It’s important to understand what a decimal number represents. A decimal number is a way of representing a fraction with a denominator of 10 or a power of 10. For example, the decimal number 0.75 represents the fraction 75/100, which can be simplified to 3/4.
When we convert a decimal number into a fraction, we want to express it as a ratio of two integers. To do this, we need to determine the numerator and denominator of the fraction.
The first step is to identify the place value of the last digit in the decimal. In the case of 1.75, the last digit is 5, which is in the hundredths place. This means that the fraction will have a denominator of 100.
Next, we need to convert the decimal number into an equivalent fraction with a denominator of 100. To do this, we multiply both the numerator and the denominator of the fraction by the same factor that will make the denominator 100. In this case, we need to multiply both the numerator and denominator by 100 to get:
1.75 = 1.75/1 x 100/100 = 175/100
Now we have an equivalent fraction with a denominator of 100. However, this fraction is not in its simplest form, as both the numerator and the denominator can be divided by a common factor. In this case, we can divide both 175 and 100 by 25 to get:
175/100 = 7/4
Therefore, the decimal number 1.75 can be expressed as the fraction 7/4.
It’s worth noting that we can also convert a mixed number like 1.75 into an improper fraction before simplifying it. To do this, we multiply the whole number by the denominator of the fraction and add the numerator. This gives us the numerator of the improper fraction, which is then written over the denominator. For example:
1.75 = 1 + 0.75 = 1 x 4/4 + 75/100 = 4/4 + 75/100 = 400/400 + 75/100 = 475/100
Now we have an improper fraction, which we can simplify as before by dividing both the numerator and the denominator by a common factor.
In summary, converting a decimal number into a fraction involves identifying the place value of the last digit, converting the decimal into an equivalent fraction with the appropriate denominator, and simplifying the fraction if necessary. The process can be simplified for mixed numbers by converting them into improper fractions first. However, it’s important to remember that the simplest form of a fraction should always be used whenever possible.