Examkin

Soru

Zorluk: OrtaDecimals and Scientific Notation

If A=0.00048×10−3A = 0.00048 \times 10^{-3} and B=1.2×10−5B = 1.2 \times 10^{-5}, what is the value of A+B4×10−8\frac{A + B}{4 \times 10^{-8}} expressed in scientific notation?

  1. 3.12×1023.12 \times 10^2Cevap
  2. B
    1.5×1031.5 \times 10^3
  3. C
    4.2×1024.2 \times 10^2
  4. D
    3.12×10−43.12 \times 10^{-4}
  5. E
    3.12×1013.12 \times 10^1

Cevap

3.12×1023.12 \times 10^2
Converting A=0.00048×10−3A = 0.00048 \times 10^{-3} to powers of 10 gives 4.8×10−74.8 \times 10^{-7}, which equals 0.048×10−50.048 \times 10^{-5}. Adding B=1.2×10−5B = 1.2 \times 10^{-5} yields (0.048+1.2)×10−5=1.248×10−5(0.048 + 1.2) \times 10^{-5} = 1.248 \times 10^{-5}. Dividing by 4×10−84 \times 10^{-8} gives 1.2484×10−5−(−8)=0.312×103=3.12×102\frac{1.248}{4} \times 10^{-5 - (-8)} = 0.312 \times 10^3 = 3.12 \times 10^2.

Adım Adım Çözüm

1
Express AA in standard scientific notation and then match its exponent to BB's exponent.
A=0.00048×10−3=4.8×10−7=0.048×10−5A = 0.00048 \times 10^{-3} = 4.8 \times 10^{-7} = 0.048 \times 10^{-5}
To perform addition between numbers in scientific notation, their exponents must be equal.
2
Add AA and BB.
A+B=0.048×10−5+1.2×10−5=1.248×10−5A + B = 0.048 \times 10^{-5} + 1.2 \times 10^{-5} = 1.248 \times 10^{-5}
Combine the coefficients once the powers of 10 match.
3
Divide A+BA + B by 4×10−84 \times 10^{-8} and express the final result in scientific notation.
1.248×10−54×10−8=(1.2484)×10−5−(−8)=0.312×103=3.12×102\frac{1.248 \times 10^{-5}}{4 \times 10^{-8}} = \left(\frac{1.248}{4}\right) \times 10^{-5 - (-8)} = 0.312 \times 10^3 = 3.12 \times 10^2
Divide the coefficients and subtract the exponent in the denominator from the exponent in the numerator.

Anahtar Kavram

Decimals, Place Value, and Operations in Scientific Notation
Bu soruyu puanla

Konular

Decimals and Scientific Notation

Bu konudan daha fazla soru