Question

1.8 repeating as a mixed number in simplest form

0.46 repeating as a tion simplest form
3.01 repeating as a mixed number in simplest form
2.5 repeating as a mixed number in simplest form
A) 1 8/9
B) 23/50
C) 3 1/33
D) 2 1/2

Answer 1

The repeating decimals 1.8, 0.46, 3.01, and 2.5 can be converted to the mixed numbers 1 8/9, 23/50, 3 1/33, and 2 1/2 respectively. This requires understanding that repeating decimals can be rewritten as fractions which can then be simplified.

Step-by-step explanation:

The student is asking how to represent certain repeating decimals as mixed numbers in simplest form. The answers provided in the options correspond to different repeating decimals:

• A) 1 8/9 - This is the mixed number for the repeating decimal 1.8 repeating.
• B) 23/50 - This is the fraction for the repeating decimal 0.46 repeating, simplified.
• C) 3 1/33 - This is the mixed number for the repeating decimal 3.01 repeating.
• D) 2 1/2 - This is the mixed number for the repeating decimal 2.5 repeating.

These conversions are based on the principle that repeating decimals can be expressed as fractions or mixed numbers by using algebra to find an equivalent fraction. For instance, to convert 0.46 repeating, you can set x = 0.464646..., then multiply by 100 to get 100x = 46.464646..., subtract x from 100x to find 99x, and then solve for x to find the fractional form. Simplifying the resulting fraction gives the simplest form.