Change The Decimal 0.0112 To A Fraction.A. $\frac{112}{100,000}$ B. $\frac{112}{100}$ C. $\frac{112}{1,000}$ D. $\frac{112}{10,000}$

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Understanding Decimals and Fractions

In mathematics, decimals and fractions are two ways to represent a part of a whole. Decimals are numbers that have a decimal point, while fractions are numbers that have a numerator and a denominator. Converting decimals to fractions is an essential skill in mathematics, as it helps us to simplify and compare numbers.

What is a Decimal?

A decimal is a number that has a decimal point, which separates the whole number part from the fractional part. For example, 0.0112 is a decimal number. It has a whole number part (0) and a fractional part (0.0112).

What is a Fraction?

A fraction is a number that has a numerator and a denominator. The numerator is the top number, and the denominator is the bottom number. For example, 112/100 is a fraction. It has a numerator of 112 and a denominator of 100.

Converting Decimals to Fractions

To convert a decimal to a fraction, we need to follow these steps:

  1. Identify the decimal: We need to identify the decimal number that we want to convert to a fraction. In this case, the decimal number is 0.0112.
  2. Count the number of decimal places: We need to count the number of decimal places in the decimal number. In this case, the decimal number 0.0112 has 4 decimal places.
  3. Multiply the numerator and denominator by 10: We need to multiply the numerator and denominator by 10 for each decimal place. In this case, we need to multiply the numerator and denominator by 10 four times.
  4. Simplify the fraction: We need to simplify the fraction by dividing the numerator and denominator by their greatest common divisor (GCD).

Applying the Steps to the Decimal 0.0112

Let's apply the steps to the decimal 0.0112:

  1. Identify the decimal: The decimal number is 0.0112.

  2. Count the number of decimal places: The decimal number 0.0112 has 4 decimal places.

  3. Multiply the numerator and denominator by 10: We need to multiply the numerator and denominator by 10 four times. This gives us:

    112 × 10 × 10 × 10 × 10 = 112,000 100 × 10 × 10 × 10 = 10,000

    So, the fraction becomes 112,000/10,000.

  4. Simplify the fraction: We can simplify the fraction by dividing the numerator and denominator by their GCD, which is 1,000. This gives us:

    112,000 ÷ 1,000 = 112 10,000 ÷ 1,000 = 10

    So, the simplified fraction is 112/10.

Conclusion

In conclusion, converting decimals to fractions is an essential skill in mathematics. By following the steps outlined above, we can convert the decimal 0.0112 to a fraction. The correct answer is A. 11210,000\frac{112}{10,000}.

Why is this the correct answer?

This is the correct answer because we multiplied the numerator and denominator by 10 four times to get 112,000/10,000, and then simplified the fraction by dividing the numerator and denominator by their GCD, which is 1,000. This gives us 112/10, which is equivalent to 112/10,000.

What are the other options?

The other options are:

  • B. 112100\frac{112}{100}: This is not the correct answer because we multiplied the numerator and denominator by 10 four times to get 112,000/10,000, not 112/100.
  • C. 1121,000\frac{112}{1,000}: This is not the correct answer because we multiplied the numerator and denominator by 10 four times to get 112,000/10,000, not 112/1,000.
  • D. 11210\frac{112}{10}: This is not the correct answer because we simplified the fraction by dividing the numerator and denominator by their GCD, which is 1,000, to get 112/10, not 112/10.

What is the importance of converting decimals to fractions?

Converting decimals to fractions is an essential skill in mathematics because it helps us to:

  • Simplify numbers: Converting decimals to fractions helps us to simplify numbers and make them easier to work with.
  • Compare numbers: Converting decimals to fractions helps us to compare numbers and determine which one is larger or smaller.
  • Perform calculations: Converting decimals to fractions helps us to perform calculations and solve problems more easily.

Conclusion

Q: What is the difference between a decimal and a fraction?

A: A decimal is a number that has a decimal point, while a fraction is a number that has a numerator and a denominator. For example, 0.0112 is a decimal number, while 112/100 is a fraction.

Q: How do I convert a decimal to a fraction?

A: To convert a decimal to a fraction, you need to follow these steps:

  1. Identify the decimal: Identify the decimal number that you want to convert to a fraction.
  2. Count the number of decimal places: Count the number of decimal places in the decimal number.
  3. Multiply the numerator and denominator by 10: Multiply the numerator and denominator by 10 for each decimal place.
  4. Simplify the fraction: Simplify the fraction by dividing the numerator and denominator by their greatest common divisor (GCD).

Q: What is the greatest common divisor (GCD)?

A: The greatest common divisor (GCD) is the largest number that divides both the numerator and the denominator of a fraction without leaving a remainder.

Q: How do I simplify a fraction?

A: To simplify a fraction, you need to divide the numerator and denominator by their greatest common divisor (GCD).

Q: What is the importance of converting decimals to fractions?

A: Converting decimals to fractions is an essential skill in mathematics because it helps us to:

  • Simplify numbers: Converting decimals to fractions helps us to simplify numbers and make them easier to work with.
  • Compare numbers: Converting decimals to fractions helps us to compare numbers and determine which one is larger or smaller.
  • Perform calculations: Converting decimals to fractions helps us to perform calculations and solve problems more easily.

Q: Can I convert a decimal to a fraction using a calculator?

A: Yes, you can convert a decimal to a fraction using a calculator. Most calculators have a function that allows you to convert a decimal to a fraction.

Q: What are some common mistakes to avoid when converting decimals to fractions?

A: Some common mistakes to avoid when converting decimals to fractions include:

  • Not counting the number of decimal places: Make sure to count the number of decimal places in the decimal number.
  • Not multiplying the numerator and denominator by 10: Make sure to multiply the numerator and denominator by 10 for each decimal place.
  • Not simplifying the fraction: Make sure to simplify the fraction by dividing the numerator and denominator by their greatest common divisor (GCD).

Q: Can I convert a decimal to a fraction using a computer program?

A: Yes, you can convert a decimal to a fraction using a computer program. Many computer programs, such as Excel and Python, have functions that allow you to convert a decimal to a fraction.

Q: What are some real-world applications of converting decimals to fractions?

A: Some real-world applications of converting decimals to fractions include:

  • Cooking: Converting decimals to fractions is useful in cooking when you need to measure ingredients in fractions.
  • Building: Converting decimals to fractions is useful in building when you need to measure materials in fractions.
  • Science: Converting decimals to fractions is useful in science when you need to measure quantities in fractions.

Conclusion

In conclusion, converting decimals to fractions is an essential skill in mathematics. By following the steps outlined above, you can convert a decimal to a fraction. Remember to count the number of decimal places, multiply the numerator and denominator by 10, and simplify the fraction by dividing the numerator and denominator by their greatest common divisor (GCD).