3.12 is a decimal representation of the fraction (\frac{312}{100}). Understanding the concept of decimals is crucial for performing various mathematical operations and interpreting numerical data in everyday life. This article aims to provide a comprehensive guide to working with 3.12 as a decimal, covering topics such as its conversion to other forms, common mistakes to avoid, and practical applications.
3.12 can be expressed as a fraction by multiplying the decimal by 100, which gives us:
$$3.12 \times 100 = \frac{312}{100}$$
Therefore, 3.12 is equivalent to the fraction (\frac{312}{100}).
To convert 3.12 to a percentage, we need to multiply the decimal by 100 and add the % symbol. Hence,
$$3.12 \times 100 = 312%$$
Thus, 3.12 is equal to 312%.
When working with decimals, several common mistakes should be avoided:
3.12 finds applications in various fields, including:
To add decimals, align the numbers by their decimal points and perform addition as usual.
3.12
+ 1.45
-----
4.57
Similar to addition, align the decimals and subtract as normal.
3.12
- 1.45
-----
1.67
Multiply the numbers as with whole numbers, remembering to count the decimal places in the answer.
3.12
x 1.45
-----
4.536
Long division is performed until the desired level of precision is reached.
1.45
3.12
-----
2.155
The following table compares the representations of 3.12 as a fraction, decimal, and percentage:
Fraction | Decimal | Percentage |
---|---|---|
(\frac{312}{100}) | 3.12 | 312% |
Fraction | Decimal |
---|---|
(\frac{1}{2}) | 0.5 |
(\frac{1}{4}) | 0.25 |
(\frac{3}{4}) | 0.75 |
(\frac{1}{5}) | 0.2 |
(\frac{1}{10}) | 0.1 |
Decimal | Fraction |
---|---|
0.5 | (\frac{1}{2}) |
0.25 | (\frac{1}{4}) |
0.75 | (\frac{3}{4}) |
0.2 | (\frac{1}{5}) |
0.1 | (\frac{1}{10}) |
Decimal | Percentage |
---|---|
0.5 | 50% |
0.25 | 25% |
0.75 | 75% |
0.2 | 20% |
0.1 | 10% |
"My annual salary was \$31,200, which equates to \$3.12 per hour," stated Kelly. After receiving a 10% raise, her hourly wage increased to \$3.432, which is a (\frac{312}{100} \times 1.10 = 343.2) hourly wage in decimal form. This highlights how decimals are used in salary calculations.
In a laboratory experiment, the mass of a sample was measured as 0.0312 grams. Expressing this measurement in scientific notation, we get (3.12 \times 10^{-2}) grams. Decimals are essential for accurately representing measurements in scientific research.
The current ratio, a measure of a company's financial liquidity, is calculated as current assets divided by current liabilities. For a company with current assets of \$1,200,000 and current liabilities of \$600,000, the current ratio is (1,200,000 / 600,000 = 2), or 200% in decimal form. Decimals are used to express financial ratios in a clear and concise manner.
Understanding and manipulating decimals, including 3.12, is crucial in various domains. By avoiding common mistakes, following the step-by-step approach, and utilizing conversion tables, individuals can confidently work with decimals. The applications of decimals are vast, ranging from finance and science to engineering and everyday life.
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