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Ronch [10]
3 years ago
13

How do you multiply and divide decimals ?

Mathematics
1 answer:
valina [46]3 years ago
7 0
Multiplying Decimals

If you already know how to multiply, then multiplying decimals will be easy, there is just one extra step you need to take.
First, you multiply the numbers just like normal, as if the decimal point wasn't there.
Next, you need to add in the decimal point to the answer. This is the only tricky part. You add up the decimal places there are in the numbers you multiplied. Then you put that many decimal places in the answer.
Let's try some examples:

1) 4.22 x 3.1 = ?

If you first just multiply 422 x 31 you get

422
x 31
13082


Now, there are 2 decimal places in 4.22 and 1 decimal place in 3.1. This is a total of 3 decimal places. We then put three decimal places in 13082 and we finally get the answer:

13.082

1) 4.220 x 3.10 = ?

To show how the decimal part works, we'll solve the same problem again, but this time we will add a zero to the right of each number we multiply. This doesn't change the value of the numbers, so it shouldn't change the answer we get.

First we multiply without worrying about the decimals:

4220
x 310
1308200


Now, we count the total amount of decimals. There are 5 total decimals places this time. If we count over 5 decimal places from the end of 1308200 we get the same answer:

13.08200

Note: the extra zeros to the right of the decimal point do not change the value of the number.

Dividing Decimals

When you are dividing a number with a decimal point by a whole number, dividing decimals is pretty simple.
Divide the number as you normally would, using long division.
Bring the decimal point directly up from the dividend.
Example:

9.24 ÷ 7 = ?



If both divisor and dividend are decimals:

If the divisor is a decimal number rather than a whole number, then you need to take an extra step. In this step you convert the divisor from a decimal number to a whole number. You do this by moving the decimal point to the right in the divisor until there are no more numbers other than zero to the right of the decimal point. Then you move the decimal point to the right the same number of places in the dividend.

Example of moving the decimal point for division:

9.24 ÷ 7.008

You want the divisor 7.008 to be a whole number, so you need to move the decimal point 3 places to the right:

7008

Now you need to move the decimal point for the dividend 3 places to the right:

9240

In this case you have to add a zero to move it 3 places.

Now you divide 9240 by 7008 to get the answer:

Example:

0.64 ÷ 3.2 = ?

First move the decimal points so the divisor is a whole number:

6.4 ÷ 32 = ?



Important things to remember:
Move the decimal point directly up in your long division.
Always move the decimal points on BOTH to divisor and the dividend to where the divisor is a whole number.

hope this helps!! tell me if you need more assistance!!
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Answer:

Part 1) m∠1 =(1/2)[arc SP+arc QR]

Part 2) PR^{2} =PS*PT

Part 3) PQ=PR

Part 4) m∠QPT=(1/2)[arc QT-arc QS]

Step-by-step explanation:

Part 1)

we know that

The measure of the inner angle is the semi-sum of the arcs comprising it and its opposite.

we have

m∠1 -----> is the inner angle

The arcs that comprise it and its opposite are arc SP and arc QR

so

m∠1 =(1/2)[arc SP+arc QR]

Part 2)

we know that

The <u>Intersecting Secant-Tangent Theorem,</u> states that the square of the measure of the tangent segment is equal to the product of the measures of the secant segment and its external secant segment.

so

In this problem we have that

PR^{2} =PS*PT

Part 3)

we know that

The <u>Tangent-Tangent Theorem</u>  states that if from one external point, two tangents are drawn to a circle then they have equal tangent segments

so

In this problem

PQ=PR

Part 4)

we know that

The measurement of the outer angle is the semi-difference of the arcs it encompasses.

In this problem

m∠QPT -----> is the outer angle

The arcs that it encompasses are arc QT and arc QS

therefore

m∠QPT=(1/2)[arc QT-arc QS]

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