Decimal Conversion Practice Questions with Answers

Concept Explanation

Decimal conversion is the mathematical process of changing a number from one representation, such as a fraction, percentage, or binary, into a base-10 decimal format, or vice versa. This skill is fundamental for performing calculations in science, finance, and engineering, where precise values are often expressed in decimal form. The decimal system is based on powers of ten, meaning each position to the right of the decimal point represents a decreasing power of 10 (tenths, hundredths, thousandths, etc.). For instance, according to Wikipedia, the decimal system is the most widely used numeral system in modern civilization.

Converting Fractions to Decimals

To convert a fraction to a decimal, you divide the numerator (top number) by the denominator (bottom number). If the division results in a remainder that eventually reaches zero, it is a terminating decimal. If the numbers repeat infinitely, it is a repeating decimal, often denoted with a bar over the repeating digits. This process is often a precursor to simplifying expressions in algebra.

Converting Percentages to Decimals

Because "percent" means "per hundred," converting a percentage to a decimal involves dividing the number by 100. A quick shortcut is to move the decimal point two places to the left. For example, 45% becomes 0.45.

Converting Decimals to Fractions

To convert a decimal to a fraction, place the number over its corresponding power of ten based on its place value. A decimal like 0.75 is "seventy-five hundredths," written as 75/100, which can then be simplified to 3/4. Mastery of these basics is as essential as understanding exponents and powers when dealing with scientific notation.

Solved Examples

Review these step-by-step examples to understand the mechanics of decimal conversion.

1. Convert 3/8 into a decimal.

   1. Identify the division problem: 3 ÷ 8.

   2. Perform long division. 8 goes into 30 three times (24), leaving a remainder of 6.

   3. 8 goes into 60 seven times (56), leaving a remainder of 4.

   4. 8 goes into 40 exactly five times.

   5. The final result is 0.375.

2. Convert 12.5% into a decimal.

   1. Remove the percentage sign.

   2. Divide the value by 100 (12.5 / 100).

   3. Move the decimal point two places to the left.

   4. The final result is 0.125.

3. Convert 0.64 into a simplified fraction.

   1. Identify the place value. The last digit (4) is in the hundredths place.

   2. Write the decimal as a fraction: 64/100.

   3. Divide both the numerator and denominator by their greatest common divisor (4).

   4. 64 ÷ 4 = 16 and 100 ÷ 4 = 25.

   5. The simplified fraction is 16/25.

Practice Questions

Test your skills with the following decimal conversion problems, ranging from basic to advanced.

1. Convert 7/20 into a decimal.

2. Express 88% as a decimal.

3. Convert the decimal 0.005 into a fraction in simplest form.

4. Convert 5/6 into a decimal (round to three decimal places if necessary).

5. Convert 145% into a decimal.

6. Write 2.125 as a mixed number in its simplest form.

7. Convert 9/11 into a repeating decimal.

8. Express 0.0625 as a fraction in simplest form.

9. Convert 0.4% into a decimal.

10. A chemical solution is 3/16 concentrated. What is this concentration expressed as a decimal?

Answers & Explanations

1. 0.35: Divide 7 by 20. 7 ÷ 20 = 0.35. Alternatively, multiply both numerator and denominator by 5 to get 35/100.

2. 0.88: Divide 88 by 100 or move the decimal two places to the left.

3. 1/200: 0.005 is 5/1000. Dividing both by 5 yields 1/200.

4. 0.833...: Dividing 5 by 6 results in 0.8333... The 3 repeats infinitely.

5. 1.45: 145 ÷ 100 = 1.45.

6. 2 1/8: The whole number is 2. The decimal 0.125 is 125/1000. Dividing both by 125 gives 1/8. Result: 2 1/8.

7. 0.8181...: Dividing 9 by 11 shows a repeating pattern of 81.

8. 1/16: 0.0625 is 625/10000. Dividing both by 625 results in 1/16.

9. 0.004: Move the decimal two places left from 0.4. This adds two leading zeros.

10. 0.1875: Divide 3 by 16 using long division to get 0.1875. This is common in laboratory measurements similar to mean, median, and mode data sets.

Quick Quiz

Frequently Asked Questions

How do you convert a decimal to a percentage?

To convert a decimal to a percentage, multiply the decimal by 100 and add the percent symbol. This is equivalent to moving the decimal point two places to the right.

What is a repeating decimal?

A repeating decimal is a decimal representation of a number whose digits are periodic and continue infinitely. For more complex numerical patterns, students often study Khan Academy's decimal resources.

How do you convert a fraction to a decimal without a calculator?

Use long division by dividing the numerator by the denominator. If the denominator can easily be converted to 10, 100, or 1000, multiply both the top and bottom by the same factor to reach that power of ten.

Why is decimal conversion important in science?

Science requires precise measurements, and data collected in fractions or percentages must often be standardized into decimals for calculation. This is particularly true in chemistry and physics, as noted by NIST regarding the metric system.

Can all fractions be converted into terminating decimals?

No, only fractions whose denominators have prime factors of only 2 and 5 will result in terminating decimals. Other fractions, like 1/3 or 1/7, result in infinite repeating decimals.

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