16. Identify whether the given number is rational or irrational, if yes then give its p/q
form.
Rational, 3
Answers
Step-by-step explanation:
Rational Numbers
What type of numbers would you get if you started with all the integers and then included all the fractions? The numbers you would have form the set of rational numbers. A rational number is a number that can be written as a ratio of two integers.
RATIONAL NUMBERS
A rational number is a number that can be written in the form pqpq, where pp and qq are integers and q≠oq≠o.
All fractions, both positive and negative, are rational numbers. A few examples are
45,−78,134,and−20345,−78,134,and−203
Each numerator and each denominator is an integer.
We need to look at all the numbers we have used so far and verify that they are rational. The definition of rational numbers tells us that all fractions are rational. We will now look at the counting numbers, whole numbers, integers, and decimals to make sure they are rational.
Are integers rational numbers? To decide if an integer is a rational number, we try to write it as a ratio of two integers. An easy way to do this is to write it as a fraction with denominator one.
3=31−8=−810=013=31−8=−810=01
Since any integer can be written as the ratio of two integers, all integers are rational numbers. Remember that all the counting numbers and all the whole numbers are also integers, and so they, too, are rational.
What about decimals? Are they rational? Let’s look at a few to see if we can write each of them as the ratio of two integers. We’ve already seen that integers are rational numbers. The integer −8−8 could be written as the decimal −8.0−8.0. So, clearly, some decimals are rational.
Think about the decimal 7.37.3. Can we write it as a ratio of two integers? Because 7.37.3 means 73107310, we can write it as an improper fraction, 73107310. So 7.37.3 is the ratio of the integers 7373 and 1010. It is a rational number.
In general, any decimal that ends after a number of digits such as 7.37.3 or −1.2684−1.2684 is a rational number. We can use the place value of the last digit as the denominator when writing the decimal as a fraction.
EXAMPLE
Write each as the ratio of two integers:
1. −15−15
2. 6.816.81
3. −367−367
Solution:
1.
Answer: