2-6 Decimals to Fractions and vice versa The relationship between fractions and decimals.

2-6 Decimals to Fractions and vice versa

The relationship between fractions and decimals

2

What fraction of the rectangle is shaded?

What decimal part of the rectangle is shaded?

10

6

.6

They sound alike!!!

To write a decimal as a fraction, write the fraction as you would

say the decimal

0.12345

tenths

Hundredths

Thousandths

Ten-thousandths

Hundred-thousandths

Say the decimal….Write it as a fraction

• .5

• .65

• .22

• .2

• .225

Notice….when you change a decimal to a fraction the denominator is always 10, 100, 1000 (powers of ten!)

51065

100221002

10

2251000

Is that all there is?

You have to simplify the fraction if possible

Write .6 as a fraction

.6 = 10

610

6 Can be simplified to:

5

35

3.6 =

What about fractions to What about fractions to decimals?decimals?

You can write a fraction as a decimal by dividing the numerator by the denominator…..the fraction symbol means division!

344

3 To make a

decimal…do the division!

34 .0028

20200

.75

One more thing………One more thing………

When you divide, REMEMBER, add zeros to finish your division.

2 THINGS CAN HAPPEN

4.255

2

1.) The division problem ends

Which is called A TerminatingTerminating decimal

.......333333333333333.266

2

2.) or the division problem goes on forever…. Which is called a RepeatingRepeating decimal

Repeating DecimalsRepeating Decimals

A single digit might repeat….

.3333….

Or a group of digits might repeat…

.275275275….

Show repeating decimals by placing a line over the digit or

group of digits that repeats

.33333…. Becomes .3

And

.275275….becomes .275

Remember

5

21 Will be 1.4

1.2 will be 10

21 Simplified to:

5

11

Whole numbers stay the same!Whole numbers stay the same!

Order 45

0.93, and 0.9 from least to greatest.,

45 = 0.80

Graph the numbers on a number line.

0 0.2 0.4 0.6 0.8 1

0.93

Write as decimals with the same number of places.

0.93 = 0.93 0.9 = 0.90

0.80 < 0.90 < 0.93 Compare the decimals.

45From least to greatest, the numbers are , 0.9, 0.93.

Ordering Fractions and Decimals from least to greatestOrdering Fractions and Decimals from least to greatest

Order 45

0.93, and 0.9 from least to greatest.,

45 = 0.80

Can also treat it like money

Write as decimals with the same number of places.

0.93 = 0.93 0.9 = 0.90

0.80 cents 0.80 cents < 0.90 cents 0.90 cents < 0.93 cents0.93 cents

45From least to greatest, the numbers are , 0.9, 0.93.

Ordering Fractions and Decimals from least to greatestOrdering Fractions and Decimals from least to greatest

Homework

Page 99 in your textbook….

Problems 8-36 even

Show your work

Can use a calculator