Class 3 Mathematics: Length Conversion (Long and Short)

Curriculum Context and Fundamental Principles

  • Curriculum Level and Unit Details:

    • Subject: Class 3 Mathematics

    • Chapter: Long and Short (Meters to Centimeters)

    • Focus: Length conversion from standard meters (m\text{m}) to centimeters (cm\text{cm})

  • The Fundamental Metric Equivalence:

    • 1 meter (m)=100 centimeters (cm)1\,\text{meter (m)} = 100\,\text{centimeters (cm)}

  • The Golden Rule for Conversion:

    • To convert any value from meters (m\text{m}) to centimeters (cm\text{cm}), always multiply the measurement by 100100.

    • Alternatively, write or append two zeros (0000) at the end of the number representing whole meters.

Step-by-Step Conversion Procedures and Worked Examples

  • Procedure 1: Converting Whole Meters to Centimeters:

    • Rule: Take the numerical quantity of meters and multiply it directly by 100100.

    • Example 1: Convert 4 m4\,\text{m} into cm\text{cm}.

    • Step: Multiply 44 by 100100.

    • Calculation: 4×100=400 cm4 \times 100 = 400\,\text{cm}

    • Example 2: Convert 7 m7\,\text{m} into cm\text{cm}.

    • Step: Multiply 77 by 100100.

    • Calculation: 7×100=700 cm7 \times 100 = 700\,\text{cm}

  • Procedure 2: Converting Mixed Units (Meters and Centimeters):

    • Rule: Execute the conversion in two distinct chronological steps: convert the meter component into centimeters first, and then add the existing centimeter component to that product.

    • Example: Convert 5 m  45 cm5\,\text{m}\;45\,\text{cm} into cm\text{cm}.

    • Step 1: Convert the whole meter portion into centimeters by multiplying by 100100.

      • 5 m=5×100=500 cm5\,\text{m} = 5 \times 100 = 500\,\text{cm}

    • Step 2: Add the remaining centimeter portion to the converted value.

      • 500 cm+45 cm=545 cm500\,\text{cm} + 45\,\text{cm} = 545\,\text{cm}

Practice Worksheet

  • Part A: Simple Conversion Exercises:

    • 1) 2 m=____________ cm2\,\text{m} = \text{\_\_\_\_\_\_\_\_\_\_\_\_}\,\text{cm}

    • 2) 6 m=____________ cm6\,\text{m} = \text{\_\_\_\_\_\_\_\_\_\_\_\_}\,\text{cm}

    • 3) 9 m=____________ cm9\,\text{m} = \text{\_\_\_\_\_\_\_\_\_\_\_\_}\,\text{cm}

    • 4) 15 m=____________ cm15\,\text{m} = \text{\_\_\_\_\_\_\_\_\_\_\_\_}\,\text{cm}

  • Part B: Mixed Conversion Exercises:

    • 1) 3 m  25 cm=____________ cm3\,\text{m}\;25\,\text{cm} = \text{\_\_\_\_\_\_\_\_\_\_\_\_}\,\text{cm}

    • 2) 8 m  50 cm=____________ cm8\,\text{m}\;50\,\text{cm} = \text{\_\_\_\_\_\_\_\_\_\_\_\_}\,\text{cm}

    • 3) 1 m  7 cm=____________ cm1\,\text{m}\;7\,\text{cm} = \text{\_\_\_\_\_\_\_\_\_\_\_\_}\,\text{cm}

    • 4) 4 m  99 cm=____________ cm4\,\text{m}\;99\,\text{cm} = \text{\_\_\_\_\_\_\_\_\_\_\_\_}\,\text{cm}

Answer Key and Verification

  • Part A Solutions (Simple Conversions):

    • (1) 200 cm200\,\text{cm}

    • Verification: 2×100=200 cm2 \times 100 = 200\,\text{cm}

    • (2) 600 cm600\,\text{cm}

    • Verification: 6×100=600 cm6 \times 100 = 600\,\text{cm}

    • (3) 900 cm900\,\text{cm}

    • Verification: 9×100=900 cm9 \times 100 = 900\,\text{cm}

    • (4) 1500 cm1500\,\text{cm}

    • Verification: 15×100=1500 cm15 \times 100 = 1500\,\text{cm}

  • Part B Solutions (Mixed Conversions):

    • (1) 325 cm325\,\text{cm}

    • Verification: (3×100 cm)+25 cm=300 cm+25 cm=325 cm(3 \times 100\,\text{cm}) + 25\,\text{cm} = 300\,\text{cm} + 25\,\text{cm} = 325\,\text{cm}

    • (2) 850 cm850\,\text{cm}

    • Verification: (8×100 cm)+50 cm=800 cm+50 cm=850 cm(8 \times 100\,\text{cm}) + 50\,\text{cm} = 800\,\text{cm} + 50\,\text{cm} = 850\,\text{cm}

    • (3) 107 cm107\,\text{cm}

    • Verification: (1×100 cm)+7 cm=100 cm+7 cm=107 cm(1 \times 100\,\text{cm}) + 7\,\text{cm} = 100\,\text{cm} + 7\,\text{cm} = 107\,\text{cm}

    • (4) 499 cm499\,\text{cm}

    • Verification: (4×100 cm)+99 cm=400 cm+99 cm=499 cm(4 \times 100\,\text{cm}) + 99\,\text{cm} = 400\,\text{cm} + 99\,\text{cm} = 499\,\text{cm}