Solved on Dec 04, 2023

Divide the decimal 0.16 by 4,692.08 and express the exact answer as a decimal.

STEP 1

Assumptions
1. We need to divide $0.16$ by $4,692.08$ .
2. The division should give an exact answer in decimal form.

STEP 2

First, we need to set up the division. Since we are dividing by a number with a decimal point, we need to adjust the divisor to be a whole number.
$4,692.08 = 469208 \times 10^{-2}$

STEP 3

To adjust the divisor to a whole number, we multiply both the divisor and the dividend by $10^2$ (or 100).
$0.16 \times 10^2 = 16$

STEP 4

Now we divide the adjusted dividend by the adjusted divisor.
16 \longdiv {469208}

STEP 5

Perform the division. Since $16$ is less than $469208$ , we will have a $0$ before the decimal point.
$0.0000...$

STEP 6

Continue the division process by adding zeros to the dividend and bringing them down one at a time to continue the division until we get a non-zero quotient digit.

STEP 7

After bringing down enough zeros, we find that $469208$ goes into $1600000$ (after bringing down four zeros) a certain number of times.
$1600000 \div 469208 = 3 \text{ (approximately)}$

STEP 8

Place the quotient digit in the correct place after the decimal point.
$0.00003...$

STEP 9

Subtract the product of the divisor and the current quotient digit from the current dividend to get the new remainder.
$1600000 - (469208 \times 3) = 1600000 - 1407624 = 192376$

STEP 10

Bring down another zero to continue the division.

STEP 11

Divide $1923760$ by $469208$ to get the next quotient digit.
$1923760 \div 469208 = 4 \text{ (approximately)}$

STEP 12

Place the next quotient digit in the correct place after the decimal point.
$0.000034...$

STEP 13

Continue this process of bringing down zeros, dividing, and finding the next quotient digit until we have a sufficient number of decimal places for the exact answer.

STEP 14

Once we have the exact answer, we write it out in decimal form.

STEP 15

The exact answer in decimal form is the quotient we found from the division process.
$0.16 \div 4692.08 = 0.0000341...$
Since the problem asks for the exact answer written as a decimal, we would need to continue the division process until it terminates or repeats. However, without further division, we cannot provide more digits of the quotient. The exact answer would be a decimal with a non-terminating sequence of digits unless a repeating pattern emerges.

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Divide the decimal 0.16 by 4,692.08 and express the exact answer as a decimal.

STEP 1

Assumptions
1. We need to divide $0.16$ by $4,692.08$ .
2. The division should give an exact answer in decimal form.

STEP 2

First, we need to set up the division. Since we are dividing by a number with a decimal point, we need to adjust the divisor to be a whole number.
$4,692.08 = 469208 \times 10^{-2}$

STEP 3

To adjust the divisor to a whole number, we multiply both the divisor and the dividend by $10^2$ (or 100).
$0.16 \times 10^2 = 16$

STEP 4

Now we divide the adjusted dividend by the adjusted divisor.
16 \longdiv {469208}

STEP 5

Perform the division. Since $16$ is less than $469208$ , we will have a $0$ before the decimal point.
$0.0000...$

STEP 6

Continue the division process by adding zeros to the dividend and bringing them down one at a time to continue the division until we get a non-zero quotient digit.

STEP 7

After bringing down enough zeros, we find that $469208$ goes into $1600000$ (after bringing down four zeros) a certain number of times.
$1600000 \div 469208 = 3 \text{ (approximately)}$

STEP 8

Place the quotient digit in the correct place after the decimal point.
$0.00003...$

STEP 9

Subtract the product of the divisor and the current quotient digit from the current dividend to get the new remainder.
$1600000 - (469208 \times 3) = 1600000 - 1407624 = 192376$

STEP 10

Bring down another zero to continue the division.

