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