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Rules for changing a number from ordinary notation to scientific notation. 1. Locate the decimal point. If none is showing place the decimal point on the right end. 25000000000000 has no decimal showing so we put one on the right end, like this 25000000000000. -------------- 23420000 has no decimal showing so we put one on the right end, like this 23420000. 0.000000586 shows its decimal. -------------- 0.00000000000000000000000000167 shows its decimal. -------------- -------------- 2. Starting at the far left find the first digit that isn't a zero. Put a red decimal just to the right of that digit. (You can choose another color, or just make a different looking decimal there, maybe a little cross mark or something, or you can use a pencil to write one decimal and a pen to write the other one. But I'll use a red decimal here) 25000000000000. The digit 2 is the first digit that isn't a zero. So we put a red decimal after that 2, like this: 2.5000000000000. -------------- 23420000. The digit 2 is the first digit that isn't a zero. So we put a red decimal after that 2, like this: 2.3420000. -------------- 0.000000586 The digit 5 is the first digit that isn't a zero. So we put a red decimal after that 5, like this: 0.0000005.86 -------------- 0.00000000000000000000000000167 The digit 1 is the first digit that isn't a zero. So we put a red decimal just to the right of that 1, like this: 0.000000000000000000000000001.67 -------------- -------------- 3. Count the number of digits between the black decimal and the red decimal, and that will be the magnitude of the exponent of 10. 2.5000000000000. There are 13 digits between the black and red decimals. So the magnitude of the exponent of 10 is 13 -------------- 2.3420000. There are 7 digits between the black and red decimals. So the magnitude of the exponent of 10 is 7 0.0000005.86 There are 7 digits between the black and red decimals. So the magnitude of the exponent of 10 is 7. -------------- 0.000000000000000000000000001.67 There are 27 digits between the black and red decimals. So the magnitude of the exponent of 10 is 27 -------------- -------------- 4. Now we determine whether the exponent is positive or negative. If the black decimal is on the right of the red decimal, the exponent of 10 is positive. If the red decimal is on the right of the black decimsl, the exponent of 10 is negative. 2.5000000000000. The black decimal is right of the red decimal so the exponent of 10 is positive, and is therefore +13 -------------- 2.3420000. The black decimal is right of the red decimal so the exponent of 10 is positive, and is therefore +7 -------------- 0.0000005.86 The red decimal is right of the black decimal so the exponent of 10 is negative, and is therefore -7 -------------- 0.000000000000000000000000001.67 The red decimal is right of the black decimal so the exponent of 10 is negative, and is therefore -27. -------------- -------------- 5. Erase the black decimal and trim any leading or trailing zeros. 2.5000000000000. We erase the black decimal at the end 2.5000000000000 Now we trim off all the trailing zeros: 2.5 -------------- 2.3420000. We erase the black decimal at the end 2.3420000 Now we trim off all the trailing zeros: 2.342 -------------- 0.0000005.86 We erase the black decimal: 00000005.86 Now we trim off all the leading zeros: 5.86 -------------- 0.000000000000000000000000001.67 We erase the black decimal: 0000000000000000000000000001.67 Now we trim off all the leading zeros: 1.67 -------------- -------------- 6. Finally we put " ×10EXPONENT OF 10 " after it: 2.5 × 1013 -------------- 2.342 × 107 -------------- 5.86 × 10-7 -------------- 1.67 × 10-27 Edwin