Question

Express the number as a ratio of integers.
0.46 = 0.46464646

Answer 1

To convert the repeating decimal 0.464646... to a ratio of integers, represent it as 'x', multiply by 100 to shift the decimal, and subtract the original 'x' to eliminate the repeating part. This results in a ratio of 46/99.

Step-by-step explanation:

Expressing a Repeating Decimal as a Ratio of Integers

To express the repeating decimal 0.46 (where 46 repeats indefinitely) as a ratio of integers, we can use algebraic methods:

1. Let x equal the repeating decimal: x = 0.464646...
2. Multiply both sides by 100, because two digits are repeating: 100x = 46.464646...
3. Subtract the original equation from this result: 100x - x = 46.464646... - 0.464646... This gives us 99x = 46.
4. Now, divide both sides by 99 to solve for x: x = 46/99.

Therefore, the repeating decimal 0.464646... is expressed as the ratio 46/99 of integers.

Answer 2

3.45

Step-by-step explanation:

this is how it is supposed to be