Drag the numbers to the boxes labeled irrational numbers, Rational numbers, integers, Whole numbers, and natural numbers.
Check mark 8
Check mark with a line over 49
pi
1.333333333
7/8
-4 3/5
0
-5
Irrational Numbers:
π (pi)
Rational Numbers:
8
7/8
1.333333333 (this is the decimal representation of 4/3)
Integers:
8
49 (although it is rational, it is an integer as well)
-4 3/5
0
-5
Whole Numbers:
8
49 (although it is rational, it is a whole number as well)
0
-5
Natural Numbers:
8
49 (although it is rational, it is a natural number as well)
Irrational numbers: pi,
Rational numbers: 1.333333333, 7/8, -4 3/5, 0,
Integers: -4 3/5, 0, -5,
Whole numbers: 0, -5,
Natural numbers: None of the given numbers are natural numbers.
Sure! Let's categorize the given numbers into different types:
1. Irrational numbers: A number that cannot be expressed as a fraction or a decimal that terminates or repeats. In this case, π (pi) is an irrational number.
2. Rational numbers: A number that can be expressed as a fraction. Rational numbers can either be integers, whole numbers, or natural numbers. Examples of rational numbers include fractions, terminating decimals, and repeating decimals.
- To determine whether a number is rational, check if you can express it as a fraction. Let's go through each number:
- 8: This can be expressed as a fraction by putting it over 1 (8/1). Therefore, it is rational.
- 49 with a line over it: This is the square root of 49, which is 7. It can be expressed as a fraction (7/1), thus it is rational.
- 1.333333333: This is a repeating decimal. To convert it into a fraction, count the number of repeating digits, which in this case is one digit (3). Write the digit as the numerator and put the same number of 9's as the denominator (3/9). Simplify the fraction (divide both numerator and denominator by 3) to get 1/3. Therefore, it is rational.
- 7/8: This is a fraction. It is already in the form of a fraction, so it is rational.
- -4 3/5: This is a mixed number, which is a combination of a whole number and a fraction. To convert it into a fraction, multiply the whole number by the denominator and add the numerator. In this case, -4 times 5 is -20, and adding 3 gives -17. So, it can be written as -17/5, making it a rational number.
- 0: As a fraction, 0 can be expressed as 0/1. It is rational.
3. Integers: Integers are numbers that include all positive and negative whole numbers, including zero. Essentially, integers are rational numbers without any fractions or decimals. Let's identify the integers among the given numbers:
- 8: This is an integer.
- 49 with a line over it (7): This is an integer.
- 1.333333333 (1/3): This is not an integer as it is a fraction.
- 7/8: This is not an integer as it is a fraction.
- -4 3/5 (-17/5): This is an integer.
- 0: This is an integer.
4. Whole numbers: Whole numbers include all positive numbers without fractions or decimals, including zero. Let's identify the whole numbers:
- 8: This is a whole number.
- 49 with a line over it (7): This is a whole number.
- 1.333333333 (1/3): This is not a whole number as it is a fraction.
- 7/8: This is not a whole number as it is a fraction.
- -4 3/5 (-17/5): This is not a whole number as it includes a fraction.
- 0: This is a whole number.
5. Natural numbers: Natural numbers refer to positive whole numbers excluding zero. Let's identify the natural numbers:
- 8: This is a natural number.
- 49 with a line over it (7): This is a natural number.
- 1.333333333 (1/3): This is not a natural number as it is a fraction and not a whole number.
- 7/8: This is not a natural number as it is a fraction and not a whole number.
- -4 3/5 (-17/5): This is not a natural number as it is a negative number.
- 0: This is not a natural number as it is zero.
By categorizing the given numbers, we have:
Irrational numbers: π (pi)
Rational numbers: 8, 49 with a line over it (7), 1.333333333 (1/3), 7/8, -4 3/5 (-17/5), 0
Integers: 8, 49 with a line over it (7), -4 3/5 (-17/5), 0
Whole numbers: 8, 49 with a line over it (7), 0
Natural numbers: 8, 49 with a line over it (7)