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Measurement - Operations on Metric Measures

Grade 5ICSE

Review the key concepts, formulae, and examples before starting your quiz.

🔑Concepts

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The Metric System Base Units: The metric system uses specific base units for different types of measurement: meters (mm) for length, grams (gg) for mass (weight), and liters (LL) for capacity. Visualize these as the 'home base' from which all other units are derived by adding prefixes.

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Prefix Meanings and The Metric Staircase: Metric units use prefixes to indicate size. Imagine a staircase with seven steps: Kilo, Hecto, Deca, [Base Unit], Deci, Centi, and Milli. Moving up the stairs represents larger units, and moving down represents smaller units. Each step represents a factor of 1010.

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Rule of Conversion: To convert from a higher (larger) unit to a lower (smaller) unit, we multiply by 1010, 100100, or 10001000. To convert from a lower unit to a higher unit, we divide by 1010, 100100, or 10001000. Remember: 'Big to Small →\rightarrow Multiply' and 'Small to Big →\rightarrow Divide'.

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Addition with Regrouping: When adding metric measures, align the units in columns (e.g., kmkm in one column and mm in another). If the sum of the smaller unit exceeds its limit (like 10001000 mm in a kmkm), carry the extra over to the larger unit column. Visualize this like a standard addition carry-over, but based on metric conversion rates.

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Subtraction with Borrowing: In subtraction, if the top number in the smaller unit column is less than the bottom number, you must 'borrow' from the larger unit column. For example, borrowing 11 kgkg adds 10001000 gg to the grams column. Visualize the larger unit breaking down into smaller pieces to help the subtraction.

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Multiplication of Metric Measures: To multiply a metric measure by a whole number, you can either multiply each unit separately and then regroup, or convert the entire measure into a decimal form. For example, 55 mm 2020 cmcm can be treated as 5.205.20 mm before multiplying.

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Division of Metric Measures: To divide metric measures by a whole number, it is often easiest to convert the entire quantity into the smallest unit mentioned first. After dividing the total, you can convert the result back into mixed units (like kgkg and gg).

📐Formulae

1 km=1000 m1 \text{ km} = 1000 \text{ m}

1 m=100 cm1 \text{ m} = 100 \text{ cm}

1 cm=10 mm1 \text{ cm} = 10 \text{ mm}

1 kg=1000 g1 \text{ kg} = 1000 \text{ g}

1 g=1000 mg1 \text{ g} = 1000 \text{ mg}

1 L=1000 mL1 \text{ L} = 1000 \text{ mL}

Value in Higher Unit×10n=Value in Lower Unit\text{Value in Higher Unit} \times 10^n = \text{Value in Lower Unit}

Value in Lower Unit÷10n=Value in Higher Unit\text{Value in Lower Unit} \div 10^n = \text{Value in Higher Unit}

💡Examples

Problem 1:

Add 1414 kg 650650 g and 88 kg 550550 g.

Solution:

  1. Create two columns: one for kilograms (kg) and one for grams (g).
  2. Write the values: kg | g 14 | 650
  • 8 | 550
  1. Add the grams: 650+550=1200650 + 550 = 1200 g.
  2. Since 10001000 g = 11 kg, we have 12001200 g = 11 kg 200200 g.
  3. Write 200200 in the grams column and carry 11 to the kg column.
  4. Add the kg: 14+8+114 + 8 + 1 (carried) = 2323 kg.
  5. Final result: 2323 kg 200200 g.

Explanation:

We use the columnar method to keep units separate and regroup grams into kilograms whenever the total exceeds 10001000.

Problem 2:

A rope of length 1212 m 8080 cm is divided into 44 equal pieces. What is the length of each piece?

Solution:

  1. Convert the entire length to the smaller unit (cm): 1212 m = 12×100=120012 \times 100 = 1200 cm. Total length = 12001200 cm + 8080 cm = 12801280 cm.
  2. Divide the total length by 44: 1280÷4=3201280 \div 4 = 320 cm.
  3. Convert the result back to meters and centimeters: 320320 cm = 300300 cm + 2020 cm. Since 100100 cm = 11 m, 300300 cm = 33 m.
  4. Final result: 33 m 2020 cm.

Explanation:

Converting to a single unit (the smaller unit) before dividing makes the calculation straightforward and avoids dealing with decimals or remainders across different units.