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Rational numbers and whole numbers are two different categories of numbers with a specific relationship between them.
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Definition of Whole Numbers: Whole numbers are the set of numbers that include zero and all positive integers. Examples of whole numbers are zero, one, two, three, and so on.
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Definition of Rational Numbers: Rational numbers are numbers that can be expressed as the ratio of two integers, where the denominator is not zero. This includes whole numbers, fractions, and negative numbers. Examples of rational numbers are one-half, negative three, and four (which can be expressed as four over one).
Relationship Between Rational Numbers and Whole Numbers:
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Are all rational numbers also whole numbers?: No, not all rational numbers are whole numbers. While whole numbers can be expressed as rational numbers (for instance, the whole number three can be represented as three over one), not all rational numbers are whole numbers. For example, the fraction one-half is a rational number but not a whole number.
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Are all whole numbers also rational numbers?: Yes, all whole numbers are rational numbers. Since every whole number can be expressed as the ratio of itself to one (like three can be expressed as three over one), they fit within the definition of rational numbers.
Examples:
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Example of a rational number that is not a whole number: One-half is a rational number because it can be written as the ratio of one and two. However, it is not a whole number.
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Example of a whole number that is also a rational number: The number four is a whole number and can also be written as four over one, making it a rational number as well.
In summary, while all whole numbers are rational numbers, not all rational numbers are whole numbers.
Write 6,739 in expanded form.
To express the number 6,739 in expanded form, we'll break it down by place value. Each digit in the number has a specific value depending on its position:
- The digit 6 is in the thousands place, so it represents 6,000.
- The digit 7 is in the hundreds place, so it represents 700.
- The digit 3 is in the tens place, so it represents 30.
- The digit 9 is in the ones place, so it represents 9.
Now, we combine these values to write 6,739 in expanded form:
6,739 = 6,000 + 700 + 30 + 9
This shows the value of each digit according to its place in the number.