Place Value & Powers of 10 (SQA National 5 Applications of Mathematics): Revision Note

Multiplying & dividing by powers of 10

What is place value?

• Each digit of a number represents a value depending on its position (place) within the number

• Each place has a value ten times larger than the place to the right of it

• Consider the number 9876

  • The 6 represents 6 ones (or units) (6)

  • The 7 represents 7 tens (70)

  • The 8 represents 8 hundreds (800)

  • The 9 represents 9 thousands (9000)

• Consider the number 14.37

  • The 1 represents 1 ten (10)

  • The 4 represents 4 ones (or units) (4)

  • The 3 represents 3 tenths (0.3)

  • The 7 represents 7 hundredths (0.07)

How do I multiply by 10, 100 or 1000?

• Multiplying a number by powers of 10 increases the place value of its digits

How do I divide by 10, 100 or 1000?

• Dividing a number by powers of 10 decreases the place value of its digits

How do I multiply and divide by multiples of 10, 100 or 1000?

• The multiple of 10, 100 or 1000 can be written as a value multiplied by a power of 10

  • e.g.

• To multiply or divide a number by a multiple of a power of 10:

  • Multiply or divide the number by both parts

    • e.g. and