1 / 16

Standard Form

Standard Form. 2 is multiplied by itself 3 times. Revision. Powers:. On calculator:. Try these:. 6 5. 5 4. 3 6. 2 5. 9 4. 10 4. 10 000. Answers:. 7776. 625. 729. 32. 6561. 3 zeros. Powers of 10. Powers of 10 are easy. e.g.10 3 = 10 x 10 x 10 =1000.

bern
Télécharger la présentation

Standard Form

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. Standard Form

  2. 2 is multiplied by itself 3 times Revision Powers: On calculator: Try these: 65 54 36 25 94 104 10 000 Answers: 7776 625 729 32 6561

  3. 3 zeros Powers of 10 Powers of 10 are easy e.g.103 = 10 x 10 x 10=1000 Look at these sequences Divide by 10 From this we see that

  4. Working with big numbers Scientists often have to work with big numbers. Example: The distance the earth travels in one orbit is 558 000 000 miles. We can express this number in a more concise form as follows. 558 000 000 = 5.58 x 100 000 000 = 5.58 x 108 is said to be in Standard Form 5.58 x 108 or Scientific Notation is said to be in Normal Form 558 000 000

  5. the power is a positive or negative whole number exactly one digit before the point watch this 5 jumps 63. x 105 630. 6300. 630000. 63000. 2 1 3 4 5 Look at this number which is in Standard Form 6.3 x 105 6.3 x 105 = 630 000 = 6.3 x 10 x 10 x 10 x 10 x 10 Standard form Ordinary Number 6.3

  6. Example: Write 2.45 x 104 as an ordinary number. • Write the question • List the digits without the point • 4 jumps from position of “old” point • Write the answer Method: Add zeros as required 0 0 0 0 2 4 5 1 3 4 2 Now try these: Write as ordinary numbers: 4 x 103 4.88 x 101 1.47 x 102 9.08 x 106 1.3 x 100 147 9080000 1.3 4000 48.8

  7. 4 1 5 3 2 watch this 5 jumps Therefore 630 000 = 6.3 x 105 x 105 Ordinary Number Standard form 630 000 = 6.3 x 100 000 = 6.3 x 105 63000. 630000. 0 0 0 6300. 0 0 0 0 0 0 0 0 0 0 0 630. 6.3 63.

  8. Make the number “look” like standard form Positive power since large number Put in a decimal point to make the number “look” like a number between 1 and 10. = 2 7 0 6 Example: Write 2706 in standard form. Method: • Write the number • Insert “new” decimal point • Count jumps to position of “old” decimal point 2 7 0 6 3 2 1 x 3 10 Now try these: Write in standard form: 34560 1023.6 12.8 4.6 230000 3.456 x 104 1.0236 x 103 1.28 x 101 4.6 x 100 2.3 x 105

  9. the power is a positive or negative whole number exactly one digit before the point watch this 3 jumps x 10-3 1 2 3 Numbers less than 1 Consider the number 2.03 x 10-3 This number is in standard form but is different from previous examples. Look again at powers of 10 Notice the power is negative = 0.00203 2.03 x 10-3 = 2.03 x 0.001 Standard form Ordinary Number x 10-3 2.03 .203 .0203 .00203 = 0.00203

  10. Example: Write 1.07 x 10-4 as an ordinary number. • Write the question • List the digits without the point • 4 jumps from position of “old” point • Write the answer Method: Add zeros as required That means the answer starts with 0.----- Note: When the power is negative the ordinary number is always less than 1. 0 0 0 1 3 4 2 0 1 0 7 0 0 0 Now try these: Write as ordinary numbers: 4.081 x 10-4 4 x 10-3 1.47 x 10-2 9.08 x 10-5 1.3 x 10-1 0.0147 0.0000908 0.13 0.004 0.0004081

  11. 1 3 2 watch this 3 jumps Therefore 630 000 = 6.31 x 10-3 x 10-3 Ordinary Number Standard form 0.00631 = 6.31 x 0.001 = 6.31 x 10-3 0.00631 0 0 0 0.631 0.0631 0 0 0 6.31

  12. Make the number “look” like standard form 0 0 0 2 7 Negative power since tiny number Put in a decimal point to make the number “look” like a number between 1 and 10. = 2 7 Example: Write 0.0027 in standard form. Method: • Write the number • Insert “new” decimal point • Count jumps to position of “old” decimal point 3 2 1 3 x 10 - Now try these: Write in standard form: 0.3456 0.00102 0.0128 0.000046 0.0000000023 3.456 x 10-1 1.02 x 10-3 1.28 x 10-2 4.6 x 10-5 2.3 x 10-9

  13. We use EXP button as shown on the calculator to enter numbers already in standard form. 2 6 EXP 8 = check this is correct Too large to convert 3 5 EXP 1 2 = Standard Form on the Calculator Examples: 2.6 x 108 260 000 000 3.5 x 1012 Calculator’s way of writing 3.5 x 1012 – does not mean 3.5 to the power 12! 3.5 12

  14. calculator display calculator display (2.484 x 107) (4.6 x 10-4) • Only enter EXP before power, never x 10 EXP • For negative powers use the ( - ) key not the key, we are not subtracting. Calculations Giving your Answer in Standard Form Example 1: (2.6 x 108) x (4.2 x 106) = 1.092 x 1015 1.092 15 Example 2: = 5.4 x 1010 5.4 10 Note: See calculators again • Remember to change number on display to ---- x 10-- Click button to end presentation

  15. ( - )

  16. END

More Related