Jeremy is playing a game called “Rational Round Up” where he has to collect all the numbers in a maze that are rational and then get to the end of the maze. When he collects a number he must prove it is rational by writing it as a quotient of two integers. Help him determine how to prove that each of the following numbers is rational.
1. 2.4
1/1
2/2
4/2 or 4/1
in fact since every integer is divisible by one every integer is a rational number. You have to get far out to get irrational, like sqrt( 2 ) or pi or e
Remember that fractions are generally ratios of whole numbers so rational
like 3/273 is rational
What about 74 how would I change that?
74 is an integer 74/1
Now if you had said 7.4
I would have said
74/10
so still rational
17.3333333?
Identify all sets to which the number 3 Belongs
87.125
To prove that a number is rational, we need to demonstrate that it can be written as a fraction or a quotient of two integers.
Let's take the number 2.4 as an example.
Step 1: Write the number as a fraction with the decimal part as the numerator and a denominator that is a power of 10.
In this case, the decimal part of 2.4 is 4, so we write it as 4/10.
Step 2: Simplify the fraction if possible.
Both the numerator and the denominator in this fraction can be divided by 2. Therefore, we can simplify the fraction to 2/5.
Step 3: Check if the fraction is in its simplest form.
In this case, the fraction 2/5 is already in its simplest form because there are no common factors that can be canceled out.
Step 4: Confirm that the fraction represents the original decimal number.
To confirm that 2/5 indeed represents 2.4, let's convert the fraction back to a decimal.
Divide 2 by 5: 2 ÷ 5 = 0.4
The decimal equivalent of 2/5 is indeed 0.4, which matches the original number we started with.
Therefore, by following these steps, we can prove that the number 2.4 is rational and can be written as the fraction 2/5.