7. Decimal operations

Lesson

In previous years we have learned how to multiply whole numbers by 10 and can relate the multiplication to place value. Let's review.

Complete these number sentences.

a

9\times10=⬚

Worked Solution

b

90\times10=⬚

Worked Solution

Idea summary

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.

This video looks at what happens to numbers with decimals when we multiply by 10 or 100.

Find the value of 29.34\times100.

Worked Solution

Idea summary

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.

This video looks at what happens to numbers with decimals when we divide by 10 or 100.

Find the value of 15.8 \div 10.

Worked Solution

Idea summary

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.

This video looks at what we can do when multiplying and dividing by 10\,000.

Find the value of 63.05\times10\,000.

Worked Solution

Idea summary

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.

Multiply and divide decimals by powers of 10