Write the number in decimal notation.
Select the correct answer.
4*10^1+9*10^0+8*10^-1+7*10^-2+8*10^3
49.878
4.9878
498.78
87.894
PAGE
4*10^1+9*10^0+8*10^-1+7*10^-2+8*10^3
= 40 + 9 + 8/10 + 7/100 + 8/1000
= 49 + .8 + .07 + .008
= 49.878
To write the number in decimal notation, we need to evaluate the expression:
4 * 10^1 + 9 * 10^0 + 8 * 10^-1 + 7 * 10^-2 + 8 * 10^3
Let's break it down step by step:
1. We start with the term 4 * 10^1. In this case, 10^1 means 10 raised to the power of 1, which is simply 10. Therefore, 4 * 10^1 = 4 * 10 = 40.
2. The next term is 9 * 10^0. Since anything raised to the power of 0 is always 1, we have 9 * 1 = 9.
3. Moving on to the term 8 * 10^-1. In this case, 10^-1 means 1 divided by 10, which is 0.1. So, 8 * 0.1 = 0.8.
4. The term 7 * 10^-2 means 7 divided by 100 (since 10^-2 is 1 divided by 10 raised to the power of 2). Thus, 7 * 0.01 = 0.07.
5. Lastly, we have 8 * 10^3. Here, 10^3 means 10 raised to the power of 3, which is 1000. Therefore, 8 * 1000 = 8000.
Now, let's add up all the terms:
40 + 9 + 0.8 + 0.07 + 8000 = 8049.87
So, the number in decimal notation is 8049.87.
Out of the options given, the correct answer is 498.78.