In Grade 4 you saw that each place is worth ten times the place to its right, and you met tenths and hundredths. The same pattern runs both ways and keeps going past the decimal point.
Key idea
Moving one place to the left makes a digit worth 10 times as much. Moving one place to the right makes it worth $\frac{1}{10}$ as much.
Why it works
Ten ones make a ten, and ten tens make a hundred. Going the other way, cut one whole into 10 equal parts and each part is a tenth; cut a tenth into 10 parts and each is a hundredth. So every place is 10 of the place to its right, and $\frac{1}{10}$ of the place to its left.
Worked examples
Worked example: Ten times as much
In $4{,}444$, compare the 4 in the hundreds place with the 4 in the tens place.
- The hundreds 4 is worth $400$. The tens 4 is worth $40$.
- $40 \times 10 = 400$.
Answer: The hundreds 4 is worth 10 times as much.
Worked example: Across the decimal point
In $7.77$, compare the 7 in the tenths place with the 7 in the hundredths place.
- The tenths 7 is worth $0.7$. The hundredths 7 is worth $0.07$.
- $0.07 \times 10 = 0.7$, so the tenths 7 is worth 10 times as much.
- Turned around: the hundredths 7 is worth $\frac{1}{10}$ of the tenths 7.
Answer: 10 times as much (or $\frac{1}{10}$ as much, the other way)
Worked example: Two places apart
In $3{,}030$, how many times as much is the 3 in the thousands place as the 3 in the tens place?
- Thousands are two places left of tens.
- Each place is a factor of 10: $10 \times 10 = 100$.
- Check: $30 \times 100 = 3{,}000$.
Answer: 100 times as much
Common mistake
Thinking a digit further right is worth more because it is “bigger” or comes later. In $0.55$, the first 5 (tenths) is worth 10 times the second 5 (hundredths). Check by writing each value: $0.5$ and $0.05$.