wait, 17/20 is 0.85, so 4.85. 4.55 is less than 4.85, so the sign is <. Wait, but let's check again. 4.55 vs 4.85. 4.55 is 4 and 0.55, 4.85 is 4 and 0.85. So 0.55 < 0.85, so 4.55 < 4.85. So the sign is <.

Wait, wait, no, wait I think I made a mistake. Wait, 17 divided by 20: 20 × 0.8 = 16, 17 - 16 = 1, so 1/20 = 0.05, so 0.8 + 0.05 = 0.85. So \(4\frac{17}{20}=4.85\). Then 4.55 compared to 4.85: 4.55 is less than 4.85, so the sign is <.

Answer:

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