Answer:
1. 49.02 = 40 + 9 + 0.0 + 0.02
2.![49.02 = 4 \times (10)^1 + 9 \times (10)^0 +0 \times (10^{-1} + 2 \times (10)^{-2}](https://tex.z-dn.net/?f=49.02%20%20%3D%204%20%5Ctimes%20%2810%29%5E1%20%20%2B%209%20%5Ctimes%20%2810%29%5E0%20%20%2B0%20%5Ctimes%20%2810%5E%7B-1%7D%20%20%2B%202%20%5Ctimes%20%2810%29%5E%7B-2%7D)
Step-by-step explanation:
Part : 1
To write 49.02 as EXPANDED FORM
Now, by place value chart, we know
Ten Th. , Thousand, Hundreds, Tens , units DECIMAL, Tenth, Hundredth
Putting the value of decimal just below decimal ,we get:
Place value of 4 = 4 tens = 4 x 10 = 40
Place value of 9 = 9 ones = 9 x 1 = 9
Place value of 0 = 0 tenth = 0 / 10 = 0
Place value of 2 = 2 hundredth = 2 / 100 = 0.02
⇒ 49.02 = 40 + 9 + 0.0 + 0.02
Part : 2
Now, rewriting terms using powers of 10, we get:
40 = 4 x 10 = 4 x ![(10)^1](https://tex.z-dn.net/?f=%2810%29%5E1)
9 = 9 x ![(10)^0](https://tex.z-dn.net/?f=%2810%29%5E0)
0 = 0 x ![(10)^{-1}](https://tex.z-dn.net/?f=%2810%29%5E%7B-1%7D)
0.02 = 2 x ![(10)^{-2}](https://tex.z-dn.net/?f=%2810%29%5E%7B-2%7D)
⇒![49.02 = 4 \times (10)^1 + 9 \times (10)^0 +0 \times (10^{-1} + 2 \times (10)^{-2}](https://tex.z-dn.net/?f=49.02%20%20%3D%204%20%5Ctimes%20%2810%29%5E1%20%20%2B%209%20%5Ctimes%20%2810%29%5E0%20%20%2B0%20%5Ctimes%20%2810%5E%7B-1%7D%20%20%2B%202%20%5Ctimes%20%2810%29%5E%7B-2%7D)