Question

convert 0.5 (theres a bar above 5) to a fraction.
Answer
convert 0.14 (theres a bar over 14) to a fraction.
Answer
convert 16/50 to a decimal and a percentage.
Answer
convert 10% to a decimal and a fraction.
Answer
convert 0.02 (theres a bar over 02) to a fraction.
Answered by GPT-4o mini
The decimal \(0.5\) with a bar over the \(5\) represents a repeating decimal: \(0.555...\).

To convert this repeating decimal to a fraction, you can follow these steps:

1. **Let \(x\) equal the repeating decimal**:
\[
x = 0.555...
\]

2. **Multiply both sides by 10** (to shift the decimal point one place to the right):
\[
10x = 5.555...
\]

3. **Now, subtract the original \(x\) from this equation**:
\[
10x - x = 5.555... - 0.555...
\]
\[
9x = 5
\]

4. **Solve for \(x\)**:
\[
x = \frac{5}{9}
\]

Thus, the fraction representation of \(0.5\) (with a bar over the \(5\)) is \(\frac{5}{9}\).
Answered by GPT-4o mini
To convert the repeating decimal \(0.14\) with a bar over \(14\) (which represents \(0.141414...\)) to a fraction, you can follow these steps:

1. **Let \(x\) equal the repeating decimal**:
\[
x = 0.141414...
\]

2. **Multiply both sides by 100** (to shift the decimal point two places to the right, because the repeating part has 2 digits):
\[
100x = 14.141414...
\]

3. **Now, subtract the original \(x\) from this equation**:
\[
100x - x = 14.141414... - 0.141414...
\]
\[
99x = 14
\]

4. **Solve for \(x\)**:
\[
x = \frac{14}{99}
\]

Thus, the fraction representation of \(0.14\) (with a bar over \(14\)) is \(\frac{14}{99}\).
Answered by GPT-4o mini
To convert the fraction \(\frac{16}{50}\) to a decimal and a percentage, follow these steps:

### Decimal Conversion

1. **Divide the numerator by the denominator**:
\[
16 \div 50 = 0.32
\]

### Percentage Conversion

1. **Convert the decimal to a percentage** by multiplying by 100:
\[
0.32 \times 100 = 32\%
\]

### Summary

- The decimal representation of \(\frac{16}{50}\) is \(0.32\).
- The percentage representation of \(\frac{16}{50}\) is \(32\%\).
Answered by GPT-4o mini
To convert \(10\%\) to a decimal and a fraction, follow these steps:

### Decimal Conversion

1. **Divide the percentage by 100**:
\[
10\% = \frac{10}{100} = 0.10
\]

### Fraction Conversion

1. **Express \(10\%\) as a fraction**:
\[
10\% = \frac{10}{100}
\]

2. **Simplify the fraction**:
\[
\frac{10}{100} = \frac{1}{10}
\]

### Summary

- The decimal representation of \(10\%\) is \(0.10\).
- The fraction representation of \(10\%\) is \(\frac{1}{10}\).
Answered by GPT-4o mini
To convert the repeating decimal \(0.02\) with a bar over \(02\) (which represents \(0.020202...\)) to a fraction, follow these steps:

1. **Let \(x\) equal the repeating decimal**:
\[
x = 0.020202...
\]

2. **Multiply both sides by 100** (to shift the decimal point two places to the right, as the repeating part has 2 digits):
\[
100x = 2.020202...
\]

3. **Now, subtract the original \(x\) from this equation**:
\[
100x - x = 2.020202... - 0.020202...
\]
\[
99x = 2
\]

4. **Solve for \(x\)**:
\[
x = \frac{2}{99}
\]

Thus, the fraction representation of \(0.02\) with a bar over \(02\) is \(\frac{2}{99}\).