Lesson ane: Introduction to Decimals
What are decimals?
A decimal is another fashion to write a fraction. Y'all tin think of a decimal every bit a function of a whole number. It is less than i whole thing, but more than 0 .
You may not realize it, simply you see decimals a lot in existent life. Ane of the most common examples is money.
Do you recognize these coins? We have a quarter, a dime, and two pennies. Yous could write each of these as a decimal. That'south because each coin is worth less than a whole dollar.
Click through the slideshow to learn how decimals work.
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This is a dollar. A dollar represents a whole number. It is equal to 1.
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We could besides write that as i.00. In other words, 1 = 1.00.
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one.00 is a decimal. Here, information technology means nosotros have 1 dollar and 0 cents.
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As you may already know, there are 100 pennies in a dollar. This ways 100 pennies equals 1.00.
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One penny is part of a dollar. More than specifically, information technology's i cent. Nosotros could as well write that as a decimal: 0.01.
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Permit's look at a few more decimals. ix cents is 0.09 of a dollar.
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A quarter, or 25 cents, is 0.25 of a dollar. Any time y'all have part of a whole, you tin write it as a decimal.
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Let's await at some other example. This pitcher holds 1 liter of water. Right now it'due south full.
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Nosotros could write this as a decimal: 1.00 liters.
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The pitcher is split into 10 parts. This means each part is equal to 0.ten liters.
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Equally the day goes on, the bullpen gets emptier. At present it has 0.lxx liters. That's because nosotros used up 0.xxx liters.
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Now it has 0.fifty liters, or half a liter.
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Now it has 0.xx liters. Even though we have less than one liter, nosotros have more zero liters, so we can write information technology equally a decimal.
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Reading decimals
As you saw on the last page, decimals look a lot similar a regular numbers, with a few important differences. First, all decimals have a decimal point ( . ). The decimal bespeak looks like a period. Any number to the left of the decimal point is a whole number. The numbers to the right are like a fraction—they're less than 1 whole merely more than 0.
For instance, let'southward take a await at this decimal.
9.6
ix is on the left of the decimal point, so we have 9 whole things. 6 is on the correct, so we likewise take 6 parts of a whole.
Nosotros encounter written decimals all the time in real life. For example, you lot might know that the average body temperature is 98.6 degrees. Or you might tune in to a radio station like 97.5. Merely do yous know how to read these decimals out loud?
Click through the slideshow to learn how to read decimals.
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Let'southward try reading this decimal: 9.6.
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Kickoff, we'll read the number to the left of the decimal point. That's nine.
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Next, we'll read the decimal point. Usually, you'll just say "point ".
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Finally, we'll read any number to the right of the decimal point. That's six.
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So, we'd read 9.half dozen like this: nine bespeak half-dozen.
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But you lot could also read it like this: nine and half-dozen-tenths.
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When you read decimal numbers, each identify to the right of the decimal point has a special proper name.
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The place immediately to the correct of the decimal bespeak is the tenths identify.
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Here, the decimal means we accept .half-dozen, or half-dozen-tenths, of a whole.
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You might think from Introduction to Fractions that vi-tenths is just another manner of proverb 6/10.
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So ix.six means we have 9 whole things and 6/10, or six-tenths, of another matter.
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Since we have nine and six-tenths, the give-and-take "and" replaces the decimal point.
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Let'south try some other instance. How would you read this decimal? 0.25.
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We can read 0.25 as nothing point two v...
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We tin can read 0.25 as zippo betoken 2 five...or leave out the zero and just say point two v.
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But we could also read it like this: twenty 5-hundredths.
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Let's look at our decimal places again. 2 is in the tenths identify, so we take two-tenths.
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Adjacent is the hundredths place. In this case, 5 is in the hundredths place, so we have five-hundredths.
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When we read this number aloud, we'll say the 2 and five together as "twenty-v ".
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We'll also say the decimal place that is farthest to the right. In our example, that's the hundredths place.
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And then nosotros'll read 0.25 as twenty v-hundredths.
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This is just another way of writing 25/100.
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To figure out how many hundredths we had total, we could have added these numbers: two-tenths and five-hundredths.
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ii tenths is the aforementioned as 0.twenty , or xx-hundredths.
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0.twenty plus 0.05 equals 0.25, or twenty 5-hundredths.
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Endeavor This!
Effort reading the decimals below aloud.
Decimals and money
What if you had to read this decimal out loud?
Fifty-fifty though nosotros use decimals when we use coin, nosotros read them slightly differently. Instead of three point two three, or three and twenty iii-hundredths, we'll say three dollars and twenty-iii cents.
You could likewise read information technology similar this: "3 twenty three ". To save time, virtually people get out out the decimal bespeak when talking about money. How about $v.99? That would be five dollars and ninety-9 cents, or five 90-ix.
Remember, these rules only piece of work with money. They can't be used to read other decimals.
Endeavour This!
Try reading these dollar amounts.
Comparing decimals
Permit's imagine you're shopping for a new water pitcher. You find two y'all like—one holds 0.7 gallons, while the other holds 0.v gallons. Exercise y'all know which pitcher is larger? Click the arrows to observe out.
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To find out which bullpen holds more, you could simply compare the decimals to run across which is larger.
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7 is larger than 5, and then 0.7 is larger than 0.5. The larger the number to the right of the decimal betoken, the larger the decimal.
How about these two decimals:
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Over again, yous'll only compare the numbers to the right of the decimal point.
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74 is larger than 72, then 0.74 is larger than 0.72.
Now permit'due south compare these decimals:
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Since the whole number, 1, is the same for both decimals, we'll compare the numbers to the right of the decimal point.
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If you idea .two was larger than than .xix, yous were right!
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Remember, one.2 could likewise be written as 1.20.
twenty is larger than 19, so one.20 is larger than 1.19.
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