Exponents
What is a power of ten?
A number that can be written as a product of tens, such as 10, 100, or 1,000.
When you multiply a number by 10, how many places does the decimal move and in which direction?
One place to the right
What does it mean that multiplication and division are "inverse operations"?
They undo each other; multiplying and then dividing by the same number returns the original value.
Write 10^2 in standard form.
100
What is 0.6 × 10?
6
In 3×10=30 and 3×100=300, what pattern do you see in the zeros?
The number of zeros in the product matches the number of zeros in the power of ten.
How many times is 10 used as a factor in 10^4
4
What is 0.005 × 10^3?
5
How many times as large is 0.5 compared to 0.05? Explain using place value.
10 times as large, because 0.5 is one place to the right of 0.05.
Fill in the blank: 10 × 10 × 10 × 10 × 10 = 10^?
10^5
Write 7 ÷ 10^4 as a decimal.
0.0007
A student says 8.0 × 10^6 = 8.000000. What is wrong, and what is the correct answer?
Adding zeros after a decimal does not change the value. The decimal should move 6 places right, giving 8,000,000.
Chang wrote 100,000 as a product of tens and using exponent notation. What are both forms?
10×10×10×10×10
and
10^5
Find the missing exponent: 300 ÷ 10^? = 3
2
A student says, “To multiply by 100, you just add two zeros.”
Another student says, “To multiply by 100, you move the decimal point two places to the right.”
Are these statements always the same? If not, which one is always correct, and why?
They are not always the same.
Moving the decimal point two places to the right is always correct because multiplying by 100 means multiplying by 10^2