Question

How do I explain 1.82 divided by 140.14

Answer 1

Answer:

  0.012987...(6-digit repeat)

Step-by-step explanation:

You explain it the same way you explain any division of decimal numbers.

The usual procedure is to adjust both numbers so that the divisor is an integer. Here, that is accomplished by multiplying each number by 100. This makes the problem ...

  1.82/140.14 = 182/14014

Now, division proceeds in the usual way. The first non-zero quotient digit will appear in the hundredths place. The quotient is a repeating decimal with a 6-digit repeat. You recognize the repeat as soon as you see 182 as a remainder.

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Additional comment

The ratio reduces to ...

  $\dfrac{1.82}{140.14}=\dfrac{182}{14014}=\dfrac{1}{77}=0.\overline{012987}$