Lesson 21 Section 2
Any number (except 0) with exponent 0 is defined to mean 1.
a0 = 1
Problem 8. Evaluate the following..
To see the answer, pass your mouse over the colored area.
h) 5 + 50(5 + 50) = 5 + 1(5 + 1) = 5 + 6 = 11
See the order of operations.
Why do we define a0 as 1?
For one thing, we have this rule:
Therefore, we must define a0 as 1.
As for 00, that could be any number! For,
Therefore we must conclude that 00 could be any number.
Problem 9. Use the rules of exponents to evaluate the following.
"Scientific notation" has one non-zero digit to the left of the decimal point.
That number is written in scientific notation. There is one digit to the left of the decimal point -- 2 -- and it is not 0.
In general, a number written in scientific notation will be multiplied by 10 raised to an exponent.
Example 1. 6.45 × 103. This is the scientific notation for what number?
Answer. Since the exponent is positive, we will be multiplying 6.45. To multiply a decimal by a power of 10, move the decimal point right the number of places indicated by the exponent:
6.45 × 103 = 6,450
Move the point three places right. To do that, we must add on a 0.(Skill in Arithmetic, Lesson 4.)
Example 2. 6.45 × 10−3. This is the scientific notation for what number?
Answer. Since the exponent is negative, we will be dividing 6.45. (For,
point left the number of places indicated by the exponent:
6.45 × 10−3 = .00645
Move the point three places left. To do that, we must add on 0's.
Problem 10. Each of these is written in scientific notation. Multiply out.
Example 3. Write in scientific notation.
a) 562.4 = 5.624 × 102
To change 562.4 into 5.624, we moved the decimal point two places left. To compensate, we must multiply by 10 with exponent +2.
b) .00395 = 3.95 × 10−3
To change .00395 into 3.95, we moved the decimal point three places right. To compensate, we must multiply by 10 with exponent −3.
Problem 11. Write in scientific notation.
Copyright © 2017 Lawrence Spector
Questions or comments?
Private tutoring available.