Adding Subtracting And Multiplying Decimals
How to add, subtract, multiply, and split decimal numbers
Arithmetic with decimals
Nosotros can add, decrease, multiply, and divide decimal numbers.
Improver and subtraction of decimal numbers works the aforementioned style every bit whole number addition and subtraction; we but need to make sure that we line up the decimal points.
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Finding the sum and difference of decimals
Example
Detect the sum and difference.
???13.16+viii.74???
???thirteen.xvi-8.74???
To find the sum, we'll line up the decimal points, making sure that they're stacked directly on tiptop of each other.
Then we'll bring the decimal bespeak direct down and add the numbers every bit usual, starting with the digits in the ones place, carrying anything extra to the tens identify, calculation the digits in the tens identify (including annihilation extra from the addition of the digits in the ones identify), carrying anything extra to the hundreds place, etc.
We tin can say that the sum is ???thirteen.16+8.74=21.90???.
To find the difference, we'll line up the decimal points, making sure that they're stacked straight on top of each other.
So nosotros'll bring the decimal point straight downwards and decrease the numbers as usual, starting with the digits in the hundredths place, borrowing from the tenths place if necessary, subtracting the digits in the tenths place (excluding anything we borrowed for the subtraction in the hundredths place), borrowing from the ones place if necessary, etc.
Nosotros tin say that the difference is ???xiii.16-eight.74=4.42???.
Let's try an example with multiplication and sectionalization of decimal numbers.
To notice the difference, we'll line up the decimal points, making certain that they're stacked directly on top of each other.
Example
Detect the product and quotient.
???13.1\times8.74???
???thirteen.1\div8.74???
To notice the product, we'll right-align the decimal numbers.
We'll ignore the decimal points for now, and multiply the numbers as usual.
Now we'll count the number of digits to the right of the decimal point in each of the two decimal numbers, and then add. There's one digit (a ???1???), after the decimal betoken in ???13.1???. There are two digits (a ???7??? and a ???four???), afterward the decimal bespeak in ???eight.74???. That's a total of three digits later the decimal points.
To decide where to place the decimal point in our answer, we start by putting information technology on the far right of the result, and we go "???114494.???". Then, since nosotros had a total of 3 digits later on the decimal points, nosotros move the decimal point three places to the left to get our final answer. Therefore, ???13.one\times8.74=114.494???.
To discover the quotient, we'll do long division, simply not until after we decide where to place the decimal indicate in our answer.
To figure out where it should get, we need to change both numbers into whole numbers. In order to change ???viii.74??? to a whole number, nosotros need to move the decimal point two spots to the right. In order to modify ???thirteen.ane??? to a whole number, we need to move the decimal point one spot to the right. But we e'er have to move the decimal point the aforementioned number of places in both numbers.
Moving the decimal point one spot will alter ???xiii.1??? to a whole number, but will change ???viii.74??? into ???87.4???, which is still a decimal number. So we need to move the decimal signal ii spots in both numbers, calculation a ???0??? to the end of ???13.1???. So ???thirteen.1??? becomes ???1310??? and ???8.74??? becomes ???874???. Then we can do the long sectionalization every bit if nosotros were doing division with whole numbers, instead of decimal numbers.
As you tin run into, ???8.74??? doesn't divide evenly into ???xiii.ane???, and so we can finish later a few decimal places and but give the interpretation as ???xiii.1\div8.74\approx1.4988???.
If yous want to multiply a decimal number by ???ten???, you lot tin easily get the respond by just moving the decimal point i place to the right. If you desire to multiply a decimal number by ???100???, yous can just motility the decimal bespeak two places to the correct; and and then on.
Similarly, if you want to split up a decimal number by ???10???, you tin easily go the reply past moving the decimal indicate one place to the left. If you desire to divide a decimal number past ???100???, you tin can just move the decimal point two places to the left; and so on.
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Adding Subtracting And Multiplying Decimals,
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