Connection's:math 7 unit 6
Which statement describes 0.34 ̄ select three answers?
To determine which statement describes the repeating decimal 0.34 ̄ (0.343434...), we need to look at the pattern of the repeating digits. Let's break down the decimal representation of 0.34 ̄:
0.34 ̄ = 0.343434...
Now, let's analyze the pattern of the repeating digits "34". We can observe that the digit "34" repeats infinitely. Based on the pattern, we can describe the repeating decimal 0.34 ̄ in three ways:
1. 0.34 ̄ is a non-terminating decimal: This statement indicates that the decimal representation of 0.34 ̄ goes on indefinitely without reaching a terminating point. The repetition of "34" confirms this.
2. 0.34 ̄ is a repeating decimal: This statement signifies that two or more digits repeat in a pattern. In this case, the digits "34" repeat indefinitely.
3. 0.34 ̄ can be expressed as a fraction: This statement highlights that the repeating decimal 0.34 ̄ can be converted into a fraction. To find the fraction form, we can designate "x" as 0.34 ̄ and subtract it from 100x. Let's solve this:
100x - x = 34.34 ̄
99x = 34.34 ̄
Multiply both sides by 100 to eliminate the decimal:
9900x = 3434.34 ̄
Subtract the original equation from the new equation:
9900x - 99x = 3434.34 ̄ - 34.34 ̄
Simplifying further:
9801x = 3400
x = 3400/9801
Therefore, the repeating decimal 0.34 ̄ can be expressed as the fraction 3400/9801.
In summary, the three statements that describe 0.34 ̄ are: it is a non-terminating decimal, it is a repeating decimal with the pattern "34," and it can be expressed as the fraction 3400/9801.
34/99
rational
maybe more.