Lesson 76 - Writing Repeating Decimals as Fractions
Comparing/Ordering Rational and Irrational #s
Do Now: Identify each underlined place value below.
1) 4.025 ____________
2) 81.71 _____________
4) Write the decimal as a fraction.
3) 0.936 __________
.72 __________
5) What is another way of writing the decimal .33333333…? ________
Now let’s write a repeating decimal as a fraction.
.6666666 . . .
Step 1: Determine the place value where the decimal begins to repeat. ____________
Step 2: Subtract one (1) from that place value number. ________________
Step 3: Write the fraction…The repeating number is the numerator
and Step 2 is the denominator. Reduce the fraction, if possible. ___________
Now try:
1) .44444 . . . _________
2) .57 __________
On Your Own:
3) .251 __________
4) 3.2 __________
5) .77777 . . . __________
6) .39 __________
Comparing Rational and Irrational Numbers
When you are comparing numbers, it is best to convert all the numbers to decimals.
Then determine which is greater by comparing the place values from left to right.
Another way to compare fractions is to find the cross products. The side with the
larger cross product is the larger fraction.
3
7
4
9
8
10
4
5
7
3
10
4
Ordering Rational and Irrational Numbers
When you are ordering numbers, it is best to convert all the numbers to decimals.
Then determine which the order by comparing the place values from left to right.
You MUST write the ORIGINAL numbers on the line as your final answer.
Place these numbers in order from least to greatest.
50 ,
-3.454,
0,
4
,
9
.38,
81 ,
2π,
2
9
1.44 ,
____________________________________________________________
ON YOUR OWN: (1-5) Circle the correct multiple choice answer.
1) What do all rational numbers have in common?
2) Which statement is true?
A) They can be expressed as fractions
B) They have positive values
C) They can be expressed as terminating decimals
D) They do not include perfect square roots
A) All integers are whole numbers
B) Rational numbers cannot be fractions
C) Irrational #’s are repeating decimals
D) Irrational #s will never terminate
3) Which of the following is an integer?
4) Which of the following is irrational?
A)
3
5
B)
3
C) 0.852
D) – 12
A)
1
3
B) 0.275275275…
C) 8.123467… D) 49
5) The baby T-Rex at the museum weighs 851 pounds, to the nearest integer. Which weight listed
cannot be the actual weight of the baby T-Rex?
A) 850.6
B) 851.2
C) 851.6
D) 850.5
6) Place the following numbers in order from greatest to least.
______________________________________
3,
49 ,
1
, 0.57,
3
π
Convert the following decimals to fractions in simplest form.
7) 0.7
8) 0.25
9) 0.8888̅…
̅̅̅̅…
10) 0.343434
Compare the following using <, >, or =
11) √7 ___________ 3
5
12) _______________ √5
2
13) 0.35 ____________
Review
1) Solve for x in the triangle below. Then find the measure of angle B.
2) Find the value of x in the figure below.
7
20