Powerful numbers on the TI-15
- 10 5 is a simple way of writing 10 x 10 x 10 x 10 x 10 = 100 000
- To see the powers of 10 use the Op1 action on the calculator:
Set Op1 tostore “x 10”
- To do this, press keys .
This sets Op1, and the small Op1 icon
on the screen confirms it.
- Enter and the screen shows this.
- Repeatedly pressing Op 1 will show all the powers of 10 up to 10 10, and from there the answer is written only as a power of 10.
- [An “overflow error” shows at 1 x 10100.]
Activity: To learn about“Index laws” using the TI-15
When eg 8 is written in the form 2 3, we say “2 to the power 3”, and it is written in index form.
The 2 is called the BASE of the number and the 3 is called the Power[sometimes Index or Exponent].
- Copy this table below.
- Using your calculator, as necessary, complete the table of powers of 2.
[A simple way to do this is to set Op1 as x2, and record the powers as they appear on the screen. To set Op1 Press .
Note the first entry is 2^0 and the answer is NOT 0.]
Index form / Number / Index form / Number / Index form / Number20 / 2 5 / 2 10
2 1 / 2 6 / 2 11
2 2 / 2 7 / 2 12
2 3 / 2 8 / 2 13
2 4 / 2 9 / 2 15
Question 1.
Example: Use the calculator to find 23 x 2 4
Check if this answer appears in your table.
So 23 x 24 = 128 = 27 from the table.
- Copy and complete the table below using this method.
Question / Answer from calculator / Power form of answer from table above
a. / 2 7 x 2 6
b. / 2 8 x 2 4
c. / 2 0 x 2 11
d. / 2 3 x 2 4 x 2 3
e. / 2 8 2 4
f. / 2 12 2 9
g. / 2 8 2 8
h. / 22 + 23
- Predict the answer to each of the following and check with you calculator
- 2 5 x 2 4ii. 2 8 x 2 3iii. 2 11 2 6
- Explain what you have noticed
______
Question 2.
To calculate (2 5) 2, care needs to be taken with the use of brackets
Check these calculations:
2^5^2 (2^5)^2
2^(5^2)
Note the very different larger answer in the third form!
- Complete this table using your table of powers of 2.
Question / Answer from calculator / Power form
a / (2 4) 3
b / (2 4) 2
c / (2 3) 3
d / (2 3) 4
- Predict the answer to each of the following and check with you calculator
- (2 2 ) 5ii. (2 2 ) 3iii. (2 3) 2iv. 2^3^2
- Explain what you have noticed
______
Question 3.
In this part the index number can be a fraction.
a.Calculate Press keys = 2
Check
[Again Brackets are important because this answer is wrong! ]
Check
Brackets are not needed if the fraction
part is entered as a fraction.
b.From the table of powers of 2, = = 2
Check on your calculator.
c.Complete this table using your table of powers of 2.
Question / Answer from calculator / Power forma /
b /
c /
d /
e /
d.Predict the answer to each of the following and check with your calculator.
i. ii. iii. iv.
e. Explain what you have noticed
______
Question 4.
In this part the index number can be a negative number.
- To calculate negative powers of 2, use is made of the button
NOT the .
- Check
Example: To calculate
Press keys
Now press to change the decimal answer to a fraction and simplify if necessary.
We see = 0.125 = =
a.Complete this table using your table of powers of 2.
Question / Answer from calculator / Power forma /
b /
c /
d /
b.Predict the answer to each of the following and check with your calculator.
i. 8 – 2 ii. 4 – 3 iii. 16 – 1 iv.
c. Explain what you have noticed
______
To summarise the INDEX LAWS
- bn is a number written in index form.
- b is the BASE,
- n is the power/index/ exponent.
- When multiplying two numbersin index form
- the bases MUST be the same
- the powers are added together
- When dividing two numbersin index form
- the bases MUST be the same
- the powers are subtracted
- When a number in index form is raised to another power
eg (2 5) 2 the two powers are multiplied ( 210 )
- When a power is ZERO, the answer is 1 (Except for 00 which has no meaning.)
- Negatives powers turn the number “upside down”. ie the reciprocal of the original number.
- Fractional powers generally make the number smaller
eg ½ finds the square root. (Numbers smaller than one actually get bigger!)
- These laws do not apply to numbers being added or subtracted.
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