Fractions, Decimals, Percents, & Scientific Notation

Converting, Comparing, & OrderingSOL 7.1

FractionsA fraction is a way of

representing division of a ‘whole’ into ‘parts’.

𝑁𝑢𝑚𝑒𝑟𝑎𝑡𝑜𝑟𝐷𝑒𝑛𝑜𝑚𝑖𝑛𝑎𝑡𝑜𝑟

Part

Whole

ExamplesA graphical example of fraction is shown by the marching men below. There are five marching men in the illustration. There are 2 men in orange uniform, thus .

Is there another fraction that can be made from the picture below?

Create a fraction for the pictures below.

35

34 𝑜𝑟

14

46=

23 𝑜𝑟

16

Ordering FractionsThere are three major ways to order

fractions:1.Drawing a picture2.Converting3.Thinking about it!!!

Vocabulary:

• Descending: Greatest to Least• Ascending: Least to Greatest• Numerator: the part, the top of the fraction• Denominator: the whole, the bottom of the fraction• Quotient: answer to a division problem

Before we start ordering we need to learn/review …

Ordering by Drawing a Picture

Suppose you have to place the following in ascending order…

Least to Greatest!

1. Draw a box.

2. Draw lines in your box to create rows. You need as many rows as you have fractions.

3. Now break each row up into the number of whole parts of each fraction…the denominator.

4. Now shade each part of the whole…the numerator.

5. The row with the least color is the smallest and so on.

2

13

You try it!

Place in descending order:

24 ,512 ,

38

Ordering by ConvertingFractions can be converted into fractions for easy

ordering.

To convert a fraction, like into a decimal you must…

5 2

Divide the numerator (2) by the denominator (5). The quotient is your decimal.

0

-02

.

0

4

0-200

Do this for each fraction you

have!

But first…

Common Fraction Conversions Chart

Copy these down and learn them…it’ll save

you some time!

Once you have your fractions converted… 2

5 ,19 ,110

0.4, 0.111, 0.1

1. Line the decimals up by their decimal points.

2. Look at the numbers in the first column, the smallest number corresponds to the smallest fraction.

3. If the numbers are the same, move on to the next column… then the next, and the next.

0

They were already in descending order!

0 .40 .1 1 10 .1

Try It!34 ,16 ,38

0 . 7 50 . 1 6 70 . 3 7 5

Place in order from least to greatest.

16 ,38 ,34

Ordering by Thinking!Fractions can arranged in 4 categories

when it comes to size….

Less than half!Half!

More than half!A Whole!

Placing your fractions in these categories can help you order them quickly!

How do you know if a Fraction is…Less Than Half?

Half?

More Than Half?

A Whole?

Try It!58 ,36 ,19

Place in ascending order!

5 is more than half of 8!

3 is half of 6!

1 is less than half of 9!

So… 19 ,36 ,58

Your Assignment…1. Order the following fractions from greatest to least by drawing a

picture!

2. Place the following fractions in ascending order by converting!

3. Order the following fractions from least to greatest by thinking about it!

𝑎 ¿12 ,46 ,38

b¿ 58 ,13 ,35

𝑎 ¿79 ,310 ,

14 b¿ 23 ,

44 ,15

𝑎 ¿29 ,17 ,68 b¿ 56 ,

14 ,25

Decimals A decimal is similar to a fraction in that it is not a whole number. It is a

part of a number.

13.032Whole

Number Decimal Point

Decimal

Place ValueIn our decimal number system, the value of a digit depends on its place, or position, in the number. Each place has a value of 10 times

the place to its right.Th

ousa

nds

Hun

dred

sTe

nsO

nes

Dec

imal

Poi

nt (.

)Te

nths

Hun

dred

ths

Thou

sand

ths

Ten

Thou

sand

ths Decimals can be

named and ordered by their

place value!

Always line decimals up to the chart and each other by their decimal

point.The decimal with biggest number that is farthest left is the

largest!

Let’s try it!

Ordering DecimalsRemember

Descending- Greatest to LeastAscending- Least to Greatest

Let’s place 0.45, 0.123, and 0.1045 in ascending order!

1. Line up your decimals by the decimal point.

0 . 4 50 . 1 2 30 . 1 0 4 5

You cannot tell which decimal is biggest by which

is longest!

