Online Pre-Algebra Tutoring: Decimals and Fractions

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Learn  Decimal and fractions  from Certified Online Pre-Algebra Tutor

Decimals and fractions represent the same thing: a number that is not exactly a whole number. Decimals are fractions that have powers of ten as their denominators. Or, to say another way, they have 10, 100, 1000, and so on as the denominator (bottom number) of the fraction.

Rules for converting Decimals to Fractions:

First, convert the terminating decimal to a fraction by counting the number of decimal places and putting the decimal’s digits over 1 followed by the appropriate number of zeroes. If there are two decimal places (number of digits to the right side of the decimal point), put the number over 100 and reduce. If there are three places, put it over 1000 and so on.

Next, simplify the fraction part to the lowest common term.

Let’s understand with an example

Here’s how to convert 0.78 to a fraction…

There is not much that can be done to figure out how to write 0.78 as a fraction, except to literally use what the decimal portion of your number, the .78, means.

Since there are 2 digits after the decimal point in 78, the very last digit is the “100th” decimal place.

So we can just say that .78 is the same as 78/100.

The fraction 78/100 is not reduced to lowest terms. We can reduce this fraction to lowest terms by dividing both the numerator and denominator by 2.

Why divide by 2? 2 is the Greatest Common Divisor (GCD) or Greatest Common Factor (GCF) of the numbers 78 and 100.
So, this fraction reduced to lowest terms is 39/50

So your final answer is: 0.78 can be written as the fraction 39/50

Note : Common fractions are usually written in simplest form /lowest term

Check Point

a) Write 0.75 as a fraction in simplest form.
b) Write 0.543 as a fraction in simplest form.
c) Write 0.986 as a fraction in simplest form.
d) Write 0.754 as a fraction in simplest form.
e) Write 0.248 as a fraction in simplest form.

Answer Key

a) 3/4
b) 543/1000
c) 493/500
d) 377/500
e) 31/125

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