To convert the decimal 1.146 to a fraction, follow these steps:
1. Identify the integer and fractional parts of the decimal:
- The integer part is 1.
- The fractional part is 0.146.
2. Express the fractional part as a fraction:
- Write 0.146 as a fraction: [tex]\( 0.146 = \frac{146}{1000} \)[/tex].
3. Simplify the fraction [tex]\( \frac{146}{1000} \)[/tex]:
- Find the greatest common divisor (GCD) of 146 and 1000. The GCD is 2.
- Divide both the numerator and the denominator by their GCD:
[tex]\( \frac{146 \div 2}{1000 \div 2} = \frac{73}{500} \)[/tex].
4. Combine with the integer part:
- Add 1 to the simplified fraction: [tex]\( 1 + \frac{73}{500} \)[/tex].
5. Express this as a single fraction:
- Convert the integer to a fraction with the same denominator:
[tex]\( 1 = \frac{500}{500} \)[/tex].
- Add the two fractions:
[tex]\[
1 + \frac{73}{500} = \frac{500}{500} + \frac{73}{500} = \frac{500 + 73}{500} = \frac{573}{500}.
\][/tex]
Thus, the decimal 1.146 as a fraction is [tex]\( \frac{573}{500} \)[/tex].
