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Addition and Subtraction Operations quiz

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  • What must be true about the exponents when adding or subtracting numbers in scientific notation?
    The exponents must be the same before you can add or subtract the coefficients.
  • How do you adjust a number in scientific notation if its exponent is smaller than the other number's exponent during addition or subtraction?
    Increase the exponent to match the larger one and decrease the coefficient by moving the decimal point to the left for each increase in the exponent.
  • What happens to the coefficient when you increase the exponent by 1 in scientific notation?
    The coefficient decreases by one decimal place (moves left) for each increase of 1 in the exponent.
  • When adding 8.17×10⁸ and 1.25×10⁹, what is the first step?
    Convert 8.17×10⁸ to 0.817×10⁹ so both numbers have the same exponent.
  • After matching exponents, how do you combine the numbers in scientific notation?
    Add or subtract the coefficients and keep the exponent the same.
  • When adding or subtracting in scientific notation, how do you determine the number of decimal places in the final answer?
    The final answer should have the least number of decimal places from the original coefficients.
  • What is the reciprocal relationship between the coefficient and exponent in scientific notation?
    If you increase the exponent, you must decrease the coefficient by the same number of decimal places, and vice versa.
  • How do you handle subtraction with numbers like 8.9295×10⁻¹¹ and values with different exponents?
    Convert all numbers to have the same exponent, then subtract the coefficients.
  • If you have 10⁻¹² and need to convert it to 10⁻¹¹, what do you do to the coefficient?
    Move the decimal point one place to the left in the coefficient to increase the exponent by one.
  • What is the rule for significant figures when multiplying or dividing numbers in scientific notation?
    The answer should have the least number of significant figures from the original numbers.
  • Why do you round the final answer to 2 decimal places when adding 0.817 and 1.25?
    Because 1.25 has 2 decimal places, which is the least among the numbers being added.
  • What is the final answer for 8.17×10⁸ + 1.25×10⁹, rounded correctly?
    2.07×10⁹, rounded to 2 decimal places.
  • When subtracting numbers with exponents 10⁻¹¹, 10⁻¹², and 10⁻¹³, to what exponent should you convert all numbers?
    Convert all numbers to the largest exponent, which is 10⁻¹¹ in this case.
  • If a coefficient has 4 decimal places and another has 2, how many decimal places should the answer have after addition or subtraction?
    The answer should have 2 decimal places, matching the least number of decimal places.
  • What is the final answer for 8.9295×10⁻¹¹ minus values with exponents 10⁻¹² and 10⁻¹³, rounded correctly?
    8.93×10⁻¹¹, rounded to 2 decimal places.