5.9(line over it)
0.1515...
1.20(line over it)
0.35(line over it)
0.72(line over it)
1.12(line over it)
need to change these from decimals to fractions, im confused as to how to do it and get the answer, sub teacher taught it different and I am not getting the same answer that is in my book. Im feeling like an idiot because I am not understanding it
I will do one.
1.12121212... is that it? Your indication is not clear.
multiply by 10
12.12121212
subtract 1.12121212
answer 12
12=10n-n=9n
n=12/9
you want to get rid of the repeating decimal.
one more.
.353535.. multipy by 100
35.353535 then subtract .353535
ans: 35
so 35=100n-1n=99n
n= 35/99
we are writing a repeating decimal.
example is n=1.21(line over it)
-multiply both sides of the equation by a power of 10 determined by the number of digits in the block of repeating digits; since there are 2 digits that repeat we multiply by 100
-100n=121.21(repeat)
subtract n=1.21
99n=120 n=120/99=40/33
I don't understand how you get 121.12 and where 120 comes from; I understand you subtract 1 from 100 to get 99, but not seeing how you get 120 from 1.21
121.212121...
-1.212121...
____________________
120
Converting decimals to fractions can seem confusing at first, but once you understand the process, it becomes easier. Here's how you can convert the decimals you provided to fractions:
1. 5.9: To convert this decimal to a fraction, we need to determine the place value of the decimal. Since 5.9 has one digit after the decimal point, we can express it as the fraction (5.9/10). To simplify this fraction, we divide both the numerator and denominator by their greatest common divisor (GCD), which is 1. In this case, the simplified fraction is 59/10.
2. 0.1515... : This decimal has a recurring pattern of "15." To convert it to a fraction, we can assign the repeating pattern "15" to a variable, say "x." Then, we can subtract "x" from the whole number, which in this case is 0.15:
100x - x = 15.15 - 0.15
99x = 15
After solving the equation, we find that x = 15/99. Therefore, the fraction equivalent of 0.1515... is 15/99.
3. 1.20: This decimal can be expressed as the fraction 1 2/10. To simplify, we divide both the numerator and denominator by their GCD, which is 2. Thus, the simplified fraction is 6/5.
4. 0.35: To convert this decimal to a fraction, we need to express it as 35/100. Simplifying the fraction by dividing both the numerator and denominator by their GCD, which is 5, gives us 7/20.
5. 0.72: To express this decimal as a fraction, we can write it as 72/100. Simplifying the fraction by dividing both the numerator and denominator by their GCD, which is 4, we get 18/25.
6. 1.12: We can express this decimal as the fraction 1 12/100. Simplifying the fraction by dividing both the numerator and denominator by their GCD, which is 4, we obtain 7/25.
Remember, when simplifying fractions, it's important to find the GCD to ensure that the numerator and denominator are reduced to their simplest form.