Question

(c) based on your answers above, compare the numbers below using <, >, o
0.35 □ 25%
\\(\frac{7}{20}\\) □ 0.4

Explanation:

Step1: Convert 25% to decimal

To compare 0.35 and 25%, we first convert 25% to a decimal. Recall that to convert a percentage to a decimal, we divide by 100. So, \(25\%=\frac{25}{100} = 0.25\). Now we compare 0.35 and 0.25. Since 0.35 is greater than 0.25, we have \(0.35>25\%\).

Step2: Convert \(\frac{7}{20}\) to decimal

To compare \(\frac{7}{20}\) and 0.4, we convert \(\frac{7}{20}\) to a decimal. We can do this by dividing 7 by 20: \(7\div20 = 0.35\)? Wait, no, \(7\div20 = 0.35\)? Wait, 20 times 0.35 is 7, but we need to compare with 0.4. Wait, no, let's recalculate: \(7\div20=0.35\)? Wait, no, 200.35 = 7, but we have 0.4. Wait, no, maybe I made a mistake. Wait, 7 divided by 20: 20 goes into 7 zero, add decimal, 20 goes into 70 three times (320=60), remainder 10, bring down 0, 20 goes into 100 five times. So \(7\div20 = 0.35\)? Wait, no, that's not right. Wait, 0.4 is equal to \(\frac{4}{10}=\frac{8}{20}\). So \(\frac{7}{20}\) is 0.35? Wait, no, 7 divided by 20: 200.3 = 6, 7-6=1, 1/20=0.05, so 0.3+0.05=0.35. And 0.4 is 0.40. So we compare 0.35 and 0.4. Since 0.35 is less than 0.4? Wait, no, wait the fraction is \(\frac{7}{20}\). Wait, maybe I messed up. Wait, \(\frac{7}{20}\) as a decimal: 7 ÷ 20. Let's do the division: 20 into 7.00. 200.3 = 6.0, subtract 6.0 from 7.0, we get 1.0. Bring down a 0: 10.0. 20 into 10.0 is 0.5. So 0.3 + 0.05 = 0.35. So \(\frac{7}{20}=0.35\). Now compare 0.35 and 0.4. Since 0.35 < 0.4, so \(\frac{7}{20}<0.4\)? Wait, no, wait 0.35 is less than 0.4, so \(\frac{7}{20}<0.4\)? Wait, but let's check again. \(\frac{7}{20}\) is 0.35, and 0.4 is 0.40. So 0.35 is less than 0.4, so \(\frac{7}{20}<0.4\). Wait, but maybe I made a mistake in the fraction. Wait, no, 7 divided by 20 is 0.35. And 0.4 is 0.4. So 0.35 < 0.4, so \(\frac{7}{20}<0.4\). Wait, but the problem is \(\frac{7}{20}\) and 0.4. So that's correct.

Answer:

For \(0.35\) and \(25\%\): \(0.35 > 25\%\)

For \(\frac{7}{20}\) and \(0.4\): \(\frac{7}{20} < 0.4\)