Question

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3.64)28.5376

Explanation:

Step1: Convert divisor to integer

To make the divisor \(3.64\) an integer, we multiply both the divisor and the dividend by \(100\) (since there are two decimal places in \(3.64\)). So we get \(364\) as the new divisor and \(2853.76\) as the new dividend (because \(28.5376\times100 = 2853.76\) and \(3.64\times100=364\)). Now we have the division problem \(\frac{2853.76}{364}\).

Step2: Perform long division

We start by seeing how many times \(364\) goes into \(2853\). \(364\times7 = 2548\). Subtract \(2548\) from \(2853\): \(2853 - 2548=305\). Bring down the next digit (which is \(7\)) to make \(3057\). Now, \(364\times8 = 2912\). Subtract \(2912\) from \(3057\): \(3057 - 2912 = 145\). Bring down the next digit (which is \(6\)) to make \(1456\). Now, \(364\times4=1456\). Subtract \(1456\) from \(1456\) and we get \(0\). So putting it all together, \(7\times10 + 8\times1+4\times0.01=70 + 8+ 0.04 = 78.04\)? Wait, no, wait. Wait, the dividend after conversion is \(2853.76\) and divisor is \(364\). Let's do it step by step:

• \(364\times7 = 2548\), \(2853.76-2548 = 305.76\) (wait, I made a mistake earlier, I forgot the decimal in the dividend after conversion. The dividend is \(2853.76\), so when we divide \(2853.76\) by \(364\)):

First, \(364\times7 = 2548\), \(2853.76 - 2548=305.76\). Now, bring down the decimal (or consider the next digit as part of the decimal). Now, \(364\times0.8 = 291.2\) (since \(364\times8 = 2912\), so \(364\times0.8=291.2\)). Subtract \(291.2\) from \(305.76\): \(305.76 - 291.2 = 14.56\). Now, \(364\times0.04=14.56\). So adding up the parts: \(7 + 0.8+0.04 = 7.84\). Wait, let's check: \(3.64\times7.84\). Let's calculate \(3.64\times7 = 25.48\), \(3.64\times0.8 = 2.912\), \(3.64\times0.04 = 0.1456\). Now sum them: \(25.48+2.912 = 28.392\), \(28.392+0.1456 = 28.5376\). Yes! So the result is \(7.84\).

Wait, let's redo the long division properly:

Dividend: \(28.5376\), Divisor: \(3.64\)

We can also use the formula for division of decimals: \(\frac{28.5376}{3.64}=\frac{28.5376\times100}{3.64\times100}=\frac{2853.76}{364}\)

Now, divide \(2853.76\) by \(364\):

• \(364\times7 = 2548\), \(2853.76 - 2548 = 305.76\)
• \(364\times0.8 = 291.2\) (because \(364\times8 = 2912\), so \(364\times0.8 = 291.2\)), \(305.76 - 291.2 = 14.56\)
• \(364\times0.04 = 14.56\) (because \(364\times4 = 1456\), so \(364\times0.04 = 14.56\)), \(14.56 - 14.56 = 0\)

So adding the quotients: \(7 + 0.8+0.04 = 7.84\)

Answer:

\(7.84\)