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Zorluk: KolayExponents, Roots, and Scientific Notation

What is the correct order of the following numbers from least to greatest?

  1. 16.8×10−56.8 \times 10^{-5}
  2. 27.1×10−47.1 \times 10^{-4}
  3. 31.5×10−31.5 \times 10^{-3}
  4. 42.4×10−32.4 \times 10^{-3}

Cevap

The correct order from least to greatest is: 6.8×10−56.8 \times 10^{-5}, 7.1×10−47.1 \times 10^{-4}, 1.5×10−31.5 \times 10^{-3}, and 2.4×10−32.4 \times 10^{-3}.
The correct order is determined by first arranging the values by their power of 10 exponent from least to greatest: −5<−4<−3-5 < -4 < -3. This places 6.8×10−56.8 \times 10^{-5} as the smallest and 7.1×10−47.1 \times 10^{-4} as the second smallest. For the remaining two values that share the exponent −3-3, we compare their coefficients: 1.5<2.41.5 < 2.4, placing 1.5×10−31.5 \times 10^{-3} before 2.4×10−32.4 \times 10^{-3}.

Adım Adım Çözüm

1
Compare the exponents of the base 10 to establish the primary order of magnitude.
The exponents are −5-5, −4-4, and −3-3. Since −5<−4<−3-5 < -4 < -3, we know that any number with an exponent of −5-5 is smaller than one with −4-4, which in turn is smaller than one with −3-3.
In scientific notation, a smaller exponent on the power of 10 indicates a smaller overall value because it represents shifting the decimal point further to the left.
2
Place the numbers with unique exponents in order.
The smallest number is 6.8×10−56.8 \times 10^{-5}, followed by 7.1×10−47.1 \times 10^{-4}.
These have the smallest exponents (−5-5 and −4-4, respectively).
3
Compare the coefficients of the remaining numbers that share the same exponent.
Both 1.5×10−31.5 \times 10^{-3} and 2.4×10−32.4 \times 10^{-3} share the exponent −3-3. Comparing their coefficients, 1.5<2.41.5 < 2.4, so 1.5×10−3<2.4×10−31.5 \times 10^{-3} < 2.4 \times 10^{-3}.
When the powers of 10 are identical, the values can be compared directly by their coefficients.

Anahtar Kavram

Comparing and ordering numbers written in scientific notation by analyzing their powers of 10 and coefficients.
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Exponents, Roots, and Scientific Notation

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