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Hello Natasha

This is Mrs. Bisanz , I am your teacher today

Our Lesson : Review of Decimals

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Warm Up

Represent these in standard form

5.342 x 10 -4 = 0.0005342

2.812 x 106 = 2,812,000

Solve the following

3.61 ÷ 0.03 = 120.3334

15.012 ÷ 2.33 = 6.4429

Solve the following

5.81 + 6.32 = 12.13

3.91 + 0.1 = 4.01

Solve the following

9.11 – 3.9 = 5.21

921.8 – 865.329 = 56.471

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Decimals are numbers, with a decimal point in it, like these:

1.5, 0.6, 3.14 their opposites, and zero

Comparing and ordering Decimals

Lets take an example

673,67.3, 6.73, 0.673

These three numbers above have the same three digits, in the same order, yet they are all different

Let us review what we have learnt in the last chapter

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673,67.3, 6.73, 0.673

673 is a whole number, and would be read as Six hundred and seventy three

The second number 67.3 contains a decimal point, marking the end of the whole number, and would be read as sixty seven point three.

The third also contains a decimal point, and would be read as Six point seven three

The last decimal 0.673 contains no whole number, and it begins with a zero before the decimal point. It would be read as zero point six seven three.

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DECIMALS can be shown as points on a number line

Zero is the Origin.

decimal on the right of zero are

POSITIVE.

decimal on the left of zero are NEGATIVE.

It is neither positive nor negative!

-1.0 0-3.0-4.0-5.0 1.0 2.0 3.0 4.0 5.0-2.0

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When we say words like more, less or equal to

we compare the two numbers

We can compare and order DECIMALS using the number line.

-3.2 < 1.1

bigger num

bers

Therefore...

-1.0 0-3.0-4.0-5.0 1.0 2.0 3.0 4.0 5.0-2.0

smal

ler

num

ber

s

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We can also compare two Decimals by comparingthe digits in each place value position

T O . T H Th 6 . 4 7 8

6 . 8 2Start at the left and compare the digits in each place- value position . In the ones place , the digits are the same . In the tenths place , 4 < 8 ,

So, 6.478 < 6.82

Lets take an example : Compare 3.47 and 3.82

Align the numbers by their decimal points

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Rounding of Decimal numbers is done to get to the nearest

approximate whole number. It is a kind of Estimation

that we make. We use Rounding to estimate time, money,

distances etc.

Rounding and Estimation

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Find the place value you want (the "rounding digit") and look at the digit just to the right of it.

If that digit is less than 5, do not change the rounding digit but drop all digits to the right of it.

If that digit is greater than or equal to five, add one to the rounding digit and drop all digits to the right of it.

We can round decimals to any place value.

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Let's take an example and understand

Find the place value you want and look at the digit just

to the right of it. Round 5,834 to the nearest thousandth

5,834

If that digit is less than 5, do not change the rounding digit but drop all digits to the right of it.

8 is greater than 5

If that digit is greater than or equal to five, add one to the rounding digit and drop all digits to the right of it

so we round this number as 6000

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We can round the decimals to their nearest Fractions

Lets round 83. 461 to the nearest tenth place

83.4 6 1

The place value number is 4 and number to its right is 6.

6 is greater than 5 so

We round the number to 83.5

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1.) 325.34 To the nearest Hundred 300

2.) 48,722 To the nearest Ten thousand 50,000

3.) 43.386 To the nearest Hundredth 43.39

4.) 60.584 To the nearest Tenth 60.6

Now you try some questions

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To add Decimals all we need to do is to align all decimal points in one line

We start from the right end and the carry goes across the decimal point

62 . 72

+1 8 . 51

8 1 . 23

Adding and Subtracting Decimals

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To subtract Decimals align all decimals so that the decimal points are in a vertical line.

Add zeros to the right side of the decimal with fewer decimal places so that each decimal has the same number of decimal places.

89 . 30

- 45 . 11

44 . 19

We need to add one zero here to the right of decimal to make the decimal places equal

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1.) 438 + 13.16 = 451.16

2.) 621.581 + 4.212 = 625.793

3.) 179.8 - 120.852 = 300.652

4.) 5.8 - 5.5 = 0.3

Now you try some questions

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Game Time

Click here to play a game

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To multiply decimal numbers we first ignore the decimals and multiply as we multiply whole numbers

Multiplying Decimals

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Multiplying Decimals

Starting on the right, multiply each digit in the top number by each digit in the bottom number just as you do with whole numbers

Now add the products.

Now place the decimal point in the answer by starting at the right and moving the number of places equal to the sum of the decimal places in both numbers multiplied.

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Solving the same example

1.5 1 x 6.2___________ 3 0 2 9 0 6 x__________ 9 3 6 2

Just count the numbers / places from right to left in both the numbers

to be multiplied ,and then add them and Insert the decimal after those

many places.

