Representing Powers of 10 with Exponents
Representing Powers of 10 with Exponents is a Grade 5 math skill in Eureka Math where students write powers of 10 in exponential notation (e.g., 10^3 = 1,000) and connect the exponent to the number of place value positions shifted. This introduces the concept of exponents in a concrete place-value context, laying the groundwork for scientific notation.
Key Concepts
A power of 10 can be written in exponential form as $10^n$, where the base is 10 and the exponent $n$ indicates the number of times 10 is used as a factor. The value of the exponent $n$ is equal to the number of zeros in the standard form of the number. $$10^n = \underbrace{10 \times 10 \times \dots \times 10} {n \text{ factors}}$$.
Common Questions
How do you write a power of 10 using an exponent?
Write 10 as the base and the number of zeros (or place value shifts) as the exponent. For example, 1,000 = 10 x 10 x 10 = 10^3 because there are 3 factors of 10 or 3 zeros.
What does the exponent mean in a power of 10?
The exponent tells you how many times 10 is multiplied by itself, or equivalently, how many places the decimal point shifts to the right when you multiply a number by that power of 10.
How are powers of 10 connected to place value?
Each place value is 10 times the one to its right. The ones place is 10^0, the tens place is 10^1, the hundreds place is 10^2, and so on. The exponent equals the number of positions to the left of the ones place.
Where are powers of 10 with exponents used after Grade 5?
They appear in scientific notation in middle school (e.g., 6.02 x 10^23), in algebra as properties of exponents, and in science courses when working with very large or very small quantities.