Question

Write each decimal as a fraction. 0.10203

Short answer

The fraction is \(\frac{10203}{100000}\).

Step-by-step solution

Understand the Decimal

The given decimal is 0.10203.

Write the Decimal as a Fraction with Denominator

Write 0.10203 as \(\frac{10203}{100000}\). This is because there are 5 decimal places, so the denominator is 100000.

Simplify the Fraction

Simplify \(\frac{10203}{100000}\) by finding the greatest common divisor (GCD) of 10203 and 100000. The GCD is 1, so the fraction cannot be simplified further.

Final Step: Write the Simplified Fraction

The decimal 0.10203 as a fraction is \(\frac{10203}{100000}\).

Key concepts

Decimal to Fraction Conversion

Converting a decimal to a fraction is a useful skill in math. It involves expressing the decimal number as a fraction of two integers.
To start, take your decimal number. For example, consider the decimal 0.10203.
First, note the number of places after the decimal. There are 5 places in this case. This tells you the denominator should be 10 raised to the power of 5, or 100000.
Next, you place your decimal number over this denominator. So, 0.10203 becomes \(\frac{10203}{100000}\). This fraction represents the decimal.

Greatest Common Divisor

The greatest common divisor (GCD) is a crucial concept when working with fractions. It's the largest number that can evenly divide both the numerator and the denominator.
Finding the GCD helps in simplifying fractions. Let's use our example \(\frac{10203}{100000}\).

• First, list the factors of both the numerator and the denominator.
• The factors of 10203 are: 1, 3, 3401, and 10203.
• For 100000, they are: 1, 2, 4, ..., 100000. (It's a long list!)

The largest number that appears in both lists is 1. This is our GCD. This tells us we can't simplify the fraction any further.

Simplifying Fractions

Simplifying fractions makes them easier to work with. It involves reducing the fraction so that the numerator and denominator have no common factors other than 1.
Using our example, \(\frac{10203}{100000}\), we already found the GCD is 1. So, there's no common factor to simplify here.
In general, to simplify a fraction:

• Find the GCD of the numerator and denominator.
• Divide both the numerator and the denominator by the GCD.

Since \(\frac{10203}{100000}\) has a GCD of 1, it remains the same and cannot be simplified further.
Therefore, it's already in its simplest form.