Which number is equivalent to 6.672 repeating?
What are your choices?
0.abcabcabc...
If there are 3 digits that repeat, the value is abc/999
that is, just place the digits over the same number of 9's.
To find the equivalent fraction of a repeating decimal, you can follow these steps:
Step 1: Let x be the repeating decimal number.
So, x = 6.672...
Step 2: Multiply both sides of the equation by 10 to move the decimal point one place to the right.
10x = 66.72...
Step 3: Subtract the original equation (x) from the equation in step 2 (10x).
10x - x = 66.72 - 6.672
9x = 60.048
Step 4: Divide both sides by 9 to solve for x.
x = 60.048 / 9
x = 6.671333...
Therefore, the number equivalent to 6.672 repeating is approximately 6.671333.
To find the equivalent fraction or number for the decimal 6.672 repeating, we'll follow these steps:
Step 1: Let's represent the repeating decimal as a variable. Let x = 6.672 repeating.
Step 2: Determine the number of repeating digits. In this case, it's 3 digits, which are 672.
Step 3: Multiply the repeating digits by the proper power of 10. Since there are 3 repeating digits, we'll multiply x by 1000 to eliminate the repetition. So, 1000x = 6672.672 repeating.
Step 4: Subtract the original value from the result. Now, we will subtract the value of x from 1000x to eliminate the repeating decimal. Hence, 1000x - x = 6672.672 - 6.672. This simplifies to 999x = 6666.
Step 5: Solve for x by dividing both sides of the equation by 999. x = 6666/999.
Step 6: Simplify the fraction 6666/999. To do this, both the numerator and denominator can be divided by their greatest common divisor, which is 333. Thus, 6666/999 = 20/3.
So, the number equivalent to the repeating decimal 6.672 is 20/3.