2. Since the first digits are all zeros, we can look to the right of the decimal point

The largest decimal will have the largest number in the tenths place!

3. The same rule applies for the hundredths place and so on.

0.1045, 0.123, 0.45

Let’s Try Some…1) 0.42, 0.31, 0.402 Place in descending order.

2) 0.2, 0.11, 0.3 Place in ascending order.

3) 1.02, 0.57, 1.201 Order least to greatest.

4) -0.42, 0.01, -0.2 Place in descending order.

0.42, 0.402, 0.31

0.11, 0.2, 0.3

0.57, 1.02, 1.201

0.01, -0.2, -0.42

Percent A ratio that compares a number to

100.

15% = =Percent

Symbol

A ratio compares two numbers using division!

15100

320

Percents and FractionsPercents and fractions are directly connected…with one

you can change to the other.

Percent to Fraction:1.Drop the percent sign.2.Make the number that was before the

percent sign your numerator.3.Make 100 your denominator.4.Simplify! Your answer is INCORRECT if your fraction is not in

simplest form!

25% = =25100

14

How do you simplify?!

How to Find the Simplest Form of a Fraction

1. Find the greatest common factor of the numerator and the denominator.

2. Divide both the numerator and the denominator by that number.

1218 ÷

66

23=

The greatest common factor is the largest factor between two numbers.

A factor, in this case, is a number that divides evenly into another.

Let’s trying turning some percents to fractions!

45100

÷ 55

920

=45%

Remember:1. Drop the percent sign.2. Make the number that was in front of the percent

sign the numerator!3. Make 100 your denominator.4. Simplify.

To simplify or reduce:1. Find the Greatest Common Factor.2. Divide the numerator and denominator by that

GCF!

Let’s try a few more examples!

15100

÷ 55

320

=15%

75100

÷ 2525

34

=75%

12100

÷ 44

325

=12%

Percents and DecimalsPercents and decimals are directly connected…with one

you can change to the other.

Percent to Decimal:1.Drop the percent sign.2.Move the decimal to the left twice…this is the

same as dividing by 100!

What about percents with decimals in them, like 25.5%?

The percent sign supersedes the decimal!

Even though, 25.5 is indeed a decimal it is more importantly a percent. The same steps need to be

followed to make it a “real” decimal!

Let’s trying turning some percents to decimals!

45%

Remember:1. Drop the percent sign.2. Move the decimal to the left twice!

45. 4.5one

.45two

5% 5. .5one

.05two

10% 10. 1.0one

.10two

Now that you can go from percent to decimal…Can you go from decimal to percent?

0.76 76%7.6one

76.two

Decimal to percent:1. Move the decimal to the right twice…this is the same as multiplying

by 100!2. Tack on a percent sign.

1.05 105%10.5one

105.two

Ordering PercentsRemember

Descending- Greatest to LeastAscending- Least to Greatest

Let’s place 46%, 12.3%, and 26% in descending order!

1. Look at the numbers and ignore the percent sign.

4 61 2 . 32 6

2. The larger the number, the larger a percent it is.

Percents can also be turned into decimals for ordering...follow the decimal rules for ordering.

46%, 26%, 12.3%

Your assignment…1. Convert the following percents to fractions.a) 24% b) 4% c) 19% d) 98%

2. Convert the following percents to decimals and decimals to percents.a) 2% b) .14 c) 32.5% d) .08

3. Place the following percents in descending order.a) 2.4% b) 48% c) 99% d) 9.8%

4. Place the following percents in ascending order.a) 1% b) 100% c) 10% d) 10.1%

a) b) c) d)

a) 0.02 b) 14% c) .325 d) 8%

99%, 48%, 9.8%, 2.4%

1%, 10%, 10.1%, 100%

Scientific NotationA more convenient way to express

really large or small numbers.

How old is the Earth?4, 600, 000, 000 years oldThis number is written in decimal notation or standard form. When numbers get this large, it is easier to write them in scientific notation

What does Scientific Notation look like?

# x 10#

A number between 1 and 10

Times (multiplication)

BASE- In scientific notation there will always be a base of 10!

EXPONENT- Power of ten is always an integer.

How do you put a number into Scientific Notation?

Where is the decimal point now?

After the last zero.Where would you put the decimal to make

this number be between 1 and 10?

