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Flashcards · Maths

Standard Form and Accuracy

80 cards from 5 lessons

  1. What is standard form?

    A way of writing a number as \(A \times 10^n\), with \(A\) at least 1 and less than 10.

  2. Which numbers have a positive power of 10?

    Numbers of 10 or more.

  3. Which numbers have a negative power of 10?

    Numbers between 0 and 1.

  4. What is 45 000 in standard form?

    \(4.5 \times 10^4\).

  5. What is 0.0032 in standard form?

    \(3.2 \times 10^{-3}\).

  6. Is \(45 \times 10^3\) in standard form?

    No, because 45 is not between 1 and 10.

  7. How do you write \(45 \times 10^3\) in standard form?

    \(4.5 \times 10^4\).

  8. What does \(10^{-2}\) equal?

    \(\dfrac{1}{100} = 0.01\).

  9. How do you write \(3.2 \times 10^5\) as an ordinary number?

    320 000.

  10. Which is bigger, \(5 \times 10^{-3}\) or \(8 \times 10^{-5}\)?

    \(5 \times 10^{-3}\).

  11. How do you compare numbers in standard form?

    Compare the powers first, then the first parts.

  12. What is 150 million in standard form?

    \(1.5 \times 10^8\).

  13. When the decimal point moves left, is the power positive or negative?

    Positive.

  14. When the decimal point moves right, is the power positive or negative?

    Negative.

  15. What is \(10^0\)?

    1.

  16. Why use standard form?

    To write very large or very small numbers briefly and clearly.

  17. How do you multiply numbers in standard form?

    Multiply the first parts and add the powers.

  18. How do you divide numbers in standard form?

    Divide the first parts and subtract the powers.

  19. What is \(10^3 \times 10^4\)?

    \(10^7\).

  20. What is \(10^8 \div 10^3\)?

    \(10^5\).

  21. What is \(10^7 \div 10^{-2}\)?

    \(10^9\).

  22. What if the first part is 20 after multiplying?

    Change it to 2 and increase the power by 1.

  23. How do you add numbers in standard form?

    Write them with the same power, then add the first parts.

  24. How do you subtract numbers in standard form?

    Write them with the same power, then subtract the first parts.

  25. What is \((2 \times 10^3) \times (3 \times 10^4)\)?

    \(6 \times 10^7\).

  26. What is \(3 \times 10^4 + 5 \times 10^3\)?

    \(3.5 \times 10^4\).

  27. Why not add the powers when adding?

    The numbers have different sizes, so the powers must be made the same first.

  28. What should the answer look like?

    A number in standard form, with the units.

  29. How can you check an addition?

    Write the numbers as ordinary numbers.

  30. What is \((4 \times 10^{-3}) \times (2 \times 10^{-2})\)?

    \(8 \times 10^{-5}\).

  31. What is \(\dfrac{6 \times 10^5}{2 \times 10^2}\)?

    \(3 \times 10^3\).

  32. What is \(5 \times 10^6\) divided by \(5 \times 10^6\)?

    1.

  33. How do you round to 1 decimal place?

    Look at the second decimal digit: 5 or more rounds up, and 4 or less rounds down.

  34. What is 4.678 to 1 d.p.?

    4.7.

  35. What is a significant figure?

    A digit that counts, starting from the first non-zero digit.

  36. What is 0.004567 to 2 s.f.?

    0.0046.

  37. What is 6482 to 2 s.f.?

    6500.

  38. What is 83.7 to the nearest 10?

    80.

  39. What is 87.2 to the nearest 10?

    90.

  40. How do you estimate a calculation?

    Round each number to 1 significant figure, then calculate.

  41. What does \(\approx\) mean?

    Approximately equal to.

  42. What is an estimate for \(\dfrac{4.97 \times 20.1}{0.49}\)?

    \(\dfrac{5 \times 20}{0.5} = 200\).

  43. If the bottom of a fraction is rounded up, what happens to the answer?

    The answer gets smaller.

  44. If the top of a fraction is rounded up, what happens to the answer?

    The answer gets bigger.

  45. Why show the rounded numbers?

    They show the method, and earn the marks.

  46. Do zeros at the start of a decimal count as significant figures?

    No.

  47. Which digit decides whether to round up?

    The one just after the place you are rounding to.

  48. What should you write after a rounded answer?

    The accuracy, such as "to 2 s.f.".

  49. What is an error interval?

    The set of values that would round to a given number.

  50. How is an error interval written?

    \(\text{lower bound} \leq x < \text{upper bound}\).

  51. What is the error interval for 12 cm to the nearest cm?

    \(11.5 \leq L < 12.5\).

  52. What is the error interval for 3.7 to 1 d.p.?

    \(3.65 \leq x < 3.75\).

  53. Why is the upper bound not included?

    The upper bound would round up to the next value.

  54. What is half a unit when rounding to the nearest 10?

    5.

  55. What is the error interval for 40, to the nearest 10?

    \(35 \leq x < 45\).

  56. What does truncated mean?

    Digits are cut off without rounding.

  57. What is the error interval for 5, truncated to a whole number?

    \(5 \leq n < 6\).

  58. What is the upper bound of \(a + b\)?

    The upper bound of \(a\) plus the upper bound of \(b\) (Higher tier).

  59. What is the upper bound of \(a - b\)?

    Upper bound of \(a\) minus lower bound of \(b\) (Higher tier).

  60. What is the upper bound of \(a \div b\)?

    Upper bound of \(a\) divided by lower bound of \(b\) (Higher tier).

  61. What is the lower bound of \(a \times b\)?

    Lower bound of \(a\) times lower bound of \(b\) (Higher tier).

  62. Is the upper bound of 8 cm to the nearest cm 8.5?

    Yes, although the value 8.5 itself is not included in the interval.

  63. What does limit of accuracy mean?

    The lower and upper bounds of a measurement.

  64. What error interval is 0.4 to 1 s.f.?

    \(0.35 \leq x < 0.45\).

  65. What is a terminating decimal?

    A decimal that stops.

  66. What is a recurring decimal?

    A decimal in which a digit or block of digits repeats for ever.

  67. How are recurring decimals written?

    With dots over the first and last repeating digits.

  68. What is \(\dfrac{1}{3}\) as a decimal?

    \(0.\dot{3}\).

  69. What is \(\dfrac{3}{11}\) as a decimal?

    \(0.\dot{2}\dot{7}\).

  70. What is \(\dfrac{5}{6}\) as a decimal?

    \(0.8\dot{3}\).

  71. When does a fraction give a terminating decimal?

    When the bottom number, in simplest form, has only prime factors 2 and 5.

  72. How do you write \(0.\dot{4}\) as a fraction?

    \(\dfrac{4}{9}\) (Higher tier).

  73. How do you write \(0.\dot{4}\dot{5}\) as a fraction?

    \(\dfrac{5}{11}\) (Higher tier).

  74. What is the first step in converting a recurring decimal?

    Write \(x =\) the decimal.

  75. Why do you multiply by 10, 100 or 1000?

    To line up the repeating digits so they cancel on subtracting.

  76. What is a rational number?

    A number that can be written as a fraction of two integers.

  77. What is an irrational number?

    A number that cannot be written as a fraction.

  78. Is \(\pi\) irrational?

    Yes.

  79. Is \(\sqrt{16}\) rational?

    Yes, it equals 4.

  80. Is \(\sqrt{7}\) rational?

    No, it is irrational.