Beginner math lesson
Place value and reading numbers
Place value explains what each digit is worth. A 5 can mean 5 ones, 5 tens, 5 hundreds, or more, depending on where it sits in the number.
Who this helps
This lesson is useful for grade-school learners, adults reviewing basic math, and parents helping a child read larger numbers. It is a good starting point before addition, subtraction, multiplication, decimals, and money.
Step-by-step explanation
- Read from right to left to name the places. The first place is ones, then tens, hundreds, thousands, ten thousands, and hundred thousands.
- Match each digit to its place. In 4,382, the 4 is in the thousands place, the 3 is in the hundreds place, the 8 is in the tens place, and the 2 is in the ones place.
- Find the value of each digit. The 4 in 4,382 means 4,000. The 3 means 300. The 8 means 80. The 2 means 2.
- Write expanded form. Expanded form shows the value of each digit: 4,382 = 4,000 + 300 + 80 + 2.
- Read the number by periods. Commas group digits into periods. In 27,405, say "twenty-seven thousand, four hundred five."
Worked examples
Example 1: Name the value of a digit
What is the value of 6 in 6,914?
6,914 ^ The 6 is in the thousands place. 6 thousands = 6,000
Answer: The value of 6 is 6,000.
Example 2: Write a number in expanded form
Write 38,206 in expanded form.
38,206 3 ten-thousands = 30,000 8 thousands = 8,000 2 hundreds = 200 0 tens = 0 6 ones = 6
Answer: 38,206 = 30,000 + 8,000 + 200 + 6.
Example 3: Read a number in words
Read 104,070.
104,070 104 is the thousands period. 070 is the ones period.
Answer: One hundred four thousand, seventy.
Common mistakes
- Ignoring zeros. In 5,028, the zero holds the hundreds place. Without it, the number would change.
- Reading each digit separately. 420 is "four hundred twenty," not "four two zero."
- Mixing up digit and value. In 7,500, the digit is 7, but its value is 7,000.
- Adding "and" before whole-number ones. For whole numbers, read 305 as "three hundred five." Save "and" for decimals if you study them later.
Practice questions
- What is the value of 8 in 8,451?
- What is the value of 7 in 12,734?
- Write 5,609 in expanded form.
- Write 43,080 in expanded form.
- Read 9,216 in words.
- Read 70,405 in words.
- Write the number: six thousand, two hundred thirty.
- Write the number: ninety-one thousand, eight.
Answer key
- 8,000
- 700
- 5,000 + 600 + 9
- 40,000 + 3,000 + 80
- Nine thousand, two hundred sixteen
- Seventy thousand, four hundred five
- 6,230
- 91,008