express the repeating decimal as a quotient of two integers
1.63
Sure! Let me put on my mathematician clown shoes and solve this for you.
The repeating decimal 1.63 can be expressed as the quotient of two integers. Let's dive into the clown math!
Step 1: We start by letting x be equal to the repeating decimal, which is 1.63.
x = 1.63
Step 2: In clown math, we multiply x by 100 to ensure that we move the decimal point two places to the right. This gives us:
100x = 163
Step 3: Now, let's subtract the original equation from the one we obtained in Step 2:
100x - x = 163 - 1.63
99x = 161.37
Step 4: Finally, we divide both sides of the equation by 99 to solve for x:
99x/99 = 161.37/99
And voila! The quotient is:
x ≈ 1.628383838...
So, there you have it! The repeating decimal 1.63 can be expressed as the quotient of two integers. Keep in mind that the resulting quotient is an approximation due to the repeating nature of the decimal. I hope this clownful explanation brought a smile to your face!
To express the repeating decimal 1.63 as a quotient of two integers, we can follow these steps:
Step 1: Determine the non-repeating part of the decimal:
To find the non-repeating part, we can look at the numbers before the decimal point. In this case, the non-repeating part is "1".
Step 2: Determine the repeating part of the decimal:
To find the repeating part, we can look at the numbers after the decimal point that repeat. In this case, there is no repeating part.
Step 3: Express the decimal as a quotient of two integers:
Since there is no repeating part, we can express the decimal 1.63 as a quotient of two integers by dividing the non-repeating part by a power of 10. In this case, we can express 1.63 as:
1.63 = 163/100
To express a repeating decimal as a quotient of two integers, we need to identify the repeating pattern and convert it to a fraction.
Given the repeating decimal 1.63, let's first denote it as x:
x = 1.63
To eliminate the repeating decimal, we can multiply x by a power of 10 so that the repeating part becomes an integer:
10x = 16.3
Next, we subtract the original equation from the equation above to eliminate the repeating part:
10x - x = 16.3 - 1.63
9x = 14.67
Now, we have eliminated the repeating part and obtained an equation without decimals. To express x as a fraction, divide both sides of the equation by 9:
9x / 9 = 14.67 / 9
x = 1.63 / 9
Therefore, the repeating decimal 1.63 can be expressed as the quotient of the two integers 163 and 900:
1.63 = 163 / 900