## Change each repeating decimal into fractions in lowest terms. Show your solutions in a piece of paper and upload a clear picture of your sol

Question

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

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1 month 2021-09-17T08:01:45+00:00 2 Answers 0 views 0

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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

{Lowest term}

5

—— {Lowest term}

250

—– {Lowest term}

100

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

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