Change each repeating decimal into fractions in lowest terms. Show your solutions in a piece of paper and upload a clear picture of your solution for each item.
1. 0. 6666
2. 0.612612
3 0.5777
Answers
Answer:
To convert a decimal to a fraction, we write the decimal number as a numerator, and we write its place value as the denominator.
Example 1: 0.070.070, point, 07
0.0\blueD70.070, point, 0, start color #11accd, 7, end color #11accd is \blueD77start color #11accd, 7, end color #11accd \text{\greenD{hundredths}}hundredthsstart text, start color #1fab54, h, u, n, d, r, e, d, t, h, s, end color #1fab54, end text. So, we write \blueD77start color #11accd, 7, end color #11accd over \greenD{100}100start color #1fab54, 100, end color #1fab54.
0.07=\dfrac{\blueD7}{\greenD{100}}0.07=
100
7
0, point, 07, equals, start fraction, start color #11accd, 7, end color #11accd, divided by, start color #1fab54, 100, end color #1fab54, end fraction
But what about repeating decimals?
Let's look at an example.
Rewrite 0.\overline{7}0.
7
0, point, start overline, 7, end overline as a simplified fraction.
Let xxx equal the decimal:
\large{x = 0.7777...}x=0.7777...x, equals, 0, point, 7777, point, point, point
Set up a second equation such that the digits after the decimal point are identical:
\large{\begin{aligned} 10x &= 7.7777...\\ x &= 0.7777... \end{aligned}}
10x
x
=7.7777...
=0.7777...
To convert a decimal to a fraction, we write the decimal number as a numerator, and we write its place value as the denominator.
Example 1: 0.070.070, point, 07
0.0\blueD70.070, point, 0, start color #11accd, 7, end color #11accd is \blueD77start color #11accd, 7, end color #11accd \text{\greenD{hundredths}}hundredthsstart text, start color #1fab54, h, u, n, d, r, e, d, t, h, s, end color #1fab54, end text. So, we write \blueD77start color #11accd, 7, end color #11accd over \greenD{100}100start color #1fab54, 100, end color #1fab54.
0.07=\dfrac{\blueD7}{\greenD{100}}0.07=
100
7
0, point, 07, equals, start fraction, start color #11accd, 7, end color #11accd, divided by, start color #1fab54, 100, end color #1fab54, end fraction
But what about repeating decimals?
Let's look at an example.
Rewrite 0.\overline{7}0.
7
0, point, start overline, 7, end overline as a simplified fraction.
Hope it helps you!!!
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Answer:
1) 0.6666 = 0.6 = 6 3
---- = ----
10 5
2) 0.612612 = 0.612 = 612 153
------- = ------
1000 250
3) 0.5777 = 0.57 =57 57
----- = -----
100 100
1st Answer = 3
--- {Lowest term}
5
2nd Answer = 153
------ {Lowest term}
250
3rd Answer = 57
----- {Lowest term}
100