The decimal system
Keep splitting by 10, again and again.
Splitting again
We split 1 unit into 10 tenths. Now split one tenth into 10 equal parts, and then split one of those parts into 10 equal parts again.
How many of the smallest parts would it take to make 1 whole unit?
What this lesson covers
The idea
Because of the role of 10 in place value, a unit is split into 10 equal parts, tenths, then hundredths, thousandths and so on, extending place value below one; this system based on 10 is the decimal system.
Splitting again
We split 1 unit into 10 tenths. Now split one tenth into 10 equal parts, and then split one of those parts into 10 equal parts again.
How many of the smallest parts would it take to make 1 whole unit?
- 30
- 100
- 1000
Zoom in three times
Tap a part of the line to zoom in. It is split into 10 equal parts. Do this three times.
Ten at every step
Each place in our number system is 10 times the place to its right. So when we go below one, we keep splitting by 10.
This way of writing numbers, based on 10, is called the decimal system. “Decem” means ten in Latin.
Because of the role of 10 in place value, a unit is split into 10 equal parts (tenths), then hundredths, thousandths and so on. This extends place value below one. It is the decimal system.
- One of these | is split into 10 of these
- 1 unit | 10 tenths
- 1 tenth | 10 hundredths
- 1 hundredth | 10 thousandths
Notes
A unit is split into 10 tenths, each tenth into 10 hundredths, each hundredth into 10 thousandths, and so on. This extension of place value is the decimal system.
Check yourself
1 hundredth is how many thousandths?
Answer: 10 thousandths
1 hundredth is split into 10 thousandths.
How many thousandths make 1 unit?
Answer: 1000 thousandths
10 × 10 × 10 = 1000 thousandths in 1 unit.
Why do we keep splitting into 10 equal parts?
1/100 is split into 10 equal parts. Each part is 1 over what number? Type the number.
Answer: 1000
1/100 split into 10 equal parts is 1/1000: a thousand such parts make a unit.
- Because a unit cannot be split into any other number of equal parts. It can: halves, quarters, fifths… But 10 fits our place value system.
- Because 10 is the biggest number. There are bigger numbers. We use 10 because of the way our places grow tenfold.
- Each place in our number system is 10 times the next, so tenths, hundredths and so on continue the pattern — correct. Yes! Splitting by 10 matches how the place values of whole numbers work.