Exercise 9 Page 55

Here are the approximate circumferences of Earth and Saturn from the picture shown. Earth:& 4.01 * 10^4 km Saturn:& 365 882 km First, we want to rewrite the circumference of Saturn as the product of a single digit and a power of ten. 365 882

Rewriting

Recall that when estimating a very large or very small number, we need to follow 2 steps.

1. Round the number to its greatest place value.
2. Write the number as a single digit times a power of 10.Here, rounding to the greatest place value means rounding to the nearest hundred thousands. Let's then take a look at the digit representing the ten thousands. 3 65 882 The number in the column is 6. Now, recall the rule for rounding.
   • If the number is 5 or more, round up.
   • If the number is 4 or less, round down.

   This means we will be rounding up. Let's do that! 365 882 ≈ 400 000 For the second step, we will rewrite the number as its greatest place value times a power of 10. To find the exponent, we need to count the zeros in the number. 4 00 000 We see that there are 5 zeros in the number. Now, recall how the sign of the exponent changes for different numbers.

   Numbers Greater Than 1	Numbers Less Than 1
   positive (+)	negative (-)

   Since the number is greater than 1, the exponent is positive. This means that the exponent of 10 is 5. We now have everything we need to rewrite our number. 400 000 = 4* 10^5 Let's fill in the first two blanks.

   The circumference of Saturn is \boxed{4}\times 10^\boxed{5} km.

   Comparison

   Now we want to compare the circumferences of Earth and Saturn. Let's see what we found so far. Earth:& 4.01 * 10^4 km Saturn:& 4 * 10^5 km We can see that the the circumference of Saturn is greater. 4 * 10^5_(Saturn) > 4.01 * 10^4_(Earth) If we look closely, we can see that the leading digits are almost equal. Also, the powers of ten differ by 1. This means that the circumference of Saturn is roughly 10^1=10 times greater than the circumference of Earth. Let's fill in the final blank.

   Saturn's circumference is about 10 times greater than the circumference of Earth.