Expressing Numbers Using Powers of 10
Expressing numbers using powers of 10 teaches Grade 5 students to write any number as a product of a coefficient and a power of 10, written as c × 10^n. For example, 4,000 = 4 × 10^3, and 720,000 = 7.2 × 10^5. The concept also extends to small numbers: 0.09 = 9 × 10^−2. This skill from Pengi Math (Grade 5), Chapter 1, lays the groundwork for scientific notation and deepens understanding of place value patterns. Students learn to identify the correct exponent by determining which power of 10, when multiplied by the coefficient, equals the original number.
Key Concepts
Property Any number can be expressed as a product of a coefficient and a power of 10. This form is written as $c \times 10^n$, where $c$ is a number and $n$ is an integer. This is useful for writing very large or very small numbers concisely.
Examples To write $4,000$ using a power of 10, we can express it as $4 \times 1,000$, which is $4 \times 10^3$. To write $720,000$ using a power of 10, we can express it as $7.2 \times 100,000$, which is $7.2 \times 10^5$. To write $0.09$ using a power of 10, we can express it as $9 \times 0.01$, which is $9 \times 10^{ 2}$.
Explanation This skill extends the use of powers of 10 to represent any number, not just the powers of 10 themselves. By multiplying a coefficient (a whole or decimal number) by a power of 10, we can write numbers in a more compact form. This method involves identifying the correct power of 10 that, when multiplied by your chosen coefficient, equals the original number. This concept is the foundation of scientific notation.
Common Questions
How do you write 4,000 as a product using powers of 10?
4,000 = 4 × 1,000 = 4 × 10^3. The exponent 3 tells you the coefficient is multiplied by one thousand.
How do you write 720,000 using a power of 10?
720,000 = 7.2 × 100,000 = 7.2 × 10^5. Move the decimal left until you have a number between 1 and 10; count the places moved for the exponent.
How do you write 0.09 using a power of 10?
0.09 = 9 × 0.01 = 9 × 10^−2. Negative exponents represent numbers less than 1; 10^−2 = 1/100 = 0.01.
What is the difference between a power of 10 and expressing a number using powers of 10?
A power of 10 is a number like 100 or 1,000. Expressing any number using powers of 10 means writing it as a coefficient times a power of 10, like 7.2 × 10^5.
How is this skill related to scientific notation?
Scientific notation is a specific form of this skill where the coefficient must be between 1 and 10. This Grade 5 skill introduces the concept without requiring that constraint.
What grade and chapter covers expressing numbers with powers of 10?
Grade 5, Chapter 1: Place Value and Powers of 10 in Pengi Math.