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Question

Difficulty: EasyDecimals and Scientific Notation

Given x=3.6×10−3x = 3.6 \times 10^{-3} and y=1.2×10−4y = 1.2 \times 10^{-4}, which of the following statements are true? Select all that apply.

  1. xx is greater than yy.Answer
  2. The ratio xy\frac{x}{y} is equal to 3030.Answer
  3. C
    The sum x+yx + y is equal to 4.8×10−74.8 \times 10^{-7}.
  4. D
    The product x×yx \times y is equal to 4.32×10124.32 \times 10^{12}.
  5. E
    The value of yy expressed as a standard decimal is 0.00120.0012.

Answer

The statement that xx is greater than yy and the statement that the ratio xy\frac{x}{y} is equal to 3030 are both correct.
The statement asserting that xx is greater than yy is true because 3.6×10−3=0.00363.6 \times 10^{-3} = 0.0036 is larger than 1.2×10−4=0.000121.2 \times 10^{-4} = 0.00012. The statement regarding the ratio xy\frac{x}{y} is true because dividing coefficients 3.61.2=3\frac{3.6}{1.2} = 3 and subtracting exponents −3−(−4)=1-3 - (-4) = 1 yields 3×101=303 \times 10^1 = 30.

Step-by-Step Solution

1
Convert both numbers to standard decimal notation to compare them.
x=0.0036x = 0.0036 and y=0.00012y = 0.00012.
Converting to standard form makes place value comparison direct.
2
Compare xx and yy.
0.0036>0.000120.0036 > 0.00012, so x>yx > y.
The thousandths digit of xx (33) is greater than the thousandths digit of yy (00).
3
Calculate the ratio xy\frac{x}{y} using properties of exponents.
3.6×10−31.2×10−4=(3.61.2)×10−3−(−4)=3×101=30\frac{3.6 \times 10^{-3}}{1.2 \times 10^{-4}} = \left(\frac{3.6}{1.2}\right) \times 10^{-3 - (-4)} = 3 \times 10^1 = 30.
Divide the coefficients and subtract the exponents for scientific notation division.

Key Concept

Decimals and Scientific Notation Operations
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Topics

Decimals and Scientific Notation

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