We are told that Earth is approximately 5 * 10^9 years old. We want to decide which of the ages provided in the answers can be approximated by 5 * 10^9. Here are the ages.
| Age
|
| 4 762 100 000
|
| 4 849 000 000
|
| 48 000 000 000
|
| 4.45 * 10^9
|
| 4.849999999* 10^9
|
We will estimate them one by one.
4 762 100 000
Let's consider the first age.
4 762 100 000
Recall that when estimating a very large or very small number, we need to follow 2 steps.
- Round the number to its greatest .
- Write the number as a single times a of 10.
First, we want to round 4 762 100 000 to its greatest place value. See that the digit following the greatest place value is 7, which is more than 5.
4 762 100 000This means we will be rounding up. Let's do it!
4 762 100 000≈ 5 000 000 000
For the second step, we will rewrite the number as its greatest place value times a power of 10. To find the , we need to count the zeros in the number.
5
We see that there are 9 zeros in the number. Now, recall how the of the exponent changes for different numbers.
| Numbers Greater Than 1
|
Numbers Less Than 1
|
| positive (+)
|
negative (-)
|
Since 5 000 000 000 is greater than 1, the exponent is . This means that the exponent of 10 is 9. We now have everything we need to rewrite our number.
5 000 000 000 = 5 * 10^9
We see that the number 4 762 100 000 can be approximated with 5 * 10^9.
4 849 000 000
Following the same steps as before, this is the approximation we will get for 4 849 000 000.
4 849 000 000 ≈ 5 * 10^9
The number 4 849 000 000 can also be approximated with 5 * 10^9.
48 000 000 000
One last time, we will estimate the number using the same steps as earlier. Here are the results.
48 000 000 000 ≈ 5 * 10^(10)
The number 48 000 000 000 cannot be approximated with 5 * 10^9. Instead, it can be approximated with 5 * 10^(10).
4.45 * 10^9
We want to decide if the following number can be approximated with 5 * 10^9.
4.45 * 10^9
Let's then round 4.45 to the nearest . Then we will know for sure.
4.45 ≈ 4
This is what this approximation gives us.
4.45 ≈ 4
⇓
4.45 * 10^9 ≈ 4 * 10^9
We have that 4.45 * 10^9 cannot be approximated with 5 * 10^9 .
4.849999999* 10^9
This is our last number to consider.
4.849999999* 10^9
Once again, we will round the number to the nearest integer.
4.849999999 ≈ 5
⇓
4.849999999* 10^9 ≈ 5 * 10^9
We found that 5 * 10^9 is an approximation of 4.849999999* 10^9.
