QUESTION IMAGE
Question
percent fraction decimal
- 1\frac{7}{8}
- 0.18
- 2% \frac{2}{100} 0.02
- \frac{17}{20}
- 120% 1\frac{2}{10} 1.2
- 135% 1\frac{35}{100} 1.35
- 0.204
- \frac{89}{200}
- 33% \frac{33}{100} 0.33
- 77% \frac{77}{100} 0.77
Let's solve each row one by one (we'll take row 1 as an example, and you can follow the same method for others):
Row 1:
Step 1: Convert the mixed fraction to an improper fraction
The mixed fraction is \(1\frac{7}{8}\). To convert it to an improper fraction, we use the formula: \(a\frac{b}{c}=\frac{a\times c + b}{c}\). So, \(1\frac{7}{8}=\frac{1\times8 + 7}{8}=\frac{15}{8}\)
Step 2: Convert the fraction to a decimal
Divide the numerator by the denominator: \(\frac{15}{8}=15\div8 = 1.875\)
Step 3: Convert the decimal to a percent
Multiply the decimal by 100 and add the percent sign: \(1.875\times100 = 187.5\%\)
Row 2:
Step 1: Convert decimal to percent
Multiply \(0.18\) by 100: \(0.18\times100 = 18\%\)
Step 2: Convert decimal to fraction
\(0.18=\frac{18}{100}=\frac{9}{50}\) (simplify by dividing numerator and denominator by 2)
Row 3:
Step 1: Convert percent to decimal
Divide \(2\%\) by 100: \(2\%\div100 = 0.02\)
Step 2: Simplify the fraction
The fraction \(\frac{2}{100}\) simplifies to \(\frac{1}{50}\) (divide numerator and denominator by 2)
Row 4:
Step 1: Convert fraction to decimal
\(\frac{17}{20}=17\div20 = 0.85\)
Step 2: Convert decimal to percent
\(0.85\times100 = 85\%\)
Row 5:
Step 1: Simplify the fraction
\(1\frac{2}{10}\) simplifies to \(1\frac{1}{5}\) (divide numerator and denominator of the fraction part by 2) or as an improper fraction \(\frac{6}{5}\) (since \(1\frac{2}{10}=\frac{1\times10 + 2}{10}=\frac{12}{10}=\frac{6}{5}\))
Step 2: Verify percent to decimal
\(120\%\div100 = 1.2\) (which matches the given decimal)
Row 6:
Step 1: Simplify the fraction
\(1\frac{35}{100}\) simplifies to \(1\frac{7}{20}\) (divide numerator and denominator of the fraction part by 5) or as an improper fraction \(\frac{27}{20}\) (since \(1\frac{35}{100}=\frac{1\times100 + 35}{100}=\frac{135}{100}=\frac{27}{20}\))
Step 2: Verify percent to decimal
\(135\%\div100 = 1.35\) (which matches the given decimal)
Row 7:
Step 1: Convert decimal to percent
\(0.204\times100 = 20.4\%\)
Step 2: Convert decimal to fraction
\(0.204=\frac{204}{1000}=\frac{51}{250}\) (divide numerator and denominator by 4)
Row 8:
Step 1: Convert fraction to decimal
\(\frac{89}{200}=89\div200 = 0.445\)
Step 2: Convert decimal to percent
\(0.445\times100 = 44.5\%\)
Row 9:
Step 1: Convert decimal to percent
\(0.33\times100 = 33\%\) (which matches the given percent)
Step 2: Simplify the fraction
\(\frac{33}{100}\) is already in simplest form (33 and 100 have no common factors other than 1)
Row 10:
Step 1: Simplify the fraction
\(\frac{77}{100}\) is already in simplest form
Step 2: Convert percent to decimal
\(77\%\div100 = 0.77\) (which matches the given decimal)
If you want the completed table, here it is:
| Percent | Fraction | Decimal |
|---|---|---|
| 18% | \(\frac{9}{50}\) | 0.18 |
| 2% | \(\frac{1}{50}\) | 0.02 |
| 85% | \(\frac{17}{20}\) | 0.85 |
| 120% | \(1\frac{1}{5}\) or \(\frac{6}{5}\) | 1.2 |
| 135% | \(1\frac{7}{20}\) or \(\frac{27}{20}\) | 1.35 |
| 20.4% | \(\frac{51}{250}\) | 0.204 |
| 44.5% | \(\frac{89}{200}\) | 0.445 |
| 33% | \(\frac{33}{100}\) | 0.33 |
| 77% | \(\frac{77}{100}\) | 0.77 |
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Let's solve each row one by one (we'll take row 1 as an example, and you can follow the same method for others):
Row 1:
Step 1: Convert the mixed fraction to an improper fraction
The mixed fraction is \(1\frac{7}{8}\). To convert it to an improper fraction, we use the formula: \(a\frac{b}{c}=\frac{a\times c + b}{c}\). So, \(1\frac{7}{8}=\frac{1\times8 + 7}{8}=\frac{15}{8}\)
Step 2: Convert the fraction to a decimal
Divide the numerator by the denominator: \(\frac{15}{8}=15\div8 = 1.875\)
Step 3: Convert the decimal to a percent
Multiply the decimal by 100 and add the percent sign: \(1.875\times100 = 187.5\%\)
Row 2:
Step 1: Convert decimal to percent
Multiply \(0.18\) by 100: \(0.18\times100 = 18\%\)
Step 2: Convert decimal to fraction
\(0.18=\frac{18}{100}=\frac{9}{50}\) (simplify by dividing numerator and denominator by 2)
Row 3:
Step 1: Convert percent to decimal
Divide \(2\%\) by 100: \(2\%\div100 = 0.02\)
Step 2: Simplify the fraction
The fraction \(\frac{2}{100}\) simplifies to \(\frac{1}{50}\) (divide numerator and denominator by 2)
Row 4:
Step 1: Convert fraction to decimal
\(\frac{17}{20}=17\div20 = 0.85\)
Step 2: Convert decimal to percent
\(0.85\times100 = 85\%\)
Row 5:
Step 1: Simplify the fraction
\(1\frac{2}{10}\) simplifies to \(1\frac{1}{5}\) (divide numerator and denominator of the fraction part by 2) or as an improper fraction \(\frac{6}{5}\) (since \(1\frac{2}{10}=\frac{1\times10 + 2}{10}=\frac{12}{10}=\frac{6}{5}\))
Step 2: Verify percent to decimal
\(120\%\div100 = 1.2\) (which matches the given decimal)
Row 6:
Step 1: Simplify the fraction
\(1\frac{35}{100}\) simplifies to \(1\frac{7}{20}\) (divide numerator and denominator of the fraction part by 5) or as an improper fraction \(\frac{27}{20}\) (since \(1\frac{35}{100}=\frac{1\times100 + 35}{100}=\frac{135}{100}=\frac{27}{20}\))
Step 2: Verify percent to decimal
\(135\%\div100 = 1.35\) (which matches the given decimal)
Row 7:
Step 1: Convert decimal to percent
\(0.204\times100 = 20.4\%\)
Step 2: Convert decimal to fraction
\(0.204=\frac{204}{1000}=\frac{51}{250}\) (divide numerator and denominator by 4)
Row 8:
Step 1: Convert fraction to decimal
\(\frac{89}{200}=89\div200 = 0.445\)
Step 2: Convert decimal to percent
\(0.445\times100 = 44.5\%\)
Row 9:
Step 1: Convert decimal to percent
\(0.33\times100 = 33\%\) (which matches the given percent)
Step 2: Simplify the fraction
\(\frac{33}{100}\) is already in simplest form (33 and 100 have no common factors other than 1)
Row 10:
Step 1: Simplify the fraction
\(\frac{77}{100}\) is already in simplest form
Step 2: Convert percent to decimal
\(77\%\div100 = 0.77\) (which matches the given decimal)
If you want the completed table, here it is:
| Percent | Fraction | Decimal |
|---|---|---|
| 18% | \(\frac{9}{50}\) | 0.18 |
| 2% | \(\frac{1}{50}\) | 0.02 |
| 85% | \(\frac{17}{20}\) | 0.85 |
| 120% | \(1\frac{1}{5}\) or \(\frac{6}{5}\) | 1.2 |
| 135% | \(1\frac{7}{20}\) or \(\frac{27}{20}\) | 1.35 |
| 20.4% | \(\frac{51}{250}\) | 0.204 |
| 44.5% | \(\frac{89}{200}\) | 0.445 |
| 33% | \(\frac{33}{100}\) | 0.33 |
| 77% | \(\frac{77}{100}\) | 0.77 |