Powers of Ten Worksheet (printable, online, answers) - Free Printable

Let's solve the problem step by step.

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Part 1: Find the values of the following powers of 10

We know that:
- $10^n$ means multiplying 10 by itself $n$ times.
- This results in a 1 followed by $n$ zeros.

So:

a. $10^3 = 10 \times 10 \times 10 = 1,000$
b. $10^5 = 10 \times 10 \times 10 \times 10 \times 10 = 100,000$
c. $10^6 = 1,000,000$ (1 followed by 6 zeros)
d. $10^4 = 10,000$
e. $10^1 = 10$
f. $10^7 = 10,000,000$
g. $10^2 = 100$
h. $10^9 = 1,000,000,000$
i. $10^8 = 100,000,000$
j. $10^{10} = 10,000,000,000$

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Part 2: Write the following in exponential form

We need to express each number as a power of 10.

a. $10,000 = 10^4$ (because 10,000 has 4 zeros)
b. $1,000 = 10^3$
c. $10 \times 10 = 10^2$
d. $100 \times 100 = (10^2) \times (10^2) = 10^{2+2} = 10^4$
e. $1,000,000 = 10^6$
f. $1,000 \times 1,000 = (10^3) \times (10^3) = 10^{6}$
g. $100 = 10^2$
h. $1 \times 10 = 10^1$
i. $100,000 = 10^5$
j. $100 \times 10 = (10^2) \times (10^1) = 10^{3}$
k. $100,000 = 10^5$ (same as i)
l. $10,000 \times 10 = (10^4) \times (10^1) = 10^{5}$

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✔ Final Answers:

#### Part 1: Values of Powers of 10
a. $10^3 = \boxed{1,000}$
b. $10^5 = \boxed{100,000}$
c. $10^6 = \boxed{1,000,000}$
d. $10^4 = \boxed{10,000}$
e. $10^1 = \boxed{10}$
f. $10^7 = \boxed{10,000,000}$
g. $10^2 = \boxed{100}$
h. $10^9 = \boxed{1,000,000,000}$
i. $10^8 = \boxed{100,000,000}$
j. $10^{10} = \boxed{10,000,000,000}$

#### Part 2: Exponential Form
a. $10,000 = \boxed{10^4}$
b. $1,000 = \boxed{10^3}$
c. $10 \times 10 = \boxed{10^2}$
d. $100 \times 100 = \boxed{10^4}$
e. $1,000,000 = \boxed{10^6}$
f. $1,000 \times 1,000 = \boxed{10^6}$
g. $100 = \boxed{10^2}$
h. $1 \times 10 = \boxed{10^1}$
i. $100,000 = \boxed{10^5}$
j. $100 \times 10 = \boxed{10^3}$
k. $100,000 = \boxed{10^5}$
l. $10,000 \times 10 = \boxed{10^5}$

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🔍 Explanation:

- When you raise 10 to a power $n$, you get a 1 followed by $n$ zeros.
- Multiplying powers of 10 uses the rule: $10^a \times 10^b = 10^{a+b}$
- Converting numbers like 100 or 1,000 into exponential form involves counting the zeros.

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