The Sun is about 150,000,000 kilometers from the Earth. What is this distance, written in expanded notation, using the power of 10? 


2 Answers

Samuel Chiltern Profile
Samuel Chiltern answered
I think the number you want to produce has to be written in standard form (or scientific notation in the US), rather than expanded notation.

Standard form is the technique used to shorten extremely large (or small) numbers by moving the decimal point left to shorten a large number, or right to shorten a small one (i.e. A decimal fraction).

How To Write a Number in Standard Form
It's not too difficult to write numbers in standard form once you know how. This is how I do it:

  1. Work out whether the number is 'large' or 'small' - if the number is greater than 10, it is a 'large' number, so the decimal point must be moved to the left to shorten it. If it's less than 10, then the decimal point will move to the right.
  2. Move the decimal point - for a 'large' number, the number farthest to the left before the decimal point must be less than 10, so keep moving left until it is. Keep moving right with a 'small' number, until the number farthest to the right is less than 10.
  3. Count how many positions you moved the decimal point by - this will give you a number, which is the power of 10 by which you need to multiply your shortened number. For example, 10^3 is 10 to the power of three, which equals 10 x 10 x 10, or a one with three zeros after it. So in this case, we'd multiply our shortened number by 1000.
  4. Drop as many digits from the shortened number as possible - in your example (150,000,000), you can drop all of those zeroes. With the decimal point now at the left-most point, you will be left with 1.5
  5. Write out the full number in standard form - write out your digits (1.5), then add 'x 10' to signify the base of the number we will be multiplying by (10). Finally, add your power of 10 after this. In your case, this will be eight, because you've moved the decimal point eight places to the left.
Your final number in standard form will be: 1.5 x10^8

Note: Normally, the power of 10 is superscripted (placed above the baseline of the
text), but this is not possible on all Internet forums, so we use a
caret symbol (^) to signify this instead.
Ellie Hoe Profile
Ellie Hoe answered
If you want to use power of 10, then just move the decimal point to the left side of the digit and multiply it with 10 with the power of places moved to left.

As in the 150,000,000.00 case, move the decimal to the left side and you will get 1.50,000,000, and then multiply it by 1000000000 (10^8), which is written as:
1.5 x 10^8 = 150,000,000 or 1.5 x 100000000 = 150,000,000

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