Mathwords logoMathwords

hundred — Definition, Formula & Examples

A hundred is the whole number 100, which comes after 99 and before 101. It equals ten groups of ten.

The number one hundred, denoted 100, is the natural number equal to 10210^2. In the base-ten place-value system, it occupies the third position from the right (the hundreds place), representing 1×100+0×10+0×11 \times 100 + 0 \times 10 + 0 \times 1.

Key Formula

100=10×10=102100 = 10 \times 10 = 10^2
Where:
  • 10210^2 = Ten raised to the second power, meaning ten multiplied by itself

How It Works

When you count by tens — 10, 20, 30, … , 90 — the next step lands on 100, one hundred. In place value, the digit in the hundreds place tells you how many groups of 100 are in a number. For example, in 347, the 3 is in the hundreds place and stands for 300, meaning three hundreds. Hundred is also a building block for larger numbers: ten hundreds make one thousand (10×100=1,00010 \times 100 = 1{,}000), and one hundred hundreds make ten thousand (100×100=10,000100 \times 100 = 10{,}000).

Worked Example

Problem: A school has 4 boxes of crayons with 100 crayons in each box. How many crayons are there in all?
Step 1: Identify the number of groups and the size of each group.
4 boxes×100 crayons per box4 \text{ boxes} \times 100 \text{ crayons per box}
Step 2: Multiply. Four hundreds means you write 4 in the hundreds place.
4×100=4004 \times 100 = 400
Step 3: Read the result: four hundred crayons.
Answer: There are 400 crayons in all.

Another Example

Problem: Write the number 5,623 in expanded form and identify how many hundreds it contains.
Step 1: Break the number into place values.
5,623=5,000+600+20+35{,}623 = 5{,}000 + 600 + 20 + 3
Step 2: Look at the hundreds place. The digit 6 means six hundreds.
6×100=6006 \times 100 = 600
Step 3: So 5,623 contains 6 hundreds (plus thousands, tens, and ones).
Answer: The number 5,623 has 6 hundreds, contributing 600 to its total value.

Visualization

Why It Matters

Understanding hundreds is essential in early elementary math when students learn multi-digit addition, subtraction, and place value. It also appears in everyday life — counting money (a dollar bill equals 100 cents), measuring distances, and reading three-digit numbers all rely on knowing what a hundred represents.

Common Mistakes

Mistake: Confusing the hundreds place with the tens place when reading a number like 203, and reading it as "twenty-three" instead of "two hundred three."
Correction: Remember that the third digit from the right is the hundreds place. In 203, the 2 means two hundreds (200), not two tens.
Mistake: Thinking that 10 hundreds equals one hundred (confusing 10 × 100 with 100).
Correction: Ten hundreds equals one thousand: 10×100=1,00010 \times 100 = 1{,}000. Keep track of zeros when multiplying by powers of ten.

Related Terms