Rational NumbersCircle the rational numbers and cross the ones which are not rational number. give reasons also.1. 8/19.2. 0/7.3. 7/9.4. 16/0.5. 6/12.6. 8/17.
Answers
Answer:
All fractions, both positive and negative, are rational numbers. A few examples are
4
5
,
−
7
8
,
13
4
,
and
−
20
3
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
=
3
1
−
8
=
−
8
1
0
=
0
1
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
could be written as the decimal
−
8.0
. So, clearly, some decimals are rational.
Think about the decimal
7.3
. Can we write it as a ratio of two integers? Because
7.3
means
7
3
10
, we can write it as an improper fraction,
73
10
. So
7.3
is the ratio of the integers
73
and
10
. It is a rational number.