Write 43/22 as a decimal. If necessary, use a bar to indicate which digit or group of digits repeats.
Understand the Problem
The question is asking to convert the fraction 43/22 into its decimal form, indicating any repeating digits if necessary.
Answer
$1.95\overline{45}$
Answer for screen readers
The decimal form of $\frac{43}{22}$ is $1.95\overline{45}$.
Steps to Solve
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Perform Long Division To convert the fraction $\frac{43}{22}$ into decimal form, we can use long division. We divide 43 by 22.
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Divide the Whole Numbers 22 goes into 43 one time, so we write 1 above the division line. Multiply: $1 \times 22 = 22$.
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Subtract Subtract 22 from 43: $$ 43 - 22 = 21 $$.
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Bring Down the Next Digit Since we are dividing 43 (a whole number), we can add a decimal point and a zero. Bringing down 0 gives us 210.
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Divide Again 22 goes into 210 nine times. Write 9 above the division line next to 1, making it 1.9. Multiply: $9 \times 22 = 198$.
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Subtract Again Subtract 198 from 210: $$ 210 - 198 = 12 $$.
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Bring Down Another Zero Bring down another 0 to get 120.
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Divide Again 22 goes into 120 five times. Write 5 above the division line. Multiply: $5 \times 22 = 110$.
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Subtract Again Subtract 110 from 120: $$ 120 - 110 = 10 $$.
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Bring Down Another Zero Bring down 0 to get 100.
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Divide Again 22 goes into 100 four times. Write 4 above the division line. Multiply: $4 \times 22 = 88$.
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Final Subtraction Subtract 88 from 100: $$ 100 - 88 = 12 $$.
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Recognize the Pattern Once we subtract, we see that we get 12 once again after a few steps, indicating that the digits will start to repeat.
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Write the Final Decimal with Repeating Bar We can express the decimal as $1.954545\ldots$, indicating that "45" repeats.
The decimal form of $\frac{43}{22}$ is $1.95\overline{45}$.
More Information
The fraction $\frac{43}{22}$ represents an improper fraction, and upon conversion, it yields a repeating decimal. This repeating nature is common in many fractions where the denominator does not divide evenly into the numerator.
Tips
- Incorrectly performing the long division leading to inaccurate decimal places.
- Forgetting to add the decimal point and zeroes after the whole number part is exhausted.
- Misidentifying the repeating part of the decimal.
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