Question

After how many decimal places does the decimal expansion of 63 ÷ 90 terminates

Answer 1

SOLUTION

TO DETERMINE

The number of decimal places does the decimal expansion of $\displaystyle \sf{ \frac{63}{90} }$ terminates

EVALUATION

Here the given fraction is

$\displaystyle \sf{ \frac{63}{90} }$

Which can be simplified to

$\displaystyle \sf{ \frac{63}{90} = \frac{7}{10} }$

So the denominator = 10

Now 10 = 2 × 5

So the denominator of the fraction consists only 2 and 5 as prime factors

So the given fraction is terminating

Now the exponent of 2 = 1

The exponent of 5 = 1

Now the maximum value of the exponents = 1

So the given fraction terminates after one decimal place

More precisely $\displaystyle \sf{ \frac{63}{90} = \frac{7}{10} }$ = 0.7

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Answer 2

Answer:

SOLUTION

TO DETERMINE

The number of decimal places does the decimal expansion of  terminates

EVALUATION

Here the given fraction is

Which can be simplified to

So the denominator = 10

Now 10 = 2 × 5

So the denominator of the fraction consists only 2 and 5 as prime factors

So the given fraction is terminating

Now the exponent of 2 = 1

The exponent of 5 = 1

Now the maximum value of the exponents = 1

So the given fraction terminates after one decimal place

More precisely  = 0.7

Step-by-step explanation: