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percent fraction decimal 1. 1\\frac{7}{8} 2. 0.18 3. 2% \\frac{2}{100} …

Question

percent fraction decimal

  1. 1\frac{7}{8}
  2. 0.18
  3. 2% \frac{2}{100} 0.02
  4. \frac{17}{20}
  5. 120% 1\frac{2}{10} 1.2
  6. 135% 1\frac{35}{100} 1.35
  7. 0.204
  8. \frac{89}{200}
  9. 33% \frac{33}{100} 0.33
  10. 77% \frac{77}{100} 0.77

Explanation:

Response

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:

PercentFractionDecimal
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

Answer:

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:

PercentFractionDecimal
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