Final answer:
To convert a decimal to a simplest fraction, we express it as a ratio of two integers. The simplest fractions for the given decimals are: a. 8/3 b. 7/50 c. 179/250 d. 1653/1250 e. -53213/100000.
Step-by-step explanation:
To represent a decimal as a simplest fraction, we can express it as a ratio of two integers. Here are the completed steps for each given decimal:
a. 2. overline6 = 2.6666...
Multiply both sides by 10 to get rid of the repeating decimal, resulting in: 10a = 26.6666...
Subtract the original equation from the new equation to eliminate the decimal: 10a - a = 26.6666... - 2.6666...
Simplify and solve for a: 9a = 24, a = 24/9 = 8/3.
So, 2. overline6 as a simplest fraction is 8/3.
b. 0.14 = 14/100 = 7/50.
c. 0.716 = 716/1000 = 179/250.
d. 1.3212 = 13212/10000 = 1653/1250.
e. -0.53213 = -53213/100000.