Question

jacob knows that \\(\frac{1}{20}\\) means “1 divided by 20.” he uses this to find the decimal equivalent for \\(\frac{1}{20}\\). enter a digit into each box to complete his work.

Explanation:

Step 1: Set up the long division

We are dividing \(1\) by \(20\). We write \(1\) as \(1.00\) to perform the division. The divisor is \(20\).

Step 2: Divide in the tenths place

\(20\) does not divide into \(10\) (the value of \(1.0\) in tenths), so we place a \(0\) in the tenths place of the quotient.

Step 3: Divide in the hundredths place

Now we consider \(100\) hundredths (since we bring down a zero from the hundredths place). We find how many times \(20\) goes into \(100\). Since \(20\times5 = 100\), we place a \(5\) in the hundredths place of the quotient.

Step 4: Subtract

We subtract \(20\times5=100\) from \(100\), which gives \(0\). So the subtraction is \(100 - 100\), meaning the two yellow boxes in the subtraction are \(1\) and \(0\) (for \(100\)), and the quotient has \(0\) in the tenths place and \(5\) in the hundredths place.

Answer:

The decimal equivalent of \(\frac{1}{20}\) is \(0.05\). So the first box after the decimal in the quotient is \(0\), the second is \(5\). In the subtraction step, we have \(100 - 100 = 0\) (wait, no, let's do the long division properly). Wait, \(1\div20\): we add a decimal point and zeros. \(20\) goes into \(10\) zero times, so we look at \(100\). \(20\times5 = 100\). So the quotient is \(0.05\). So the first yellow box in the quotient (after decimal) is \(0\), second is \(5\). In the subtraction part, we have \(100 - 100\)? Wait, no, let's re - do the long division:

\(1.00\div20\):

• Step 1: \(20\) doesn't go into \(1\), so we put \(0\) before the decimal. Then we consider \(1.0\) (or \(10\) tenths). \(20\) doesn't go into \(10\) (tenths place), so we put \(0\) in the tenths place of the quotient. Now we consider \(100\) hundredths.
• Step 2: \(20\times5 = 100\), so we put \(5\) in the hundredths place of the quotient. Then we subtract \(100 - 100 = 0\).

So the quotient is \(0.05\), so the first box (tenths place in quotient) is \(0\), the second (hundredths place) is \(5\). In the subtraction step, we have \(100 - 100\), but the numbers being subtracted are \(100\) (from \(20\times5\)), so the two yellow boxes in the subtraction are \(1\) and \(0\) (wait, no, \(20\times5 = 100\), so the subtraction is \(100-100\), so the first yellow box in the subtraction is \(1\), the second is \(0\)).

So to fill in the boxes:

• Quotient: \(0.05\) (so first box after decimal: \(0\), second: \(5\))
• Subtraction: \(100 - 100\), so the two yellow boxes in the subtraction are \(1\) and \(0\)