s ection 2.2 z ero and p owers of 10 © copyright all rights reserved to homework depot:
TRANSCRIPT
SECTION 2.2 ZERO AND POWERS OF 10
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ZERO EXPONENTS When a number has an exponent of zero, the value
will be equal to one
03 1 012 1 01,349,812 1 02828 1
Even zero to the power of zero is also equal to one
00 1
We need to be careful with negative bases. Can you see the difference between the three expressions?
05 1 05 1 0
5 1
The last two are the same, we take the base to the exponent of zero first. Then we multiply one by the negative sign
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If a power has an exponent of zero, it doesn’t matter what the base is. The value will be equal to one
04
3 12 22
0
252218 1,003,960
4
When simplifying an expression, we need obey the order
of operation: BEDMAS Simplify all “Brackets” first
Then we take it to the exponent. If the exponent is zero, then the value now will be equal to one
Next we multiply or divide (from left to right)
Then add or subtract (from left to right)
03 2 3 5
03 56
31 5
3 5
8
1 1
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PRACTICE: EVALUATE EACH OF THE FOLLOWING AND WRITE DOWN YOUR ANSWER
0) 5 3i 03) 3+ 11ii
2) 1 18 0iii 0 0) 3 1 12iv
0 0 0 0 0) 1 2 3 4 5v
BE DMAS
08 1 0
13 133 13 4
BE DMAS
41 032 01 1
0 024 1 1 1 0
1 1 1 1 1 5
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POWERS OF 10 When writing out powers of 10, the exponent
tells us how many zeroes are after the one
810 100,000,000
8 zeroes
Hundred million
710 10,000,000
7 zeroes
Ten million
610 1,000,000
6 zeroes
One million
510 100,000
5 zeroes
Hundred Thousand
410 10,0004 zeroes
Ten Thousand
310 1,0003 zeroes
Thousand
210 1002 zeroes
Hundred
110 101 zero
Ten
010 1No zeroes
One
110 0.1
Zero is at the left of one
Tenth
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Any number can be written as the sum of powers of 10
3000 is equal to 1000 times 3 200 is equal to 100 times 2 40 is equal to 10 times 4 5 is equal to 5 times 1 If we are asked to write to the number as a power of
10 then it will look like this:
3245 3000 200 40 5 3000 200 40 5 3 1000 2 100 4 10 5 1
33 10 22 10 14 10 05 10
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EX: WRITE THE FOLLOWING NUMBER AS A POWER OF 10
10245
3951
10000 200 40 5 1 10000 2 100 4 10 5 1
41 10 22 10 14 10 05 10
3000 900 50 1 3 1000 9 100 5 10 1 1
33 10 29 10 15 10 01 10
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When asked to write the value in “standard form”, then simplify the equation and add them back to the original number
3 2 1 06 10 7 10 4 10 3 10 6000 700 40 3 6743
5 3 2 09 10 1 10 3 10 7 10 90000 1000 300 7 901307
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