Problem 1 :
Write the decimal 0.825 as a fraction in simplest form.
Problem 2 :
Write the decimal 0.12 as a fraction in simplest form.
Problem 3 :
Convert the following repeating decimal as fraction
0.474747...........
Problem 4 :
Convert the following repeating decimal as fraction
0.57777..........
Problem 1 :
Write the decimal 0.825 as a fraction in simplest form.
Solution :
The decimal 0.825 means “825 thousandths.” Write this as a fraction.
To write “825 thousandths”, put 825 over 1000.
825 / 1000
Then simplify the fraction.
Both 825 and 1000 are the multiples of 25. So, divide both the numerator and the denominator by 25.
(825 ÷ 25) / (1000 ÷ 25) = 33 / 40
0.825 = 33 / 40
So, the fraction equal to 0.825 is 33/40.
Problem 2 :
Write the decimal 0.12 as a fraction in simplest form.
Solution :
The decimal 0.12 means “12 hundredths.” Write this as a fraction.
To write “12 hundredths”, put 12 over 100.
12/100
Then simplify the fraction.
Both 12 and 100 are the multiples of 4. So, divide both the numerator and the denominator by 4.
(12 ÷ 4) / (100 ÷ 4) = 3 / 25
0.12 = 3 / 25
So, the fraction equal to 0.12 is 3/25.
Problem 3 :
Convert the following repeating decimal as fraction
0.474747...........
Solution :
Let x = 0.474747............... ------(1)
Here, number of repeating digits = 2. So we have to multiply 100 on both sides.
100x = 47.4747.............. ------(2)
(2) - (1) :
100x - x = (47.4747.........) - (0.4747..........)
99x = 47
x = 47/99
So, the fraction equal to 0.474747........... is 47/99.
Problem 4 :
Convert the following repeating decimal as fraction
0.57777..........
Solution :
Let x = 0.57777........------(1)
Here, number of repeating digits = 1. So we have to multiply 10 on both sides.
10x = 5.7777..........------(2)
(2) - (1) :
10x - x = (5.7777.........) - (0.57777..........)
9x = 5.2
Divide each side by 9.
x = 5.2/9
Multiply the numerator and denominator by 10.
x = 52/90
x = 26/45
So, the fraction equal to 0.57777........... is 26/45.
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