When we divide a number by 10, we move the decimal point one place to the left. Here is how different numbers look when represented as tenths:
1/10 = 0.1 (Read as: zero point one)
2/10 = 0.2
5/10 = 0.5
12/10 = 1.2 (Read as: one point two)
125/10 = 12.5
1235/10 = 123.5
When we move to a base of 100, we are looking at “hundredths.” This requires moving the decimal point two places to the left:
1/100 = 0.01 (Read as: zero point zero one)
2/100 = 0.02
5/100 = 0.05
12/100 = 0.12
125/100 = 1.25
1235/100 = 12.35
When we divide a number by 1,000, the decimal point moves three places to the left to account for the three zeros in the denominator. Here is how various numbers appear when represented as thousandths:
$1/1000 = 0.001$: Read as “zero point zero zero one.”
$2/1000 = 0.002$
$5/1000 = 0.005$
$12/1000 = 0.012$
$125/1000 = 0.125$
$1235/1000 = 1.235$: Read as “one point two three five.”
To divide by a power of ten, move the decimal point to the LEFT by the same number of places as there are zeros in the divisor.
Let’s look at the examples from our practice sheet to see this in action.
When dividing a whole number, imagine the decimal point is hiding at the very end of the number.
$\frac{12}{100,000} = 0.00012$
There are 5 zeros in 100,000.
Start at the end of 12 and move the decimal 5 places to the left. You’ll need to add “placeholder” zeros to fill the gaps!
$\frac{123}{10,000,000} = 0.0000123$
7 zeros means moving the decimal 7 places left.
What if the number already has a decimal? The rule stays exactly the same.
$\frac{1.2}{10} = 0.12$ (Move 1 place left)
$\frac{1.2}{100} = 0.012$ (Move 2 places left)
$\frac{1.2}{1,000} = 0.0012$ (Move 3 places left)
Notice how the digits 1 and 2 never change order; they just slide further down the place value chart (from tenths to hundredths to thousandths).
The pattern remains consistent regardless of how large the starting number is.
| Problem | Number of Zeros | Movement | Result |
| $\frac{12.5}{10}$ | 1 | 1 jump left | 1.25 |
| $\frac{12.5}{100}$ | 2 | 2 jumps left | 0.125 |
| $\frac{12.5}{1,000}$ | 3 | 3 jumps left | 0.0125 |
When you divide a number by 10, 100, 1,000, and so on, the decimal point moves to the left. The number of places it moves is equal to the number of zeros in the divisor.
Let’s look at some examples:
$\frac{125.35}{10} = 12.535$: Dividing by 10 (one zero) moves the decimal point one place to the left.
$\frac{125.35}{100} = 1.2535$: Dividing by 100 (two zeros) moves it two places to the left.
$\frac{125.35}{1,000} = 0.12535$: Dividing by 1,000 (three zeros) moves it three places to the left.
$\frac{125.35}{10,000} = 0.012535$: Dividing by 10,000 (four zeros) moves it four places to the left. Note that we add a placeholder zero.
$\frac{125.35}{100,000} = 0.0012535$: Dividing by 100,000 (five zeros) moves it five places to the left.
$\frac{13.525}{100,000} = 0.00013525$: Similarly, moving the decimal point five places to the left requires adding several leading zeros.
Other simple examples include:
$\frac{2}{10} = 0.2$
$\frac{12}{10} = 1.2$
$\frac{125}{100} = 1.25$
$\frac{1.2}{10} = 0.12$
Multiplication is the opposite of division. When you multiply by 10, 100, 1,000, etc., the decimal point moves to the right. Again, the number of places it moves matches the number of zeros.
Check out these examples:
$2 \times 10 = 20$: Multiplying by 10 moves the decimal point one place to the right.
$12 \times 10 = 120$
$125 \times 100 = 12,500$
$1.2 \times 10 = 12.0 = 12$: The decimal point moves one place, making it a whole number.
$125.35 \times 10 = 1,253.5$: One zero, move one place right.
$125.35 \times 100 = 12,535.0 = 12,535$: Two zeros, move two places right.
$125.35 \times 1,000 = 125,350$: Three zeros, move three places right. We add a trailing zero as a placeholder.
$125.35 \times 10,000 = 1,253,500$: Four zeros, move four places right.
It’s also important to understand the different parts of a decimal number and how to write them cleanly.
Cleaning up zeros:
Extra zeros at the very beginning of the whole number part or at the very end of the decimal part do not change the value of the number. For instance:
$0001035.5300120000$ can be simply written as $1035.530012$.
The Three Main Parts:
Using the number $1035.530012$ as an example, we can identify its structure:
Whole Number Part ($1035$): This is everything to the left of the decimal point.
Decimal Place ($.$): This point separates the whole number part from the fractional decimal part.
Decimal Part ($530012$): This is everything to the right of the decimal point, representing a value less than one.