Question

The decimal representation of \[\dfrac{6}{{1250}}\] will terminate after how many places of decimal?

Answer 1

Hint: Convert the fraction into decimal form by simplifying the denominator in terms of 10 and its multiple. Then count the numbers after which the number will terminate, that will give you the desired result.

Complete step-by-step solution -
Terminating decimal: An ending decimal is generally characterized as a decimal number that contains a limited number of digits after the decimal point. All ending decimals are objective numbers that can be composed as diminished divisions with denominators containing no prime number factors other than five or two
Non- terminating decimal: A non-terminating, non-rehashing decimal is a decimal number that proceeds unendingly, with no gathering of digits rehashing interminably. Decimals of this sort can't be spoken to as parts, and therefore are unreasonable numbers. Models. Pi is a non-ending, non-rehashing decimal.
Simplify \[\dfrac{6}{{1250}}\] in decimal form,
\[\dfrac{6}{{1250}} = \dfrac{3}{{625}}\]
Now multiply and divide by \[{2^4}\]
\[\dfrac{3}{{625}} = \dfrac{3}{{625}} \times \dfrac{{{2^4}}}{{{2^4}}}\]
Get,
\[\dfrac{6}{{1250}} = \dfrac{{48}}{{{5^4} \times {2^4}}}\]
Implies,
\[\dfrac{6}{{1250}} = \dfrac{{48}}{{{{10}^4}}}\]
Therefore, Decimal representation of \[\dfrac{6}{{1250}}\] is \[0.0048\].
Hence the representation will terminate after four decimal places.

Note: Simplify in the simple form as if there will be a mistake in the conversion then the desired result will not correct. Count the numbers after decimal places this will give you the result. Here we could directly divide the numerator with the denominator but it would be a longer approach to solve the problem.