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Class 10MathematicsReal NumbersDecimal expansion of rational numbersHardLevel 19
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How many decimal places will the terminating decimal of (\frac{37}{2^6\cdot 5^3}) have?

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Answer and explanation

Correct answer: (6)

Step 1: The denominator is (2^6\cdot 5^3), and the fraction is in lowest form because (37) does not cancel. Step 2: The larger exponent is (6), so the decimal terminates after (6) places. Step 3: Do not add the exponents for decimal places.

Related tags

Decimal-PlacesTerminating-DecimalExponentsReal-Numbers

Frequently asked questions

What is the correct answer to this question?

(6)

Why is this the correct answer?

Step 1: The denominator is (2^6\cdot 5^3), and the fraction is in lowest form because (37) does not cancel. Step 2: The larger exponent is (6), so the decimal terminates after (6) places. Step 3: Do not add the exponents for decimal places.

Which subject and chapter does this question cover?

This is a Class 10 Mathematics question. Chapter: Real Numbers. Topic: Decimal expansion of rational numbers.

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  1. 1What type of decimal expansion will the rational number (\frac{3}{8}) have?
  2. 2What type of decimal expansion does (\frac{5}{6}) have?
  3. 3Under what condition does (\frac{p}{q}) have a terminating decimal expansion when the fraction is in lowest form?
  4. 4After reducing (\frac{15}{40}), what type of decimal expansion will it have?
  5. 5After at most how many decimal places will the decimal expansion of (\frac{7}{16}) terminate?
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  7. 7Which of the following fractions will give a terminating decimal?
  8. 8Which of the following fractions will give a non-terminating recurring decimal?
  9. 9When (0.75) is written as a rational number, which form is obtained?
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