Examkin

Soru

Zorluk: ZorDecimals and Scientific Notation

Consider the expression N=0.00048×(2.5×107)1.2×10−2N = \frac{0.00048 \times (2.5 \times 10^7)}{1.2 \times 10^{-2}}. Which of the following expressions are equal to NN? Select all such values.

  1. 1.0×1061.0 \times 10^6Cevap
  2. (4.0×104)×25(4.0 \times 10^4) \times 25Cevap
  3. C
    1.0×1021.0 \times 10^2
  4. 5.0×10−35.0×10−9\frac{5.0 \times 10^{-3}}{5.0 \times 10^{-9}}Cevap
  5. E
    0.00012×1090.00012 \times 10^9

Cevap

The expressions equal to NN are 1.0×1061.0 \times 10^6, (4.0×104)×25(4.0 \times 10^4) \times 25, and 5.0×10−35.0×10−9\frac{5.0 \times 10^{-3}}{5.0 \times 10^{-9}}.
Evaluating NN simplifies to 1.0×1061.0 \times 10^6. The expression stating 1.0×1061.0 \times 10^6 is an exact scientific notation match. The expression (4.0×104)×25(4.0 \times 10^4) \times 25 computes to 40,000×25=1,000,00040,000 \times 25 = 1,000,000. The fraction 5.0×10−35.0×10−9\frac{5.0 \times 10^{-3}}{5.0 \times 10^{-9}} evaluates to 1.0×10−3−(−9)=1.0×1061.0 \times 10^{-3 - (-9)} = 1.0 \times 10^6.

Adım Adım Çözüm

1
Express all numbers in the stem's numerator in standard scientific notation
0.00048=4.8×10−40.00048 = 4.8 \times 10^{-4} and the numerator becomes (4.8×10−4)×(2.5×107)(4.8 \times 10^{-4}) \times (2.5 \times 10^7)
Standardizing numbers into scientific notation simplifies operations involving powers of 10
2
Multiply the coefficients and combine the powers of 10 in the numerator
(4.8×2.5)×10−4+7=12×103=1.2×104(4.8 \times 2.5) \times 10^{-4 + 7} = 12 \times 10^3 = 1.2 \times 10^4
Coefficients are multiplied directly while exponents are added according to index laws
3
Divide the simplified numerator by the denominator
1.2×1041.2×10−2=(1.21.2)×104−(−2)=1.0×106=1,000,000\frac{1.2 \times 10^4}{1.2 \times 10^{-2}} = \left(\frac{1.2}{1.2}\right) \times 10^{4 - (-2)} = 1.0 \times 10^6 = 1,000,000
Subtracting a negative exponent in the denominator is equivalent to adding its positive value
4
Evaluate each given option to determine equivalence to 1.0×1061.0 \times 10^6
The expressions representing 1.0×1061.0 \times 10^6 are 1.0×1061.0 \times 10^6, (4.0×104)×25(4.0 \times 10^4) \times 25, and 5.0×10−35.0×10−9\frac{5.0 \times 10^{-3}}{5.0 \times 10^{-9}}
Direct comparison verifies which options match the calculated value of NN

Anahtar Kavram

Operations with Decimals and Scientific Notation
Bu soruyu puanla

Konular

Decimals and Scientific Notation

Bu konudan daha fazla soru