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Math 7th unit 2
| Question | Answer |
|---|---|
| What will converting a fraction to decimal help us determine | It will help us determine if a real number is rational or irrational |
| Rational numbers have decimal expansions that eventually do what | That eventually terminate in zeros or repeat and irrational numbers do not |
| Rational= | Decimal terminate or repeats |
| Irrational = | Decimals do not terminate and do not repeat |
| 12÷99 = 0.121212… | The decimal is repeating, even though it’s too repeating at a time therefore, this is a irrational number |
| Example of 78÷90 = 0.8666… | The sixth after eight repeats, therefore this is a irrational number |
| Example 18÷16 | The answer is 1.125 it stops it doesn’t repeat, but it’s still a irrational number |
| When finding decimals and converting them to fraction, especially if they’re repeating if it’s one digit repeating, then you do 10 minus one to get nine as a denominator | If it’s two digits repeating you do 100-1 and if it’s three digits, repeating you do 1000 minus one and so forth |
| For example, 0.777. It’s one digits that keep repeating so you will do 10-1 and the answer | The answer would be the fraction 7/9 that seven because seven is the one digit that kept repeating and then the nine denominator is 10-1 for one repeating digit and it gives you nine |
| Example 0.4545… | Answer would be 45/99 and in simplest form it would be 5/11 |
| Real numbers or numbers that can be found on the number line | Real numbers can either be rational with decimals that terminate or repeats or irrational |
| Irrational number is the number with a decimal expansion that does not repeat or terminate | Example 8.12345687231 |
| The square root of a perfect square is a rational number for example | Square root of 36, which is 6×6 that’s a irrational number the square root of 25 which is 5×5 that’s a irrational number |
| When a number is not the square root of a rational number | |
| When a number is not the square root of a rational number then | It is a an irrational number, for example the square root of 27 |
| True or false, we can classify all real numbers as rational or rational | True |
| If a number is rational, then we can do the following | We can classify it as a natural number we can classify it as a whole number. It also is an integer or a rational number only. |
| What are natural numbers? | They are counting numbers 1, 2, 3… |
| What are whole numbers? | They are all natural numbersplus zero….0, 1, 2, 3… |
| What are integers they’re all natural numbers, their opposites and zero | For example. -3, -2, -1, 0, 1, 2, 3 |
| What are rational numbers? | They are all integers plus fractions and decimals that terminate or repeat |
| True or false a whole number is always irrational number | True, what’s the definition of a whole number? It is all natural numbers +0 so that includes, 0, 1, 2… |
| -3/4 is an example of an integer | False that’s because the definition of integer is all natural numbers, your opposites, and zero no fractions or decimals |
Created by:
Vlucas1108