QUESTION IMAGE
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.
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):
| Fraction | Decimal | Percent |
|---|---|---|
| \(\frac{47}{100}\) | 0.47 | 47% |
| \(\frac{43}{50}\) | 0.86 | 86% |
| \(\frac{1}{4}\) | 0.25 | 25% |
| \(\frac{31}{100}\) | 0.31 | 31% |
| \(\frac{13}{20}\) | 0.65 | 65% |
| \(\frac{33}{100}\) | 0.33 | 33% |
| \(\frac{2}{5}\) | 0.4 | 40% |
| \(\frac{1}{20}\) | 0.05 | 5% |
| \(\frac{87}{100}\) | 0.87 | 87% |
| \(\frac{53}{100}\) | 0.53 | 53% |
(Note: Simplify fractions where possible, e.g., \(\frac{86}{100}=\frac{43}{50}\), \(\frac{65}{100}=\frac{13}{20}\), \(\frac{25}{100}=\frac{1}{4}\), \(\frac{5}{100}=\frac{1}{20}\).)
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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):
| Fraction | Decimal | Percent |
|---|---|---|
| \(\frac{47}{100}\) | 0.47 | 47% |
| \(\frac{43}{50}\) | 0.86 | 86% |
| \(\frac{1}{4}\) | 0.25 | 25% |
| \(\frac{31}{100}\) | 0.31 | 31% |
| \(\frac{13}{20}\) | 0.65 | 65% |
| \(\frac{33}{100}\) | 0.33 | 33% |
| \(\frac{2}{5}\) | 0.4 | 40% |
| \(\frac{1}{20}\) | 0.05 | 5% |
| \(\frac{87}{100}\) | 0.87 | 87% |
| \(\frac{53}{100}\) | 0.53 | 53% |
(Note: Simplify fractions where possible, e.g., \(\frac{86}{100}=\frac{43}{50}\), \(\frac{65}{100}=\frac{13}{20}\), \(\frac{25}{100}=\frac{1}{4}\), \(\frac{5}{100}=\frac{1}{20}\).)