Expressing 35.1457 as a fraction:

To express the decimal number 35.1457 as a fraction in the form p/q, where p and q are integers and q is not equal to zero, we can follow the steps outlined below:

Step 1: Identify the place value of the last digit after the decimal point.
The last digit after the decimal point in 35.1457 is 7, and its place value is in the thousandths place.

Step 2: Write the decimal number as a sum of its whole number and fractional parts.
The whole number part of 35.1457 is 35, and the fractional part is 0.1457.

Step 3: Convert the fractional part to a fraction.
To convert the fractional part 0.1457 to a fraction, we can use the following method:

Step 3.1: Count the number of decimal places.
There are four decimal places in 0.1457.

Step 3.2: Write the fractional part as the numerator over a denominator of 1 followed by the same number of zeros as the number of decimal places.
So, 0.1457 can be written as 1457/10000.

Step 4: Combine the whole number and fractional parts.
The whole number part, 35, can be written as 35/1.

Step 5: Simplify the fraction, if possible.
To simplify the fraction, we can find the greatest common divisor (GCD) of the numerator and denominator, and divide both by it.
In this case, the GCD of 1457 and 10000 is 1, so the fraction cannot be simplified further.

Step 6: Write the fraction in the form p/q.
Combining the whole number and fractional parts, we have 35/1 + 1457/10000.

Now, we need to find a common denominator to add these fractions together. In this case, the common denominator is 10000.

Step 7: Perform the addition.
35/1 + 1457/10000 = (35 * 10000 + 1457) / 10000 = 350000 + 1457 / 10000 = 351457 / 10000.

So, the decimal number 35.1457 can be expressed as the fraction 351457/10000.

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