Luttrell 2012
64
Name: ______________________
Date: _____
4h- Expanded Form using Powers
Do without the aid of a calculator. Check your answers with a calculator at the end.
Use the powers of 10 to expand this number:
example: 8,321 = 8(10
3
) + 3(10
2
) + 2(10
1
) + 1(10
0
)
1. 340, 073
2. 53,100
3. 830,401
4. 234,876,912
5. 32
6. 144
7. 300,045
8. 16, 230, 030
Write the following numbers in standard form:
9. 7(10
3
) + 4(10
2
) + 2(10
1
) + 6(10
0
)
10. 8(10
5
) + 8(10
3
) + 4(10
1
) + 7(10
0
)
11. 8(10
6
) + 1(10
5
) + 2(10
4
) + 1(10
3
) + 5(10
2
) + 3(10
1
)
12. 5(10
8
) + 8(10
6
) + 7(10
4
) + 9(10
2
) + 2(10
0
)
We work with base 10, probably because we have 10 fingers. But other societies used different
bases. France used to have base 20 (they used fingers and toes). It still exists in some names for
numbers, like
quatre-vingt-neuf
. The Babylonians used base 60 which remains in our time: 60
minutes in an hour and 60 seconds to a minute. Computers made wide use of counting by 2s or
16s. Follow the example of how to convert other bases into base 10 (standard form).
Example: 11101
2
= 1(2)
4
+ 1(2)
3
+ 1(2)
2
+ 0(2)
1
+ 1(2)
0
= 16 + 8 + 4 + 0 + 1= 29
10. 10111
2
= 1(2)
4
+ 0(2)
3
+ 1(2)
2
+ 1(2)
1
+ 1(2)
0
= _________________________________
11. 101
2
= 1(2)
2
+ 0(2)
1
+ 1(2)
0
= _________________________________
12. 110101
2
= 1(2)
5
+1(2)
4
+ 0(2)
3
+ 1(2)
2
+ 0(2)
1
+ 1(2)
0
= _____________________________
13. FACE
16
= F(16)
3
+ A(16)
2
+ C(16)
1
+ E(16)
0
= 15(16)
3
+ 10(16)
2
+ 12(16)
1
+ 14(16)
0
= ____________________________________________________ (calculator allowed)
