In Grade 2 you learned that 352 is 3 hundreds, 5 tens and 2 ones, and in Grade 3 you saw that 4 × 30 is 12 tens. Now look at one digit as it slides from place to place. Each move to the left makes it worth ten times as much.
Key idea
A digit in one place is worth 10 times what it would be worth one place to its right. Two places to the left is $10 \times 10 = 100$ times as much.
Why it works
Ten ones make one ten, ten tens make one hundred, and ten hundreds make one thousand. So each place holds groups that are 10 times bigger than the place before it. A 7 in the tens place means 7 tens, or 70. Move it to the hundreds place and it means 7 hundreds, or 700, which is 10 groups of 70.
Worked example: The same digit in two places
In $7{,}740$, how many times as much is the first 7 worth as the second 7?
- The first 7 is in the thousands place: it is worth $7{,}000$.
- The second 7 is in the hundreds place: it is worth $700$.
- It is one place to the left, so it is worth 10 times as much: $700 \times 10 = 7{,}000$.
Answer: 10 times as much
Worked example: Counting in a bigger unit
How many tens are in $700$?
- One hundred is 10 tens, so 7 hundreds are $7 \times 10 = 70$ tens.
- Check: $70 \times 10 = 700$.
Answer: 70 tens
Common mistake
Thinking the 7 in 700 is just "a few more" than the 7 in 70, or that 700 has only 7 tens. The 7 in 700 is worth 10 times the 7 in 70, and 700 holds 70 tens. Check by multiplying: $70 \times 10 = 700$.
| Place | Value of a 7 there | Compared with one place to the right |
|---|---|---|
| ones | 7 | — |
| tens | 70 | 10 times 7 |
| hundreds | 700 | 10 times 70 |
| thousands | 7,000 | 10 times 700 |