Question

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Explanation:

Step1: Convert divisor to integer

Multiply both dividend and divisor by 100 to eliminate decimals: \(17.20\times100 = 1720\), \(6.25\times100 = 625\). Now we divide \(1720\div625\).

Step2: Perform long division

\(625\times2 = 1250\), \(1720 - 1250 = 470\). Bring down a zero (now we have 4700). \(625\times7 = 4375\), \(4700 - 4375 = 325\). Bring down a zero (now we have 3250). \(625\times5 = 3125\), \(3250 - 3125 = 125\). Bring down a zero (now we have 1250). \(625\times2 = 1250\), remainder 0. So combining the quotients: \(2 + 0.7 + 0.05 + 0.02 = 2.776\)? Wait, no, let's do it properly. Wait, \(1720\div625\): \(625\times2 = 1250\), \(1720 - 1250 = 470\). \(470\div625 = 0.752\)? Wait, no, let's use decimal division. Alternatively, \(17.20\div6.25\). Let's write it as \(17.20\div6.25=\frac{17.20}{6.25}=\frac{1720}{625}\). Simplify numerator and denominator by 5: \(344\div125\). \(125\times2 = 250\), \(344 - 250 = 94\). \(94\div125 = 0.752\). So total is \(2 + 0.752 = 2.752\)? Wait, no, wait \(344\div125\): \(125\times2 = 250\), \(344 - 250 = 94\). \(94\div125 = 0.752\), so \(344\div125 = 2.752\). Wait, but let's check with calculator: \(17.20\div6.25\). \(6.25\times2.752 = 6.25\times2 + 6.25\times0.7 + 6.25\times0.05 + 6.25\times0.002 = 12.5 + 4.375 + 0.3125 + 0.0125 = 12.5 + 4.375 = 16.875 + 0.3125 = 17.1875 + 0.0125 = 17.2\). Yes! So the quotient is \(2.752\)? Wait, no, wait \(6.25\times2.752 = 17.2\)? Wait, \(6.25\times2.752\): \(6\times2.752 = 16.512\), \(0.25\times2.752 = 0.688\), total \(16.512 + 0.688 = 17.2\). Yes! So the division gives \(2.752\)? Wait, no, wait my long division earlier was wrong. Let's do it step by step. \(17.20\div6.25\). Move decimal of divisor two places right: 625, so move dividend two places right: 1720. Now divide 1720 by 625. 6252=1250, subtract from 1720: 470. Bring down a zero: 4700. 6257=4375, subtract: 325. Bring down a zero: 3250. 6255=3125, subtract: 125. Bring down a zero: 1250. 6252=1250, subtract: 0. So the quotient digits are 2 (from 6252), then 7 (from 4700/625=7.52? Wait no, 4700 divided by 625: 6257=4375, 4700-4375=325. Then 3250/625=5.2? Wait no, 6255=3125, 3250-3125=125. Then 1250/625=2. So putting it together: 2.752? Wait, the decimal places: when we moved the decimal two places, the dividend became 1720, which is 17.20 with two decimal places moved, so the quotient should have the same decimal places as the original? Wait no, when we multiply divisor and dividend by 100, the quotient remains the same. So 1720 divided by 625: let's do 1720 ÷ 625. 6252 = 1250, 1720-1250=470. 470/625=0.752. So total is 2 + 0.752=2.752? Wait, but 6.252.752=17.2, as we saw. So the correct answer is 2.752? Wait, no, wait 17.20 divided by 6.25. Let's use another method: 6.25 is 25/4, so dividing by 25/4 is multiplying by 4/25. So 17.20 4/25 = (17.20*4)/25 = 68.8/25 = 2.752. Yes, that's correct.

Answer:

2.752