Exercise 15 Page 56

Here are the populations of Cities A and B. Population of City A:& 2.6 * 10^5 Population of City B:& 1 560 000 We are also told that the population of City C is twice the population of City B. We want to estimate how many times greater the population of City C is than the population of City A. Here is what we are going to do.

1. Estimate the population of City B.
2. Find the population of City C.
3. Compare the population of Cities C and A.

Let's do it!

Population of City B

This is the population of City B. 1 560 000 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 leading value means rounding to the nearest million. Let's look at the digit representing the hundred thousands. 1 560 000 The number in this column is 5. 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! 1 560 000 ≈ 2 000 000 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. 2 000 000 We see that there are 6 zeros in the number. Now, recall how the sign of the exponent changes for different numbers.

Since the number is greater than 1, the exponent is positive. This means that the exponent of 10 is 6. We now have everything we need to rewrite our number. We can now write our number. 2 000 000 = 2* 10^6 The population of City B is about 2 * 10^6.

Population of City C

We know that the population of City C is twice the population of City B. Population of City B:& 2 * 10^6 This means we need to multiply the population of City B by 2. This will give us the population of City C. Let's go!

The population of City C is 4* 10^6.

Comparing Population of Cities C and A

We want to estimate how many times greater the population of City C is than the population of City A. Population of City A:& 2.6 * 10^5 Population of City C:& 4* 10^6 We need to divide the population of City C by the population of City A. Let's do it!

The population of City C is about 15 times the population of City A.