Show that 0.00320 (the "__" sign goes above the 20) is a rational number by writing it as a quotient of integers.

Answer 1

For this question, the easiest method to approach it is to look at the place value behind the decimal point. For example, we know that 0.1 is in the tenths place, so it can be the fraction 1/10. Similarly, 0.01 is in the hundredths place, so we know that it is equivalent to the fraction 1/100.

In this case, we have 0.00320 or, more simply, 0.0032.

We have a 0 in the tenths place and hundredths place, a 3 in the thousandths place, and a 2 in the ten-thousandths place. With this knowledge, we can say that we have 32 ten-thousandths. This gives us a fraction of 32 / 10000.

Let us put the fraction in its simplest form: (it is easiest to move by 2s)

32/10000

16/5000

8/2500

4/1250

2/625

Our simplest form of the fraction, or quotient of two integers, is 2/625.

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