To convert the decimal 0.946 to a fraction, we need to follow these steps:
1. Understand the Decimal: The decimal 0.946 really means 946 thousandths, or:
[tex]\[
0.946 = \frac{946}{1000}
\][/tex]
2. Simplification:
We need to simplify this fraction by finding the greatest common divisor (GCD) of the numerator (946) and the denominator (1000).
3. Find the GCD:
The greatest common divisor of 946 and 1000 is 2.
4. Divide Both Numerator and Denominator:
By dividing both the numerator and the denominator by their GCD, we simplify:
[tex]\[
\frac{946 \div 2}{1000 \div 2} = \frac{473}{500}
\][/tex]
Thus, the fraction [tex]\(\frac{946}{1000}\)[/tex] simplifies to [tex]\(\frac{473}{500}\)[/tex].
So, the decimal 0.946 as a fraction in its simplest form is:
[tex]\[
\frac{473}{500}
\][/tex]
