Transcript Rational Numbers on the Number Line
Tim is feeling nervous. He is about to jump off the high dive at the local swimming pool. There he goes! How far above the water is he shortly after jumping?
Rational Numbers on the Number Line
To answer this question, we can look at the rational numbers on the number line. Let's see. The platform is 33 feet high. The tower is like a vertical number line. The surface of the water can be represented by 0, above we have positive numbers. Below the water we have the negative numbers.
Let's rotate the number line to a horizontal position to have a more precise look at how high Tim is above the water. As you can see at a first glance, Tim is somewhere between 20 and 30 feet above the water, or between 20 and 30 feet on the number line.
Fractions on the Number Line
To more accurately determine his location, we can zoom in to display a more detailed scale. Now you can see he is somewhere between 27 and 28 feet on the number line. Let's zoom in even more.
We can divide feet in to inches. As you know, there are 12 inches in 1 foot. So if you count from left to right on the number line, you land at 27 feet and 3 inches. This represents Tim's current location above the water.
In math, we often look at the number line without units. Instead of using inch notation, we can write our position on the number line as a fraction, with a value over twelve, because we divide one whole into 12 pieces. Here we are at 27 and 3 over twelve on the number line.
You can simplify this mixed number to 27 and 1 over 4, or 27 and one fourth. As you can see, our location on the number line between 27 and 28 remains the same. We have just changed the scale.
Decimals on the Number Line
We can represent 27 and one over four in yet another way, with a different scale: It can also be represented as a decimal: 27.25. If we display decimals on the number line, we divide our units into 10, 100 and so on. Here our number is exactly between 27.2 and 27.3. We can either zoom in more and divide tenths into hundreths, or we can assume the value is 27.25.
Negative Numbers on the Number Line
Let's get back to Tim. As he dives into the water, he is below 0 on the number line, where we have the negative numbers. We can use the negative numbers to represent how far Tim dived below the surface of the water. He dived somewhere between 0 and minus ten feet.
Let's take a closer look to figure out his exact depth. Now you can see, he dived somewhere between 6 and 7 feet below the surface, or between 6 and 7 feet on our number line. To be more accurate, let's zoom in even more.
We can divide feet into inches again. Now we count downwards, from 6 to 7. So Tim dived to 6 feet and 9 inches. Remember, you can also write this as a fraction: 6 and 9 over 12 feet, or simplified: 6 and 3 over 4. You can also write this mixed number as a decimal, which is: 6.75 feet.
Tim is happy that he overcame his fear. But wait, something is not right.

Variables

Simplifying Variable Expressions

Evaluating Expressions

Order of Operations

Distributive Property

Adding Integers

Subtracting Integers

Multiplying and Dividing Integers

Types of Numbers

Transforming Terminating Decimals to Fractions and Vice Versa

Transforming Simple Repeating Decimals to Fractions and Vice Versa

Rational Numbers on the Number Line