7.05 Powers of 10
Ideas
Are you ready?
In previous years we have learned how to multiply whole numbers by 10 and can relate the multiplication to place value. Let's review.
Examples
Example 1
Complete these number sentences.
9\times10=⬚
90\times10=⬚
When we multiply a number by 10, each digit increases in place value by 1 place value.
We can use a place value table to multiply numbers by powers of 10.
Multiply decimals by 10 or 100
This video looks at what happens to numbers with decimals when we multiply by 10 or 100.
Examples
Example 2
Find the value of 29.34\times100.
We can use a place value table to multiply decimals by powers of 10.
When multiplying by 10 each digit moves one place value to the left.
When multiplying by 100 each digit moves two place values to the left.
Divide decimals by 10 or 100
This video looks at what happens to numbers with decimals when we divide by 10 or 100.
Examples
Example 3
Find the value of 15.8 \div 10.
We can use a place value table to multiply decimals by powers of 10.
When multiplying by 10 each digit moves one place value to the left.
When multiplying by 100 each digit moves two place values to the left.
Multiply and divide decimals by larger powers of 10
This video looks at what we can do when multiplying and dividing by 10\,000.
Examples
Example 4
Find the value of 63.05\times10\,000.
For each power of 10: \, 10,\,100,\,1000,\,10\,000, when you multiply or divide by these values, each digit of your number is increased or decreased by that value, and moves up or down place value positions.
The number of place value positions each digit moves is equal to the number of zeros in the power of 10.