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Find the measure of the combined angle.

Mathematics

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3. Show 19.601 two ways.

  • Way 1: Place Value Chart

    TensOnes.T (Tenths)H (Hundredths)Th (Thousandths)
    19.601
  • Way 2: Expanded Form

    10+9+0.6+0.00110 + 9 + 0.6 + 0.001

4. Make a Connection Write an expression represented by the model. Then write the decimal in standard form.

  1. Identify the value of each type of block.

    Assuming the large squares represent 1 whole, the rods represent 0.1 (tenths), the small cubes represent 0.01 (hundredths), and the tiny cubes represent 0.001 (thousandths).

    • 2 large squares: 2×1=22 \times 1 = 2
    • 8 rods: 8×0.1=0.88 \times 0.1 = 0.8
    • 6 small cubes: 6×0.01=0.066 \times 0.01 = 0.06
    • 4 tiny cubes: 4×0.001=0.0044 \times 0.001 = 0.004
  2. Write the expression.

    The expression is the sum of these values.

    2+0.8+0.06+0.0042 + 0.8 + 0.06 + 0.004
  3. Write the decimal in standard form.

    Add the values together.

    2+0.8+0.06+0.004=2.8642 + 0.8 + 0.06 + 0.004 = 2.864

    The standard form is 2.864\boxed{\text{2.864}}.

    5. Model Real Life The mass of an African penguin is 3.599 kilograms. Write three expressions that describe the mass of the penguin.

    Here are three expressions for 3.599 kilograms:

    1. Expanded form (decimal):

      3+0.5+0.09+0.009 kilograms3 + 0.5 + 0.09 + 0.009 \text{ kilograms}
    2. Expanded form (fraction):

      3+510+9100+91000 kilograms3 + \frac{5}{10} + \frac{9}{100} + \frac{9}{1000} \text{ kilograms}
    3. Word form: Three and five hundred ninety-nine thousandths kilograms.

    6. Find the measure of the combined angle.

  4. Identify the given angles.

    The two angles are 27∘27^\circ and 44∘44^\circ.

  5. Add the angles to find the combined measure.

    27∘+44∘=71∘27^\circ + 44^\circ = 71^\circ

    The combined angle is 71∘\boxed{\text{71}^\circ}.

    7. Find the measure of the combined angle.

  6. Identify the given angles.

    The two angles are 53∘53^\circ and 85∘85^\circ.

  7. Add the angles to find the combined measure.

    53∘+85∘=138∘53^\circ + 85^\circ = 138^\circ

    The combined angle is 138∘\boxed{\text{138}^\circ}.

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