Express 930,000 in scientific notation. To write any number in scientific notation requires moving the decimal point. Where is it in this number? That’s correct. It’s on the far right-hand side of the number after the last zero. Now this decimal point is going to be moved so that it’s between the nine and the three. Why did we do this? Well, the definition said so. The number M must be between 1 and 10. So by putting the decimal point between the 9 and the 3, we ensure that the number is between 1 and 10. Now the number has to retain the same value that it was, namely 930,000. To balance what we’ve done, we need to multiply the number 9.3 by a power of 10.
From earlier work on numbers, you should remember that when you multiply a number by 10 or by power of 10, the decimal point moves to the right. How many places does the decimal point move? Do you know? Good. For every 0 in the power of 10 we move the decimal point that many places. For example, when you multiply by 1,000 the decimal point moves 3 places. So if we multiply 9.3 by 1,000 the decimal point moves 3 places. Or if we multiply by 1,000,000 you’ll see that it moves 6 places. Returning to our example, to move the decimal point back to its original position, we have to multiply 9.3 by 100,000. This is because the decimal point has been moved five positions to the left to get to 9.3. Multiplying by 100,000 would move it 5 places to the right and give us the original value. Now 100,000 needs to be written as a power of 10, as the definition implies.
So, the answer is 9.3 times 10 to the power of 5. We know it’s to the power of 5 because there are 5 0’s zeros in 100,000 and it also corresponds with the number of decimal places moved. So, 930,000 in scientific notation equals 9.3 times 10 to the 5. So our 2 steps for writing a number in scientific notation are move the decimal point so the number is between 1 and 10, the number of decimal places moved to the left is the power of 10 that you multiply by.
