Place value and powers of 10 are foundational fifth-grade math skills that students use to read and write large numbers, understand how each position relates to the next by a factor of 10, and apply exponent notation to represent powers of ten. Fifth graders identify place values up to the millions, write numbers in expanded and word form, multiply and divide by powers of 10, and use expressions like 6 × 10⁵ to represent standard numbers.
The main challenge is that students misidentify place positions in multi-digit numbers — confusing ten-thousands with hundred-thousands — or confuse a digit's position with its value. Students also struggle with zeros in expanded form, omitting or incorrectly placing terms. In Grade 4, students worked with numbers up to the hundred-thousands; Grade 5 extends to millions and introduces powers of 10 with exponent notation.
Our place value and powers of 10 worksheets give fifth graders structured practice correcting place value identification errors, writing standard, expanded, and word forms, multiplying and dividing by powers of 10, reading and writing powers of 10 using exponents, and solving multi-step real-world problems involving large numbers and scientific-style notation.
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Place Value & Powers of 10
Place Value & Powers of 10
Place Value & Powers of 10
Place Value & Powers of 10
Place Value & Powers of 10
Place Value & Powers of 10
Place Value & Powers of 10
Place Value & Powers of 10
Place Value & Powers of 10
Place Value & Powers of 10
Place Value & Powers of 10
Place Value & Powers of 10
What's Included in This Download
What You'll Learn
These place value & powers of 10 worksheets help grade 5 students develop essential math skills through engaging activities.
Learning Objectives
- Place Value: Identify digit values up to the millions place
- Powers of 10: Multiply and divide by 10, 100, and 1000
- Exponent Notation: Use 10 to the 1st through 6th power
- Standard Form: Convert between expanded, word, and standard form
- Compare Numbers: Use greater than, less than, and equal to compare large numbers
Skills Covered
How to Use These Worksheets
- Download & Print: Click the download button to get the PDF. Print on standard 8.5" x 11" paper.
- Start Simple: Begin with easier pages before moving to more challenging activities.
- Daily Practice: Dedicate 10-15 minutes each day for consistent learning.
- Use Manipulatives: Pair worksheets with physical objects like blocks or counters.
- Provide Encouragement: Celebrate progress and effort to build confidence.
- Check Progress: Use the included answer key to review work together.
Common Mistakes to Watch For
- Misidentifying digit positions in large numbers — students say the 3 in 4,536,271 is in the hundred-thousands place instead of the ten-thousands place. In multi-digit numbers, counting from the right: ones, tens, hundreds, thousands, ten-thousands, hundred-thousands, millions. Each position must be counted carefully.
- Confusing a digit's position with its face value — students say the value of the 7 in 870,432 is 7,000 instead of 70,000. The value of a digit equals the face value multiplied by the place value — 7 × 10,000 = 70,000.
- Omitting zero terms in expanded form — students write the expanded form of 509,300 as 500,000 + 9,000 + 300, missing the ten-thousands and ones zeros. Expanded form must account for every place value present; zero-value positions are simply omitted from the sum, not combined with others.
Frequently Asked Questions
How do I identify the place value of a digit in a large number?
Count from the rightmost digit (ones) moving left: ones, tens, hundreds, thousands, ten-thousands, hundred-thousands, millions. In 4,536,271: the 1 is ones, 7 is tens, 2 is hundreds, 6 is thousands, 3 is ten-thousands, 5 is hundred-thousands, 4 is millions. The value of a digit is the face value times the place value — the 3 at the ten-thousands position has a value of 3 × 10,000 = 30,000. When a digit appears multiple times in the same number, each appearance has a different value based on its position.
How do I write a number in expanded form?
Write each non-zero digit as a product of its face value and its place value, then connect the products with addition signs. For 450,200: 4 is in the hundred-thousands (400,000), 5 is in the ten-thousands (50,000), 2 is in the hundreds (200) — so 450,200 = 400,000 + 50,000 + 200. Do not include terms for zero-value positions — there is no '+ 0' for a missing place. For word form, read from left to right by groups: 'four hundred fifty thousand two hundred.'
How do I multiply or divide by a power of 10?
Multiplying by 10 moves every digit one place to the left (shifts the decimal point one place right). Multiplying by 100 shifts two places; by 1,000 shifts three places. For 4.7 × 100 = 470. Dividing by 10 moves every digit one place to the right. For 620 ÷ 10 = 62. The shortcut: count the zeros in the power of 10 and shift the decimal point that many places — right for multiplication, left for division. For 6.2 × 1,000: shift right 3 places to get 6,200.
What is a power of 10 written with an exponent?
A power of 10 is 10 multiplied by itself a certain number of times. The exponent tells how many times: 10¹ = 10, 10² = 10 × 10 = 100, 10³ = 10 × 10 × 10 = 1,000, 10⁴ = 10,000, 10⁵ = 100,000, 10⁶ = 1,000,000. The exponent equals the number of zeros in the result. To evaluate an expression like 5 × 10³: compute 10³ = 1,000, then multiply 5 × 1,000 = 5,000. Numbers like 6,200 can be written as 6.2 × 10³ — moving the decimal left 3 places gives 6.2 and the exponent records the shift.
How do powers of 10 help with real-world large numbers?
Powers of 10 make very large numbers easier to read and compare. A city with 2 × 10⁶ people has 2,000,000 people; a town with 2 × 10⁴ has 20,000. The city is 100 times larger because 10⁶ ÷ 10⁴ = 10². This compact notation appears in science (Earth is 1.5 × 10⁸ km from the Sun), population data, and manufacturing figures. To compare two powers of 10, compare the exponents — a higher exponent always means a larger power of 10, and each difference of 1 in the exponent represents a factor of 10 difference in the value.
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Can I use these in my classroom?
Absolutely! Teachers are welcome to print and use these worksheets in their classrooms. Make as many copies as needed for your students.