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fraction, decimal, percent table. first row: 3/100, 0.03, 3%. second ro…

Question

fraction, decimal, percent table. first row: 3/100, 0.03, 3%. second row: empty, 0.47, empty. third row: empty, empty, 86%. fourth row: empty, 0.25, empty. fifth row: 31/100, empty, empty. sixth row: empty, empty, 65%. seventh row: 33/100, empty, empty. eighth row: 2/5, empty, empty. ninth row: empty, 0.05, empty. tenth row: empty, empty, 87%. eleventh row: empty, 0.53, empty.

Explanation:

Response

To solve the table, we use the relationships:

  • Fraction to Decimal: Divide numerator by denominator.
  • Decimal to Percent: Multiply by \(100\) (or move decimal 2 places right).
  • Percent to Decimal: Divide by \(100\) (or move decimal 2 places left).
  • Decimal to Fraction: Use place value (e.g., \(0.47=\frac{47}{100}\)).
Row 2 (Decimal = 0.47)

Step1: Decimal to Fraction

\(0.47 = \frac{47}{100}\) (since 0.47 is 47 hundredths).

Step2: Decimal to Percent

\(0.47 \times 100 = 47\%\).

Row 3 (Percent = 86%)

Step1: Percent to Decimal

\(86\% \div 100 = 0.86\).

Step2: Decimal to Fraction

\(0.86 = \frac{86}{100}=\frac{43}{50}\) (simplify by dividing numerator/denominator by 2).

Row 4 (Decimal = 0.25)

Step1: Decimal to Fraction

\(0.25 = \frac{25}{100}=\frac{1}{4}\) (simplify by dividing by 25).

Step2: Decimal to Percent

\(0.25 \times 100 = 25\%\).

Row 5 (Fraction = \(\frac{31}{100}\))

Step1: Fraction to Decimal

\(\frac{31}{100}=31\div100 = 0.31\).

Step2: Decimal to Percent

\(0.31 \times 100 = 31\%\).

Row 6 (Percent = 65%)

Step1: Percent to Decimal

\(65\% \div 100 = 0.65\).

Step2: Decimal to Fraction

\(0.65 = \frac{65}{100}=\frac{13}{20}\) (simplify by dividing by 5).

Row 7 (Fraction = \(\frac{33}{100}\))

Step1: Fraction to Decimal

\(\frac{33}{100}=33\div100 = 0.33\).

Step2: Decimal to Percent

\(0.33 \times 100 = 33\%\).

Row 8 (Fraction = \(\frac{2}{5}\))

Step1: Fraction to Decimal

\(\frac{2}{5}=2\div5 = 0.4\).

Step2: Decimal to Percent

\(0.4 \times 100 = 40\%\).

Row 9 (Decimal = 0.05)

Step1: Decimal to Fraction

\(0.05 = \frac{5}{100}=\frac{1}{20}\) (simplify by dividing by 5).

Step2: Decimal to Percent

\(0.05 \times 100 = 5\%\).

Row 10 (Percent = 87%)

Step1: Percent to Decimal

\(87\% \div 100 = 0.87\).

Step2: Decimal to Fraction

\(0.87 = \frac{87}{100}\) (87 and 100 have no common factors besides 1).

Row 11 (Decimal = 0.53)

Step1: Decimal to Fraction

\(0.53 = \frac{53}{100}\) (53 hundredths).

Step2: Decimal to Percent

\(0.53 \times 100 = 53\%\).

Completed Table (Key Entries):
FractionDecimalPercent
\(\frac{47}{100}\)0.4747%
\(\frac{43}{50}\)0.8686%
\(\frac{1}{4}\)0.2525%
\(\frac{31}{100}\)0.3131%
\(\frac{13}{20}\)0.6565%
\(\frac{33}{100}\)0.3333%
\(\frac{2}{5}\)0.440%
\(\frac{1}{20}\)0.055%
\(\frac{87}{100}\)0.8787%
\(\frac{53}{100}\)0.5353%

(Note: Simplify fractions where possible, e.g., \(\frac{86}{100}=\frac{43}{50}\), \(\frac{65}{100}=\frac{13}{20}\), \(\frac{25}{100}=\frac{1}{4}\), \(\frac{5}{100}=\frac{1}{20}\).)

