Transcript 8 - MindMeister

Changing Recurring
Decimals into Fractions
Skipton Girls’ High School
Silent Starter- Divide these numbers
1.
175 ÷ 5 =
Answers
1. 35
2.
432 ÷ 9 =
2. 48
3.
756 ÷ 12 =
3. 63
4.
1155 ÷ 15 =
4. 77
5.
*1513 ÷ 17 =
5. 89
Use the Bus
Stop Method!!
Changing Fractions to Decimals
• When changing improper (top heavy) fractions e.g
numbers we know to divide by the denominator
21
5
to mixed
Therefore..
• Remember to divide by the denominator when changing fraction
to decimals.
Example
3
8
.375
3 6 4
3. 0 00
0
8
What about this?
4
9
. 4 4 4…..
4 4 4
4. 0 00
0
9
Changing Recurring Decimal to
Fractions
Objective(L7) To be able to change decimals that recurring e.g.
0.55555555, 0.4141414141… and 0.564564564… to a fraction.
Step 1
Example 1
x = 0.5555555555....
Make the decimal equal to x
Step 2
10x = 5.555555555....
How many digits are repeated ?
So what do I need to multiply by ?
1 digit is repeated so I need to multiply
by 10
Step 3
10 x = 5.55555555…
What do I need to subtract to be left
with just a whole number?
I need to subtract x which is 0.55555…
Step 4
How do I get x on it’s own?
I divide by 9
So
x = 0.55555555… 9x = 5.00000000
9x = 5
x =
5
9
Step 1
Example 2
x = 0. 41 41 41 41....
Make the decimal equal to x
Step 2
100 x = 41. 41 41 41....
How many digits are repeated ?
So what do I need to multiply by ?
2 digits are repeated so I need to
multiply by 100
Step 3
100 x = 41. 41 41 41
What do I need to subtract to be left
with just a whole number?
I need to subtract x which is 0.41 41 41…
Step 4
How do I get x on it’s own?
I divide by 99
So
x = 0. 41 41 41 99x = 41. 00 00 00
99 x = 41
x =
41
99
Step 5
Can we cancel down or simplify the
fraction?
Always check and see if you can simplify
the fraction by dividing the numerator by
3 or 9.
Can we divide 41 by either 3 or 9?
No – so the fraction is already in it’s
simplest form
x =
41
99
Step 1
Example 2
Make the decimal equal to x
Step 2
How many digits are repeated ?
x = 0. 564 564 564....
1000 x = 564. 564 564....
So what do I need to multiply by ?
3 digits are repeated so I need to
multiply by 1000
Step 3
What do I need to subtract to be left
with just a whole number?
1000 x = 564. 564 564....
x = 0. 564 564 999x = 564. 000 000
I need to subtract x which is 0.41 41 41…
Step 4
So 999 x = 564
How do I get x on it’s own?
Divide by 999
x =
564
999
Step 5
Can we cancel down or simplify the
fraction?
x =
Always check and see if you can simplify
the fraction by dividing numerator by 3
or 9
Can we divide 564 exactly by 3 or 9?
564
999
1 8 8
3
2
2
564
3 3 3
Yes it divides exactly by 3, 188 times
3
999
3 goes exactly into 999, 333 times
x =
188
333
Your Turn!
1.
2.
3.
4.
5.
0.6767676767
0.666666666
0.44444444
0.555555555
0.888888888
6.
7.
8.
9.
10.
Make the Q
equal to x
0.2121212121
0.3939393939
0.327327327
0.865865865
0.672672672
0.780378037803
Answers
1) 67/99
6) 21/99 or 7/33
2) 2/3
7) 39/99 or 13/33
3) 4/9
8) 327/999 or 109/333
4) 5/9
9) 865/999
5) 8/9
10) 672/999 or 224/333
867/1111
What about this?
• Can we use the technique you’ve just learned on this
recurring decimal?
• What else could be we do which is similar?
To finish...
Which of these fractions give recurring decimals?
3/10
2/3
3/8
3/7