Amy has a master's degree in secondary education and has taught math at a public charter high school.
Your friend just offered to trade you negative one million dollars if you give him one dollar. It sounds like a pretty good deal. One million is a really big number. But you feel a little unsure about that word, 'negative.' If only you knew the magnitude of negative one million compared to one.
In math, magnitude is the size of one number compared to another. For instance, is negative one million bigger than one?
Let's take a closer look.
Positive numbers are the numbers you count with, like 1, 2, 3, and so on. You can visualize positive numbers using objects in the real world, such as this image of two fries.
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Now, say you are comparing the numbers 2 and 5.
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Looking at your fries, you can easily see that 5 is larger than 2. In math notation, you can use the greater than symbol to show this: 5 > 2. Notice that the greater than symbol looks like a mouth opening towards the larger number. You can also use the less than symbol to show that 2 is smaller than 5: 2 < 5.
If your two numbers are equal to each other, then you use the equal sign. For example, say you are comparing the numbers 2 and 2.000.
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When you visualize it, you can clearly see that they are the same amount. In math notation, you would write it with an equal sign like this: 2 = 2.000.
When it comes to comparing positive numbers, things make sense because you can visualize them. But, when you being comparing negative numbers, things get a little confusing. Don't simply trust what looks right.
To help you compare the magnitude of your negative numbers, keep a mental image of the negative side of the number line.
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Notice that negative numbers begin towards the left of the 0 on the number line. On the number line, as you go towards the left, numbers get smaller. When you go towards the right, numbers get larger. That means the higher the negative number, the smaller its relative magnitude.
Just remember, when it comes to negative numbers, larger numbers means smaller magnitude. So, -10 is actually smaller than -5 even though -10 is a bigger number than -5. As you can see on the number line, the -10 is to the left of the -5. You can use the greater than or less than symbols to compare negative numbers, too, such as -10 < -5 or -5 > -10.
By now, you're probably thinking that you shouldn't trade your one dollar for your friends negative one million dollars. That's right. Your dollar has a much higher relative magnitude than his negative one million.
It can be a little tricky to compare magnitude in decimals. For example, 3.4 > 3.391 even though 3.391 has more digits than 3.4. The number line is a big help here. Number 3.4 is almost halfway between 3 and 4. But 3.391 is between 3.3 and 3.4. Number 3.391 actually ends up slightly to the left of 3.4. So, it's smaller than 3.4.
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Now that you understand relative magnitude, you can put numbers in order.
For example, say you are working at a library and you are asked to put some books back in order from smallest to largest. Each book has a number on it: 3, 21, and 7. You know the 3 is smaller than both 21 and 7, so the 3 comes first. Twenty-one is larger than 3 and 7, so 21 should come last, giving you 3, 7, 21.
To order negative numbers, use the same magnitude analysis. So, if you are asked to order the numbers -10, -5, and -7, you compare the magnitude of these numbers with each other. You see that the smallest number is -10, since it is furthest to the left on a number line. Then comes -7 and, finally, -5. So, from smallest to greatest, the order is -10, -7, -5.
The same applies for ordering decimals. When you order 1.3, 1.259, and 1.4 from largest to smallest, you first find the largest numbers in the bunch and work your way down from there. Your order from largest to smallest then is 1.4, 1.3, 1.259.
Sometimes, you may have to arrange a combination of positive and negative numbers and decimals, like 1, 1.1, -2, and -3. To do this, remember the number line. You then write them from left to right, from smallest to largest. Your order from smallest to largest is -3, -2, 1, 1.1.
In math, magnitude is defined as the relative size of a number. In math notation, you use the greater than symbol, >, to show when the first number is larger than the second number. You use the less than symbol, <, when the first number is smaller than the second number. You can use visualization and the number line to determine the relative magnitude of multiple numbers.
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PECT PAPA: Practice & Study Guide27 chapters | 213 lessons | 12 flashcard sets
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