5.3. Scientific notation Sometimes we do not want to change the units of ver y large or ver y sma l l numbers. Therefore, we do not use mu ltiples and submu ltiples. In this case, we w rite the number using scientif ic notation to keep the same units. Scient i f ic notat ion is w r it ten l i ke th is: Power of 10 Decimal part 7. 82 ? 10-4 Integer part Not zero Only one digit S O LV E D P R O B L E M 3 a) Write 346 000 in scientific notation. b) Write 0.000 064 in scientific notation. 1. Integer part. Write the first digit. It is never a zero. 2. Decimal part. Then put a decimal point and the remaining digits. 3. Find the exponent of the power of 10. Count how many places you have to move the decimal point until there is only one integer left. This value is the exponent. a) b) 21 Write these numbers in scientific notation. a) 2 073 500 b) 0.000 350 002 22 Write these numbers with all of their digits. a) 2.705 ? 102 b) 1.075 ? 10-4 A C T I V I T I E S If the number is greater than one, the exponent is positive. If the number is less than one, the exponent is negative. Power of 10 Integer part Decimal part 346 000 → 3. 46 ? 105 Do not put zeros to the right of the last digit Power of 10 Integer part Decimal part 0.000 064 → 6. 4 ? 10-5 The Or ion Nebu la is 1 3 4 4 l ight yea rs away. To w r ite th is d istance in other un its, it is best to use scient i f ic notat ion: 1 l ight yea r = 9.4 6 ? 1012 k m 1 3 4 4 l ight yea rs = 1. 27 ? 1016 k m 5. Measurement 22
RkJQdWJsaXNoZXIy