Multiplying Decimals

1 2

3

.

\ \\

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When we multiply two numbers withSame sign we get +

And with Different sign we get -

Remember

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Lets take another example

Multiply 3.77 x (- 2.8)

3 .7 7 x 2.8 __________ 3 0 1 6 7 5 4 _________ -10 .5 5 6 ____________

Note the negative sign.

RememberAlways count from right side

to put the decimal

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Division with Decimals

Steps for dividing by whole numbers 1) If the division problem is written across, copy the

problem so that the first number is inside the division sign. If the problem is 35.2 ÷ 5 then write it as

5) 35.2

2) Place decimal point in the quotient directly above the decimal point in the dividend.

3) Now use the long division method as if there were

no decimal points involved.

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Steps for dividing by decimal numbers

Write the first number inside the division sign

Change the divisor to a whole number by moving the

decimal point to the right Move the decimal point of the inside number

( dividend) the same number of places to the right as you did

of the divisor.

Put the decimal point for your answer directly above the one in your inside number.

Divide the same way as you do with whole numbers

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3.33 ) 2 2.1 7 7 8

Lets take an Example

Move the decimal point of the inside number (dividend) the same number of places to the right as you did of the divisor. So we get…

Change the divisor to a whole number by moving the decimal point to the right

333 ) 2 2 1 7. 7 8

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333 ) 2 2 1 7. 7 8

Place a decimal point on top of the decimal point of the inside number and divide normally

.6

1 9 9 8

2 1 9 7

6 6

1 9 9 8

1 9 9 81 9 9 8

0

= Answer

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You can also check your answer by multiplying the quotient with the divisor . If it is same as the dividend then your answer is correct

0.5 x 0.904 = 0.452

.

0.452 ÷ 0.5 = 0.904 and

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Lets try another Example with negative numbers

-31.48 ÷ -4

-4 ) -3 1 .48 - 28 3 4 3 2 2 8 2 8 0

7 . 87

When we divide two numbers

With the same sign we get + and with different signs

we get –

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1) 8.41 ÷ 0.20 = 42.05

2) 0.56 ÷ 0.12 = 4.6667

3) 0.28 x 0.004 = 0.00112

4)34.01 x 1.01 = 34.3501

Now you try some questions

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Scientific Notation

Scientific Notation is a way to express very large or very small numbers.

It is most often used in “scientific” calculations where the analysis must be very precise

Scientific notation has two parts

• A non zero number between 1 and 10

• A power of 10

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A number in scientific notation is written as the product of a number between 1 and 10 (integer or decimal ) and an integer power of 10

A number written in scientific notation has the form

N X 10r

where, N is between 1 and 10 r is an integer

Scientific notation

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To Change from Standard form to Scientific notation

Place the decimal point so that there is one non zero digit to the left of the decimal point

Count the number of decimal places the decimal point has “ moved ” from the original number. This will be the exponent (power) of 10

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Lets take some Examples

10,000 = 1 x 104

65,000,000 = 6.5 x 107

The power of ten indicates how many places the decimal point has moved from the original number

Standard form to Scientific notation

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If the original number is less than 1, then the exponent is negative .

If the original number is greater than 1, then the exponent is positive

579,300,000 = 5.793 x 108 (Positive exponent)

0.000246 = 2.46 x 10-4 (Negative exponent)

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Now you try some

Write these in standard form or the scientific notation as required

• 72,500 = 7.2x104

• 27,100,000 = 2.7x 107

• 5.56 x 109 = 5,560,000,000

• 1.976 x 10-4 = 0.0001976

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1)Ben borrowed money from his three friends to buy a camera. He promised to return the money every week.If Ben paid $32.50 to each of his friends for five weeks

and still had $12.50 left. Find out how much money he borrowed initially and how much money is left to be returned to each.

Total money borrowed $500He has still to pay $4.1667 to each

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2.) Cooper family went for their weekly shopping at the super market. They bought five coke cans for $1.30 each, two jars of peanut butter for $8.5 each and six packs of Buns for $2.80 each. What is the total bill rounded to the nearest dollar.

$40

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3) Joseph’s math paper is given below. You be the teacher and check his paper. Explain his mistakes to him.

a. 3.14 + 6.89 = 9.93b. 6.3 x 2.1 = 132.3c. 2,34,871 = 2.34x105 rounded to the nearest thousandd. 6.82 ÷ 0.02 = 300 rounded to the nearest hundred

a. Wrong 10.03 Carry not doneb. Wrong 13.23 Did not place the decimal correctlyc. Wrong 2.35x 105 when rounded it will become 2,35,000d. Correct

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You had a GREAT lesson today!

Be sure to practice what you learned!