Between the 4 and the 6.

4, 600, 000, 000 years old

The Steps4, 600, 000, 000 years old

1. Place a decimal point after the first natural number (counting numbers).

4 . 6 0 0 0 0 0 0 0 02. Count the number of spaces you moved the

decimal point! 3. Drop all zeros AFTER the LAST natural number.

4 . 64. Write your “x 10”.

4.6 x 10 5. Tack on your exponent (step 2). Remember,

numbers larger than 1 will have positive exponents!4.6 x 10 9

The Steps0. 0 0 0 0 0 0 0 2 0 4

1. Place a decimal point after the first natural number (counting numbers).

0 . 0 0 0 0 0 0 0 2.0 42. Count the number of spaces you moved the

decimal point! 3. Drop all zeros BEFORE the FIRST natural number.

2 . 0 44. Write your “x 10”.

2.04 x 10 5. Tack on your exponent (step 2). Remember,

numbers smaller than 1 will have negative exponents!2.04 x 10 -8

Remember!!!

Numbers bigger than 1 will give you a positive

exponent!

Numbers before “x 10” must be between 1 and 10!

Numbers smaller than 1 will give you a negative

exponent!

Let’s try some!2, 000, 000, 000

0.0043

1, 203, 000, 000

0. 5

0.030201

2 𝑥109

4.3𝑥 10−3

1.203 𝑥109

5 𝑥10− 1

3 .0201𝑥 10− 2

Ordering Scientific Notation

Order by the exponent!The bigger the exponent, the bigger the

number and vice versus!

If the exponents are the same, then order by the number in front of the

“x 10”!

Place in ascending order!

2.01 𝑥102 1 .1𝑥10−2

1𝑥 108

2.4 𝑥 10−1

4 .3 𝑥102

1 .1𝑥10−2

2 .4 𝑥10− 1

2 .01𝑥102

4 .3 𝑥102

1𝑥 108

From Scientific Notation to Standard Form!1.Write down the number before the “x 10”.2.Move the decimal point the number of

spaces that the exponent tells you.Remember:

Positive moves RightNegative moves Left

Try th

ese! a)

b) c)

d)

21,000

4 ,060,000 0.00110 .5

Your AssignmentCourse 2 Textbook

Chapter 1

1. Page 45 (10-34 EVEN)

2. Place the numbers written in scientific notation in descending

order. Use the numbers from problems 10-17 on page 45.

Ordering Fractions, Decimals, Percents, and Scientific Notation!

Now that you know how to order these numbers separately let’s order them all together!

Type of Number Convert to..

Fraction Decimal

Percent Decimal

Scientific Notation Standard Form

Decimal No Conversions Needed

1. Convert all the numbers to decimal or standard form.

2. Order them the way you order decimals.

3. Place all answers back in ORIGINAL form.

Let’s Try Placing the Following Numbers in

Descending Order!0.345 3

81. Convert all the numbers to decimal or standard form.

3.6×10−2 37%

0.345 383.6×10−2 37%

0.3450.375 0.036 0.37No need to

change anything!

Numerator divided by

the denominator!

The exponent is negative, so we moved

left.

Move the decimal point left twice or divide by

100!

2. Order them the way you order decimals.

0.345 383.6×10−2

0.3450.375 0.036 0.37

0.3 450.3750.0360.37

Let’s Try Placing the Following Numbers in

Descending Order!

Start with first column, right now all of the 3’s are

equal.

Let’s move on to the

next column.

The two sevens are tied for

largest!Looking at the next column,

we can see 5 is larger than 0, making 0.375

the largest decimal.

Start from the first column

again to find the next largest!

Let’s Try Placing the Following Numbers in

Descending Order!0.345 3

83.6×10−2 37%

0.3450.375 0.036 0.37

3837%0.3453.6×10−2

3. Place all answers back in ORIGINAL form.

1 23 4

Let’s try some…

3 .02×10− 132% 0.032151 14

4% 0.404 4.11×10− 225

0.032150.320.302 1.25

3 .02×10− 1 32%0.03215 1 14

Least to Greatest

Greatest to Least

0.4040.040.4 0.0411

0.404 25 4.11×10− 2 4%

Your Assignment…

Complete the Ordering Practice

Sheet!