More on Multiplying Decimals
Multiplying by powers of 10
When you multiply a decimal number by 10, 100, 1000, etc., the number gets larger.
| thousands | hundreds | tens | ones | $\bullet$ tenths | hundredths | thousandths |
|---|---|---|---|---|---|---|
| $3$ | $\bullet$ $1$ | $2$ | ||||
| $3$ | $1$ | $\bullet$ $2$ | $\color{red}{\longleftarrow 3.12\times 10=31.2}$ | |||
| $3$ | $1$ | $2$ | $\bullet$ $0$ | $\color{red}{\longleftarrow 3.12\times 100=312}$ | ||
The table shows that when you multiply a number by $10, 100, 1000$, etc. the number gets bigger so the digits move left:
- multiplying by $10$, moves the digits one place to the left
- multiplying by $100$, moves the digits two places to the left
- multiplying by $1000$, moves the digits three places to the left
- and so on.
In practice the easiest way to multiply by $10, 100, 1000$, etc. is to move the decimal point to the right.
- multiplying by $\color{red}{10}$ the digits stay the same but the decimal point moves one place to the right
- multiplying by $\color{red}{100}$ move the decimal point two places to the right
- multiplying by $\color{red}{1000}$ move the decimal point three places to the right
- and so on.
So the decimal point moves to the right by the number of places that matches the number of zeros in the number you are multiplying by.
Complete the answers to the following questions.
| $122.45\times 10=$ |
✅ ❌ |
|
| $-60\times 100=$ |
✅ ❌ |
|
| $-7.1\times 1000=$ |
✅ ❌ |
|
| $2.3986\times 100=$ |
✅ ❌ |
|
| $-89.7\times 10000=$ |
✅ ❌ |
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