**Converting a Decimal Number into a Rational Number**

To convert a decimal number into a rational number, we need to express the decimal as a fraction in the form of m/n, where m and n are integers.

**Step 1: Identify the Place Value**

In the given decimal number 0.35, the digit 3 is in the tenths place, and the digit 5 is in the hundredths place.

**Step 2: Write the Decimal as a Fraction**

To convert the decimal number into a fraction, we need to consider the place values. The tenths place has a value of 1/10, and the hundredths place has a value of 1/100.

So, we can write the given decimal number 0.35 as:

0.35 = 3/10 + 5/100

**Step 3: Simplify the Fraction**

To simplify the fraction, we need to find the lowest common denominator (LCD) and convert the fractions into terms of the LCD.

The LCD of 10 and 100 is 100.

Converting the fractions to have the same denominator:

0.35 = 3/10 + 5/100
= 30/100 + 5/100
= 35/100

**Step 4: Simplify the Fraction**

To simplify the fraction, we can divide both the numerator and denominator by their greatest common divisor (GCD).

The GCD of 35 and 100 is 5.

Dividing the numerator and denominator by 5:

35/100 ÷ 5/5 = 7/20

**Step 5: Final Rational Number**

Therefore, the decimal number 0.35 can be expressed as the rational number 7/20.

**Example**

Let's take another example to further illustrate the conversion of a terminating decimal into a rational number.

Consider the decimal number 0.125.

Step 1: Identify the Place Value
The digit 1 is in the hundredths place, the digit 2 is in the thousandths place, and the digit 5 is in the ten-thousandths place.

Step 2: Write the Decimal as a Fraction
0.125 = 1/10 + 2/100 + 5/1000

Step 3: Simplify the Fraction
0.125 = 1/10 + 2/100 + 5/1000
= 100/1000 + 20/1000 + 5/1000
= 125/1000

Step 4: Simplify the Fraction
Dividing the numerator and denominator by their GCD:
125/1000 ÷ 125/125 = 1/8

Step 5: Final Rational Number
Therefore, the decimal number 0.125 can be expressed as the rational number 1/8.

0.35=35/100=7/20