STEP 11

Divide $1923760$ by $469208$ to get the next quotient digit.
$1923760 \div 469208 = 4 \text{ (approximately)}$

STEP 12

Place the next quotient digit in the correct place after the decimal point.
$0.000034...$

STEP 13

Continue this process of bringing down zeros, dividing, and finding the next quotient digit until we have a sufficient number of decimal places for the exact answer.

STEP 14

Once we have the exact answer, we write it out in decimal form.

STEP 15

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Divide the decimal 0.16 by 4,692.08 and express the exact answer as a decimal.

STEP 1

Assumptions1. We need to divide 0.160.160.16 by 4,692.084,692.084,692.08.2. The division should give an exact answer in decimal form.

STEP 2

First, we need to set up the division. Since we are dividing by a number with a decimal point, we need to adjust the divisor to be a whole number.4,692.08=469208×10−24,692.08 = 469208 \times 10^{-2}4,692.08=469208×10−2

STEP 3

To adjust the divisor to a whole number, we multiply both the divisor and the dividend by 10210^2102 (or 100).0.16×102=160.16 \times 10^2 = 160.16×102=16

STEP 4

Now we divide the adjusted dividend by the adjusted divisor.16 \longdiv {469208}

STEP 5

Perform the division. Since 161616 is less than 469208469208469208, we will have a 000 before the decimal point.0.0000...0.0000...0.0000...

STEP 6

Continue the division process by adding zeros to the dividend and bringing them down one at a time to continue the division until we get a non-zero quotient digit.

STEP 7

After bringing down enough zeros, we find that 469208469208469208 goes into 160000016000001600000 (after bringing down four zeros) a certain number of times.1600000÷469208=3 (approximately)1600000 \div 469208 = 3 \text{ (approximately)}1600000÷469208=3 (approximately)

STEP 8

Place the quotient digit in the correct place after the decimal point.0.00003...0.00003...0.00003...

STEP 9

Subtract the product of the divisor and the current quotient digit from the current dividend to get the new remainder.1600000−(469208×3)=1600000−1407624=1923761600000 - (469208 \times 3) = 1600000 - 1407624 = 1923761600000−(469208×3)=1600000−1407624=192376

STEP 10

Bring down another zero to continue the division.

STEP 11

Divide 192376019237601923760 by 469208469208469208 to get the next quotient digit.1923760÷469208=4 (approximately)1923760 \div 469208 = 4 \text{ (approximately)}1923760÷469208=4 (approximately)

STEP 12

Place the next quotient digit in the correct place after the decimal point.0.000034...0.000034...0.000034...

STEP 13

Continue this process of bringing down zeros, dividing, and finding the next quotient digit until we have a sufficient number of decimal places for the exact answer.

STEP 14

Once we have the exact answer, we write it out in decimal form.

STEP 15

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Assumptions
1. We need to divide $0.16$ by $4,692.08$ .
2. The division should give an exact answer in decimal form.

First, we need to set up the division. Since we are dividing by a number with a decimal point, we need to adjust the divisor to be a whole number.
$4,692.08 = 469208 \times 10^{-2}$

To adjust the divisor to a whole number, we multiply both the divisor and the dividend by $10^2$ (or 100).
$0.16 \times 10^2 = 16$

Now we divide the adjusted dividend by the adjusted divisor.
16 \longdiv {469208}

Perform the division. Since $16$ is less than $469208$ , we will have a $0$ before the decimal point.
$0.0000...$

After bringing down enough zeros, we find that $469208$ goes into $1600000$ (after bringing down four zeros) a certain number of times.
$1600000 \div 469208 = 3 \text{ (approximately)}$

Place the quotient digit in the correct place after the decimal point.
$0.00003...$

Subtract the product of the divisor and the current quotient digit from the current dividend to get the new remainder.
$1600000 - (469208 \times 3) = 1600000 - 1407624 = 192376$

Divide $1923760$ by $469208$ to get the next quotient digit.
$1923760 \div 469208 = 4 \text{ (approximately)}$

Place the next quotient digit in the correct place after the decimal point.
$0.000034...$