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Sagot :
Sure! Let's arrange the given numbers [tex]\(54\%\)[/tex], [tex]\(\frac{4}{5}\)[/tex], [tex]\(1 \frac{1}{4}\)[/tex], and [tex]\(0.72\)[/tex] in both ascending and descending order of magnitude.
First, let's convert all these numbers to their decimal form to facilitate the comparison:
1. [tex]\(54\%\)[/tex]: A percentage represents a fraction out of 100, so [tex]\(54\% = \frac{54}{100} = 0.54\)[/tex].
2. [tex]\(\frac{4}{5}\)[/tex]: This is a simple fraction, and we convert it to decimal by dividing the numerator by the denominator:
[tex]\[\frac{4}{5} = 0.8.\][/tex]
3. [tex]\(1 \frac{1}{4}\)[/tex]: This is a mixed number. To convert it to a decimal, we first convert the fractional part [tex]\(\frac{1}{4}\)[/tex] to a decimal:
[tex]\[\frac{1}{4} = 0.25.\][/tex]
Then, add it to the whole number part:
[tex]\[1 \frac{1}{4} = 1 + 0.25 = 1.25.\][/tex]
4. [tex]\(0.72\)[/tex]: This is already in decimal form.
Now that we have all numbers in decimal form, let's list them:
- [tex]\(54\% = 0.54\)[/tex]
- [tex]\(\frac{4}{5} = 0.8\)[/tex]
- [tex]\(1 \frac{1}{4} = 1.25\)[/tex]
- [tex]\(0.72\)[/tex]
Arranging in ascending order (from smallest to largest):
1. [tex]\(0.54\)[/tex] (corresponding to [tex]\(54\%\)[/tex])
2. [tex]\(0.72\)[/tex]
3. [tex]\(0.8\)[/tex] (corresponding to [tex]\(\frac{4}{5}\)[/tex])
4. [tex]\(1.25\)[/tex] (corresponding to [tex]\(1 \frac{1}{4}\)[/tex])
Thus, in ascending order, we have:
[tex]\[0.54, 0.72, 0.8, 1.25\][/tex]
Arranging in descending order (from largest to smallest):
1. [tex]\(1.25\)[/tex] (corresponding to [tex]\(1 \frac{1}{4}\)[/tex])
2. [tex]\(0.8\)[/tex] (corresponding to [tex]\(\frac{4}{5}\)[/tex])
3. [tex]\(0.72\)[/tex]
4. [tex]\(0.54\)[/tex] (corresponding to [tex]\(54\%\)[/tex])
Thus, in descending order, we have:
[tex]\[1.25, 0.8, 0.72, 0.54\][/tex]
So, the final results are:
- Ascending order: [tex]\(0.54, 0.72, 0.8, 1.25\)[/tex]
- Descending order: [tex]\(1.25, 0.8, 0.72, 0.54\)[/tex]
First, let's convert all these numbers to their decimal form to facilitate the comparison:
1. [tex]\(54\%\)[/tex]: A percentage represents a fraction out of 100, so [tex]\(54\% = \frac{54}{100} = 0.54\)[/tex].
2. [tex]\(\frac{4}{5}\)[/tex]: This is a simple fraction, and we convert it to decimal by dividing the numerator by the denominator:
[tex]\[\frac{4}{5} = 0.8.\][/tex]
3. [tex]\(1 \frac{1}{4}\)[/tex]: This is a mixed number. To convert it to a decimal, we first convert the fractional part [tex]\(\frac{1}{4}\)[/tex] to a decimal:
[tex]\[\frac{1}{4} = 0.25.\][/tex]
Then, add it to the whole number part:
[tex]\[1 \frac{1}{4} = 1 + 0.25 = 1.25.\][/tex]
4. [tex]\(0.72\)[/tex]: This is already in decimal form.
Now that we have all numbers in decimal form, let's list them:
- [tex]\(54\% = 0.54\)[/tex]
- [tex]\(\frac{4}{5} = 0.8\)[/tex]
- [tex]\(1 \frac{1}{4} = 1.25\)[/tex]
- [tex]\(0.72\)[/tex]
Arranging in ascending order (from smallest to largest):
1. [tex]\(0.54\)[/tex] (corresponding to [tex]\(54\%\)[/tex])
2. [tex]\(0.72\)[/tex]
3. [tex]\(0.8\)[/tex] (corresponding to [tex]\(\frac{4}{5}\)[/tex])
4. [tex]\(1.25\)[/tex] (corresponding to [tex]\(1 \frac{1}{4}\)[/tex])
Thus, in ascending order, we have:
[tex]\[0.54, 0.72, 0.8, 1.25\][/tex]
Arranging in descending order (from largest to smallest):
1. [tex]\(1.25\)[/tex] (corresponding to [tex]\(1 \frac{1}{4}\)[/tex])
2. [tex]\(0.8\)[/tex] (corresponding to [tex]\(\frac{4}{5}\)[/tex])
3. [tex]\(0.72\)[/tex]
4. [tex]\(0.54\)[/tex] (corresponding to [tex]\(54\%\)[/tex])
Thus, in descending order, we have:
[tex]\[1.25, 0.8, 0.72, 0.54\][/tex]
So, the final results are:
- Ascending order: [tex]\(0.54, 0.72, 0.8, 1.25\)[/tex]
- Descending order: [tex]\(1.25, 0.8, 0.72, 0.54\)[/tex]
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