Sure, let's go through the problem step-by-step.
### Step 1: Fill in the equivalents in the table
We are given two values: [tex]\( \frac{1}{2} \)[/tex] as a fraction and 0.34 as a decimal. We need to convert these values into their other forms (fractions, decimals, and percentages) and fill in the table.
1. Fraction [tex]\( \frac{1}{2} \)[/tex]:
- Decimal: To convert the fraction [tex]\( \frac{1}{2} \)[/tex] to a decimal, we divide 1 by 2:
[tex]\[
\frac{1}{2} = 0.5
\][/tex]
- Percentage: To convert the fraction [tex]\( \frac{1}{2} \)[/tex] to a percentage, we multiply it by 100:
[tex]\[
\frac{1}{2} \times 100 = 50\%
\][/tex]
2. Decimal 0.34:
- Fraction: To convert the decimal 0.34 to a fraction, we recognize this as 34 per 100:
[tex]\[
0.34 = \frac{34}{100} \text{ (which can be simplified, but usually kept simple as a decimal equivalent)}
\][/tex]
- Percentage: To convert the decimal 0.34 to a percentage, we multiply it by 100:
[tex]\[
0.34 \times 100 = 34\%
\][/tex]
3. For completeness, we fill out any other known equivalents in the table.
Filling these values into the table, we get:
[tex]\[
\begin{tabular}{|c|l|l|}
\hline
\text{Fractions} & \text{Decimal} & \text{Percentages} \\
\hline
\frac{1}{2} & 0.5 & 50\% \\
\hline
& 0.34 & 34\% \\
\hline
\end{tabular}
\][/tex]
### Step 2: Arrange the values in ascending order of magnitude
We now need to list the values from the table and sort them in ascending order. The values gathered from the table are:
- [tex]\( \frac{1}{2} = 0.5 \)[/tex]
- [tex]\( 0.34 \)[/tex]
- [tex]\( 50\% = 50 \)[/tex]
- [tex]\( 34\% = 34 \)[/tex]
Thus, we convert these to comparable forms first, if we haven’t yet:
- Decimal: [tex]\( \frac{1}{2} = 0.5 \)[/tex]
- [tex]\(\text{Decimals: } 0.34\)[/tex]
Next, we list all in a similar format (all decimals or all percentages). Using the decimal form for simplicity:
1. [tex]\( 0.34 \)[/tex]
2. [tex]\( 0.5 \)[/tex]
3. [tex]\( 34 \)[/tex] (which came from 34\%)
4. [tex]\( 50 \)[/tex] (which came from 50\%)
In ascending order:
1. [tex]\( 0.34 \)[/tex]
2. [tex]\( 0.5 \)[/tex]
3. [tex]\( 34 \)[/tex]
4. [tex]\( 50 \)[/tex]
So the ascending order of values is:
[tex]\[ 0.34, 0.5, 34\%, 50\% \][/tex]
Final Result:
(i)
[tex]\[
\begin{tabular}{|c|l|l|}
\hline
\text{Fractions} & \text{Decimal} & \text{Percentages} \\
\hline
\frac{1}{2} & 0.5 & 50\% \\
\hline
& 0.34 & 34\% \\
\hline
\end{tabular}
\][/tex]
(ii) Ascending order of values:
[tex]\[ 0.34, 0.5, 34, 50 \][/tex]