Answer:

To solve the table, we use the relationships:

  • Fraction to Decimal: Divide numerator by denominator.
  • Decimal to Percent: Multiply by \(100\) (or move decimal 2 places right).
  • Percent to Decimal: Divide by \(100\) (or move decimal 2 places left).
  • Decimal to Fraction: Use place value (e.g., \(0.47=\frac{47}{100}\)).
Row 2 (Decimal = 0.47)

Step1: Decimal to Fraction

\(0.47 = \frac{47}{100}\) (since 0.47 is 47 hundredths).

Step2: Decimal to Percent

\(0.47 \times 100 = 47\%\).

Row 3 (Percent = 86%)

Step1: Percent to Decimal

\(86\% \div 100 = 0.86\).

Step2: Decimal to Fraction

\(0.86 = \frac{86}{100}=\frac{43}{50}\) (simplify by dividing numerator/denominator by 2).

Row 4 (Decimal = 0.25)

Step1: Decimal to Fraction

\(0.25 = \frac{25}{100}=\frac{1}{4}\) (simplify by dividing by 25).

Step2: Decimal to Percent

\(0.25 \times 100 = 25\%\).

Row 5 (Fraction = \(\frac{31}{100}\))

Step1: Fraction to Decimal

\(\frac{31}{100}=31\div100 = 0.31\).

Step2: Decimal to Percent

\(0.31 \times 100 = 31\%\).

Row 6 (Percent = 65%)

Step1: Percent to Decimal

\(65\% \div 100 = 0.65\).

Step2: Decimal to Fraction

\(0.65 = \frac{65}{100}=\frac{13}{20}\) (simplify by dividing by 5).

Row 7 (Fraction = \(\frac{33}{100}\))

Step1: Fraction to Decimal

\(\frac{33}{100}=33\div100 = 0.33\).

Step2: Decimal to Percent

\(0.33 \times 100 = 33\%\).

Row 8 (Fraction = \(\frac{2}{5}\))

Step1: Fraction to Decimal

\(\frac{2}{5}=2\div5 = 0.4\).

Step2: Decimal to Percent

\(0.4 \times 100 = 40\%\).

Row 9 (Decimal = 0.05)

Step1: Decimal to Fraction

\(0.05 = \frac{5}{100}=\frac{1}{20}\) (simplify by dividing by 5).

Step2: Decimal to Percent

\(0.05 \times 100 = 5\%\).

Row 10 (Percent = 87%)

Step1: Percent to Decimal

\(87\% \div 100 = 0.87\).

Step2: Decimal to Fraction

\(0.87 = \frac{87}{100}\) (87 and 100 have no common factors besides 1).

Row 11 (Decimal = 0.53)

Step1: Decimal to Fraction

\(0.53 = \frac{53}{100}\) (53 hundredths).

Step2: Decimal to Percent

\(0.53 \times 100 = 53\%\).

Completed Table (Key Entries):
FractionDecimalPercent
\(\frac{47}{100}\)0.4747%
\(\frac{43}{50}\)0.8686%
\(\frac{1}{4}\)0.2525%
\(\frac{31}{100}\)0.3131%
\(\frac{13}{20}\)0.6565%
\(\frac{33}{100}\)0.3333%
\(\frac{2}{5}\)0.440%
\(\frac{1}{20}\)0.055%
\(\frac{87}{100}\)0.8787%
\(\frac{53}{100}\)0.5353%

(Note: Simplify fractions where possible, e.g., \(\frac{86}{100}=\frac{43}{50}\), \(\frac{65}{100}=\frac{13}{20}\), \(\frac{25}{100}=\frac{1}{4}\), \(\frac{5}{100}=\frac{1}{20}\).)