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Standard Form

Standard Form. Large Numbers. Standard form – writing large numbers. We can write very large numbers using standard form . To write a number in standard form we write it as a number between 1 and 10 multiplied by a power of ten.

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Standard Form

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  1. Standard Form Large Numbers

  2. Standard form – writing large numbers We can write very large numbers using standard form. To write a number in standard form we write it as a number between 1 and 10 multiplied by a power of ten. For example, the average distance from the earth to the sun is about 150 000 000 km. We can write this number as 1.5 × 108 km. A number between 1 and 10 A power of ten

  3. Powers of ten Our decimal number system is based on powers of ten. We can write powers of ten using index notation. 10 = 101 100 = 10 × 10 = 102 1000 = 10 × 10 × 10 = 103 10 000 = 10 × 10 × 10 × 10 = 104 100 000 = 10 × 10 × 10 × 10 × 10 = 105 1 000 000 = 10 × 10 × 10 × 10 × 10 × 10 = 106 . . . . . . 1 000 000 000 = 10 × 10 × 10 × 10 × 10 × 10 × 10 × 10 × 10 = 109

  4. Multiplying by 10, 100 and 1000 Thousands Hundreds Tens Units tenths hundredths thousandths 6 2 6 2 What is 6.2 × 10? Let’s look at what happens on the place value grid. When we multiply by ten the digits move one place to the left. 6.2 × 10 = 62

  5. Multiplying by 10, 100 and 1000 Thousands Hundreds Tens Units tenths hundredths thousandths 3 1 3 1 What is 3.1 × 100? Let’s look at what happens on the place value grid. 0 When we multiply by one hundred the digits move two places to the left. We then add a zero place holder. 3.1 × 100 = 310

  6. Multiplying by 10, 100 and 1000 Thousands Hundreds Tens Units tenths hundredths thousandths 0 7 7 What is 0.7 × 1000? Let’s look at what happens on the place value grid. 0 0 When we multiply by one thousand the digits move three places to the left. We then add zero place holders. 0.7 × 1000 = 700

  7. Standard form – writing large numbers 80 000 000 = 230 000 000 = 724 000 = 6 003 000 000 = 371.45 = How can we write these numbers in standard form? 8 × 107 2.3 × 108 7.24 × 105 6.003 × 109 3.7145 × 102

  8. Standard form – writing large numbers 5 × 1010 = 7.1 × 106 = 4.208 × 1011 = 2.168 × 107 = 6.7645 × 103 = These numbers are written in standard form. How can they be written as ordinary numbers? 50 000 000 000 7 100 000 420 800 000 000 21 680 000 6764.5

  9. Very large numbers , or 2 15 2 15 2 15 ×10 E 2 × 1015 = 2 000 000 000 000 000 Use you calculator to work out the answer to 40 000 000 × 50 000 000. Your calculator may display the answer as: What does the 15 mean? The 15 means that the answer is 2 followed by 15 zeros or:

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