Additional Practice 1-3 Decimals To Thousandths

Mastering Decimals to Thousandths: Extensive Practice and Techniques

Decimals are a fundamental part of mathematics, appearing in various fields from everyday finances to advanced scientific calculations. A strong understanding of decimals, particularly to the thousandths place, is crucial for success in many academic and professional pursuits. This comprehensive guide provides extensive practice problems, helpful strategies, and insightful explanations to solidify your understanding of decimals to thousandths. We'll cover addition, subtraction, comparison, and rounding, ensuring a well-rounded approach to mastering this essential skill.

Understanding Decimal Place Value

Before diving into practice problems, let's revisit the concept of decimal place value. The decimal point separates the whole number part from the fractional part of a number. To the right of the decimal point, we have tenths, hundredths, and thousandths places, each representing progressively smaller fractions of one.

• Tenths: The first digit to the right of the decimal point represents tenths (1/10).
• Hundredths: The second digit represents hundredths (1/100).
• Thousandths: The third digit represents thousandths (1/1000).

For example, in the number 2.345, '2' is the whole number, '3' is in the tenths place (3/10), '4' is in the hundredths place (4/100), and '5' is in the thousandths place (5/1000).

Addition of Decimals to Thousandths

Adding decimals requires careful alignment of the decimal points. This ensures that you are adding corresponding place values correctly.

Steps for Adding Decimals:

1. Write the numbers vertically: Align the decimal points. Add zeros as placeholders if necessary to ensure all numbers have the same number of digits after the decimal point.
2. Add the numbers as you would whole numbers: Starting from the rightmost column (thousandths), add the digits in each column.
3. Carry over: If the sum in any column is 10 or more, carry over the tens digit to the next column to the left.
4. Place the decimal point: Place the decimal point in the sum directly below the decimal points in the numbers being added.

Example:

Add 12.345, 5.67, and 0.987.

  12.345
   5.670
 + 0.987
------
  19.002

Practice Problems (Addition):

1. 3.145 + 2.789 + 1.001 = ?
2. 15.67 + 0.089 + 2.3456 = ?
3. 0.456 + 0.87 + 0.999 = ?
4. 234.567 + 87.9 + 12.0034 = ?
5. 1.000 + 0.999 + 0.001 = ?

Subtraction of Decimals to Thousandths

Subtracting decimals follows a similar process to addition, focusing on aligning the decimal points.

Steps for Subtracting Decimals:

1. Write the numbers vertically: Align the decimal points. Add zeros as placeholders if necessary.
2. Subtract the numbers: Start from the rightmost column (thousandths) and subtract the digits in each column.
3. Borrowing: If a digit in the minuend (top number) is smaller than the corresponding digit in the subtrahend (bottom number), you need to borrow from the digit to its left.
4. Place the decimal point: Place the decimal point in the difference directly below the decimal points in the numbers being subtracted.

Example:

Subtract 3.456 from 12.789.

  12.789
 -  3.456
------
   9.333

Practice Problems (Subtraction):

1. 5.789 - 2.345 = ?
2. 10.000 - 3.456 = ?
3. 8.976 - 4.567 = ?
4. 123.45 - 98.765 = ?
5. 0.789 - 0.345 = ?

Comparison of Decimals to Thousandths

Comparing decimals involves determining which number is greater or smaller. Start by comparing the whole number parts. If the whole number parts are the same, compare the digits in the tenths place, then hundredths, and finally thousandths.

Example:

Compare 2.345 and 2.350.

Both numbers have the same whole number part (2). Comparing the tenths place, both are 3. Comparing the hundredths place, 4 is less than 5. Therefore, 2.345 < 2.350.

Practice Problems (Comparison):

1. Compare 3.145 and 3.146.
2. Compare 0.999 and 1.000.
3. Compare 12.345 and 12.34.
4. Compare 0.001 and 0.010.
5. Compare 9.999 and 10.000.

Rounding Decimals to Thousandths

Rounding decimals involves approximating a number to a specific place value. To round to the thousandths place, look at the digit in the ten-thousandths place (the fourth digit to the right of the decimal point).

• If the ten-thousandths digit is 5 or greater: Round the thousandths digit up (add 1).
• If the ten-thousandths digit is less than 5: Keep the thousandths digit as it is.

Example:

Round 3.14159 to the thousandths place.

The ten-thousandths digit is 5, so we round the thousandths digit (1) up to 2. The rounded number is 3.142.

Practice Problems (Rounding):

1. Round 2.7895 to the thousandths place.
2. Round 1.0004 to the thousandths place.
3. Round 9.9999 to the thousandths place.
4. Round 0.0005 to the thousandths place.
5. Round 123.45678 to the thousandths place.

Advanced Practice and Word Problems

To further solidify your understanding, let's tackle some more complex problems involving decimals to thousandths.

Problem 1: A carpenter needs three pieces of wood measuring 2.345 meters, 1.789 meters, and 0.987 meters. What is the total length of wood needed?

Problem 2: A chemist has 10.000 grams of a solution. After conducting an experiment, 3.456 grams remain. How many grams of the solution were used in the experiment?

Problem 3: Three runners completed a race with times of 12.345 seconds, 12.350 seconds, and 12.340 seconds. Arrange their times from fastest to slowest.

Problem 4: A rectangular prism has dimensions of 2.345 cm, 1.789 cm, and 0.987 cm. Calculate its volume (volume = length x width x height). Round your answer to the thousandths place.

Problem 5: Sarah bought three items costing $12.345, $5.678, and $0.987. If she paid with a $20 bill, how much change did she receive?

These word problems challenge you to apply your knowledge of decimal addition, subtraction, and rounding within a real-world context. Remember to carefully read each problem, identify the relevant operations, and perform the calculations accurately.

Conclusion: Mastering Decimals to Thousandths

This extensive guide provided comprehensive practice in adding, subtracting, comparing, and rounding decimals to the thousandths place. Through consistent practice and a solid understanding of place value, you can confidently tackle more complex problems involving decimals. Remember, practice is key! The more you work with decimals, the more comfortable and proficient you will become. By mastering decimals to thousandths, you build a strong foundation for future mathematical endeavors and real-world applications. Continue practicing and refining your skills, and you will find yourself adept at handling decimals with ease and accuracy.