Sure! Let's convert each of the given rational numbers into their decimal form step-by-step:
### Part 1:
1. (a) [tex]\(\frac{3}{20}\)[/tex]
- To express the fraction [tex]\(\frac{3}{20}\)[/tex] as a decimal, we divide the numerator by the denominator:
[tex]\[
\frac{3}{20} = 0.15
\][/tex]
(b) [tex]\(\frac{11}{-16}\)[/tex]
- For [tex]\(\frac{11}{-16}\)[/tex], perform the division while considering the negative sign:
[tex]\[
\frac{11}{-16} = -0.6875
\][/tex]
(c) [tex]\(2 \frac{21}{40}\)[/tex]
- This is a mixed number. First, convert the fractional part [tex]\(\frac{21}{40}\)[/tex] into a decimal:
[tex]\[
\frac{21}{40} = 0.525
\][/tex]
- Now add this to the integer part:
[tex]\[
2 + 0.525 = 2.525
\][/tex]
### Part 2:
2. (a) [tex]\(\frac{5}{6}\)[/tex]
- To express the fraction [tex]\(\frac{5}{6}\)[/tex] as a decimal, divide the numerator by the denominator:
[tex]\[
\frac{5}{6} = 0.8333333333333334
\][/tex]
(b) [tex]\(-\frac{23}{7}\)[/tex]
- For [tex]\(-\frac{23}{7}\)[/tex], perform the division while considering the negative sign:
[tex]\[
-\frac{23}{7} = -3.2857142857142856
\][/tex]
(c) [tex]\(-\frac{3}{11}\)[/tex]
- Similarly, for [tex]\(-\frac{3}{11}\)[/tex], perform the division with the negative sign considered:
[tex]\[
-\frac{3}{11} = -0.2727272727272727
\][/tex]
Here are the final decimal forms of the given rational numbers:
1. (a) [tex]\(\frac{3}{20} = 0.15\)[/tex]
(b) [tex]\(\frac{11}{-16} = -0.6875\)[/tex]
(c) [tex]\(2 \frac{21}{40} = 2.525\)[/tex]
2. (a) [tex]\(\frac{5}{6} = 0.8333333333333334\)[/tex]
(b) [tex]\(-\frac{23}{7} = -3.2857142857142856\)[/tex]
(c) [tex]\(-\frac{3}{11} = -0.2727272727272727\)[/tex]
