Convert 0.72 to a rational number in simplest form.
To convert 0.72 to a rational number in simplest form, we can rewrite it as a fraction by placing the decimal part over 100:
0.72 = 72/100
Both 72 and 100 can be divided by 8:
72 ÷ 8 = 9
100 ÷ 8 = 25
Therefore, dividing both the numerator and the denominator of the fraction by 8 gives us:
72/100 = 9/25
So, 0.72 can be expressed as 9/25 in simplest form.
Which of the following is a rational number between 5 and 5½?
To find a rational number between 5 and 5½, we can convert 5 and 5½ to fractions.
The fraction equivalent of 5 is 5/1, and the fraction equivalent of 5½ is 11/2.
To find a rational number between these two fractions, we can find a fraction with a denominator that is between 1 and 2.
The fraction with a denominator of 2 and a numerator greater than 5, but less than 11, will give us a rational number between 5 and 5½.
One such fraction is 6/2, or simply 3.
Therefore, the rational number between 5 and 5½ is 3.
5 and 1/3
Apologies for the mistake.
To find a rational number between 5 and 5½, we can convert them to fractions:
5 = 5/1
5½ = 11/2
To find a fraction between 5/1 and 11/2, we can take their average:
(5/1 + 11/2) / 2 = (10/2 + 11/2) / 2
= 21/4
So, the rational number between 5 and 5½ is 21/4 or 5 and 1/4.
Describe the relationship between rational numbers and whole numbers. Are all rational numbers also whole numbers?
Are all whole numbers also rational numbers? Give examples to support your answer.
Rational numbers and whole numbers are related but not identical.
All whole numbers are rational numbers, but not all rational numbers are whole numbers.
A rational number is any number that can be expressed as a fraction or the ratio of two integers. This includes integers, fractions, terminating decimals, and repeating decimals.
On the other hand, whole numbers are a subset of rational numbers. Whole numbers are non-negative integers (including zero), such as 0, 1, 2, 3, etc.
Examples to support this relationship:
- The number 3 is a whole number and also a rational number because it can be expressed as the fraction 3/1.
- The number 2/5 is a rational number, but not a whole number, as it is a fraction that is not an integer.
- The number 0 is a whole number and also a rational number because it can be expressed as the fraction 0/1.
- The number 1.75 is a rational number because it can be expressed as the fraction 7/4, but it is not a whole number as it is not an integer.