Introduction

Decimal place values are an important part of understanding how to represent numbers that are not whole. In decimal numbers, each place to the right of the decimal point represents a fraction of a whole number. This is a fundamental concept for understanding money, measurements, and many real-world applications.

Key Concepts

  1. Decimal Point: Separates the whole number part from the fractional part of a number.
  2. Place Values: Each digit after the decimal point has a specific place value:
  • The first place after the decimal is tenths ( \frac{1}{10}
    ).
  • The second place is hundredths ( \frac{1}{100}
    ).
  • The third place is thousandths ( \frac{1}{1000}
    ).
  1. Rounding Decimals: Decimals can be rounded to a specified number of decimal places, similar to rounding whole numbers.

Understanding decimal place values allows students to compare, round, and manipulate decimal numbers with ease.

Decimal Place Values: Questions

Level 1: Easy

Identify the place value of the underlined digit in the following numbers:

  1. 5.\underline{6}7
  2. 9.3\underline{4}2
  3. 1.\underline{2}58
  4. 7.\underline{3}96
  5. 4.5\underline{1}7
  6. 2.7\underline{9}4
  7. 3.\underline{8}56
  8. 8.\underline{7}23
  9. 9.4\underline{0}5
  10. 6.3\underline{2}1

Convert the following decimals into fractions:

  1. 0.3
  2. 0.6
  3. 0.9
  4. 0.2
  5. 0.75
  6. 0.4
  7. 0.5
  8. 0.08
  9. 0.12
  10. 0.45

Level 2: Medium

Round the following decimals to 1 decimal place:

  1. 6.78
  2. 5.23
  3. 4.67
  4. 7.91
  5. 3.46
  6. 2.89
  7. 8.54
  8. 9.76
  9. 1.43
  10. 6.35

Round the following decimals to 2 decimal places:

  1. 3.678
  2. 7.912
  3. 5.289
  4. 9.764
  5. 6.351
  6. 4.672
  7. 8.546
  8. 1.439
  9. 2.891
  10. 5.987

Level 3: Hard

Compare the following decimals and write “<” or “>” between them:

  1. 6.789 \ \underline{\ \ }\ 6.798
  2. 7.123 \ \underline{\ \ }\ 7.12
  3. 9.456 \ \underline{\ \ }\ 9.465
  4. 4.678 \ \underline{\ \ }\ 4.687
  5. 5.764 \ \underline{\ \ }\ 5.743
  6. 3.456 \ \underline{\ \ }\ 3.465
  7. 8.999 \ \underline{\ \ }\ 8.9991
  8. 2.345 \ \underline{\ \ }\ 2.354
  9. 7.890 \ \underline{\ \ }\ 7.89
  10. 6.432 \ \underline{\ \ }\ 6.431

Add the following decimals:

  1. 4.67 + 3.58
  2. 7.89 + 6.75
  3. 5.32 + 9.47
  4. 8.23 + 4.68
  5. 3.56 + 7.89
  6. 6.78 + 5.34
  7. 9.12 + 2.89
  8. 8.34 + 1.45
  9. 4.56 + 3.78
  10. 6.54 + 7.23

Answers with Explanations

Level 1: Easy

Identify the place value of the underlined digit:

  1. 5.\underline{6}7
    — The underlined digit is in the tenths place.
  2. 9.3\underline{4}2
    — The underlined digit is in the hundredths place.
  3. 1.\underline{2}58
    — The underlined digit is in the tenths place.
  4. 7.\underline{3}96
    — The underlined digit is in the tenths place.
  5. 4.5\underline{1}7
    — The underlined digit is in the hundredths place.
  6. 2.7\underline{9}4
    — The underlined digit is in the tenths place.
  7. 3.\underline{8}56
    — The underlined digit is in the tenths place.
  8. 8.\underline{7}23
    — The underlined digit is in the tenths place.
  9. 9.4\underline{0}5
    — The underlined digit is in the hundredths place.
  10. 6.3\underline{2}1
    — The underlined digit is in the hundredths place.

Convert the following decimals into fractions:

  1. 0.3 = \frac{3}{10}
  2. 0.6 = \frac{6}{10} = \frac{3}{5}
  3. 0.9 = \frac{9}{10}
  4. 0.2 = \frac{2}{10} = \frac{1}{5}
  5. 0.75 = \frac{75}{100} = \frac{3}{4}
  6. 0.4 = \frac{4}{10} = \frac{2}{5}
  7. 0.5 = \frac{5}{10} = \frac{1}{2}
  8. 0.08 = \frac{8}{100} = \frac{2}{25}
  9. 0.12 = \frac{12}{100} = \frac{3}{25}
  10. 0.45 = \frac{45}{100} = \frac{9}{20}

Level 2: Medium

Round the following decimals to 1 decimal place:

  1. 6.78 \approx 6.8
  2. 5.23 \approx 5.2
  3. 4.67 \approx 4.7
  4. 7.91 \approx 7.9
  5. 3.46 \approx 3.5
  6. 2.89 \approx 2.9
  7. 8.54 \approx 8.5
  8. 9.76 \approx 9.8
  9. 1.43 \approx 1.4
  10. 6.35 \approx 6.4

Round the following decimals to 2 decimal places:

  1. 3.678 \approx 3.68
  2. 7.912 \approx 7.91
  3. 5.289 \approx 5.29
  4. 9.764 \approx 9.76
  5. 6.351 \approx 6.35
  6. 4.672 \approx 4.67
  7. 8.546 \approx 8.55
  8. 1.439 \approx 1.44
  9. 2.891 \approx 2.89
  10. 5.987 \approx 5.99

Level 3: Hard

Compare the following decimals:

  1. 6.789 < 6.798
  2. 7.123 > 7.12
  3. 9.456 < 9.465
  4. 4.678 < 4.687
  5. 5.764 > 5.743
  6. 3.456 < 3.465
  7. $$ 8.999 < 8.

9991 $$

  1. 2.345 < 2.354
  2. 7.890 = 7.89
  3. 6.432 > 6.431

Add the following decimals:

  1. 4.67 + 3.58 = 8.25
  2. 7.89 + 6.75 = 14.64
  3. 5.32 + 9.47 = 14.79
  4. 8.23 + 4.68 = 12.91
  5. 3.56 + 7.89 = 11.45
  6. 6.78 + 5.34 = 12.12
  7. 9.12 + 2.89 = 12.01
  8. 8.34 + 1.45 = 9.79
  9. 4.56 + 3.78 = 8.34
  10. 6.54 + 7.23 = 13.77

Explanation of Key Steps

  • Identifying Place Value: The position of a digit relative to the decimal point defines its place value. For example, in 3.45
    , the digit 4
    is in the tenths place, and 5
    is in the hundredths place.
  • Converting Decimals to Fractions: Decimals can be easily converted to fractions by placing the decimal over the appropriate power of 10. For example, 0.75
    becomes \frac{75}{100}
    , which simplifies to \frac{3}{4}
    .
  • Rounding Decimals: Rounding decimals involves looking at the digit to the right of the place you’re rounding to. If it’s 5 or more, round up. Otherwise, round down.
  • Comparing Decimals: Start from the leftmost digit and compare the corresponding digits in both numbers. The first difference determines the greater or smaller number.
  • Adding Decimals: When adding decimals, align the decimal points vertically and add the digits in the corresponding place values.

This comprehensive set of exercises covers understanding, rounding, comparing, and adding decimal numbers, progressively building students’ confidence in working with decimals.