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Numbers

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Published in: Mathematics
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Standard form Convert numbers into and out of standard form Calculation with values in standard form

Divya J / Dubai

15 years of teaching experience

Qualification: CAIE and Pearson Examiner for IGCSE an AS Levels, Masters in Mathematics

Teaches: SAT, ACT, Maths, IGCSE/AS/AL, Physics, Biology, Chemistry, Mathematics

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  1. Mathematics Lecture No.- 05 Numbers Today_'s Targets Standard form Convert numbers into and out of standard form O Calculation with values in standard form
  2. Standard form Standard Form (sometimes called Standard Index Form) is a way of writing very big and very small numbers using powers of 10. Standard form is always written as a X 10b, where a is between I and 10 , but is never equal to 10 and b is an integer which can be positive or negative. A number in standard form looks like this: 2.5 x 106 This part is written as a number between 1 and 10. This part is written as a power of 10 .
  3. Standard form Converting in standard form Standard form will be written as a x 10". Ignore the place value and find the leading non-zero digit. Write a = If the original number is smaller than 1 then n will be negative otherwise it will be positive. Count how many times you need to divide a by 10 to get the original number or multiply in other case. Write in standard form
  4. Standard form Multiply/divide the number parts first. Then multiply/divide the powers of 10 using the laws of indices. Write the final answer in standard form.
  5. Standard form If the two numbers have the same power of 10 then you can simply add/subtract the number parts and write the final answer in standard form. Otherwise convert both numbers so that they have the same power of 10 (choosing the larger power) and write the final answer in standard form. As standard form is two terms multiplied together you can split the power or root up. n k = ak X (1010k - ak X 1011k (a x 10 ) ax Ion
  6. Question Write 72000 in standard form.
  7. Question Write 0.0032 in standard form.
  8. Question Write 4 x 104 as an ordinary number.
  9. Question Multiply the following and write your answer in standard form: (2.4 x 104) x (5 x 107)
  10. Question Divide the following and write your answer in standard form: (6.4 x 107) + (1.6 x 103)
  11. Question Add the following and write your answer in standard form: (3.8 x 106) + (8.7 x 104)
  12. Question Subtract the following and write your answer in standard form: (6.5 x 107) - (9.2 x IOS)
  13. Question Write the following numbers in order of magnitude, starting with the largest: 3.6 x 102 9 x 101 4.05 X 10B 1.5 x lo- 2.1 x lo- 7.2 x lo-
  14. Question Write the following numbers in order of size. Start with the smallest number 0.038 x 102 3800 x 380 0.38 x lo-
  15. Question Write 640000000 in standard form.
  16. Question Work out (3 x 107) + (6 x 104). Give your answer in standard form.
  17. Question xy x - 8.5 x 109 Find the value of p. Give your answer in standard form correct to 2 significant figures.
  18. Question w w = 5.6 x lo- d: : 1.4 x 10-4 Work out the value of T. Give your answer in standard form correct to 3 significant figures.
  19. Question Work out (3 x 10199) + (2 x 10201). Give your answer in standard form.
  20. Question Work out (13.8 x 107) x (5.4 x 10-12). Give your answer as an ordinary number.
  21. [M19, 22, Q4] (a) Write 0.046875 correct to 2 significant figures.
  22. [M19, 22, Q4] (b) Write 2760000 in standard form.
  23. [SIB, 22, Q8] Here are some numbers written in standard form. 0 2.4 x 105 1.36 x 106 7.9 x 10 3.4 x lo- From these numbers, write down (a) the largest number. (b) the smallest number. 5.21 x lo- 4.3 x lo- [11 [11
  24. [98, 23, QB] (a) Write 4.82 x as an ordinary number.
  25. [98, 23, QB] (b) Write 52 million in standard form.
  26. [W18, 21, Q4] Work out (6.4 x 107) + (9.6 x 106). Give your answer in standard form.
  27. [W14, 21, Q9b] Work out 2.5 x 108 x 2 x 10-2. Give your answer in standard form. ... ... ... ... ...... [21

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